$$$$ KONV NOTICE CHAT 11/09/12 21:16:46 7124 DATE 11/09/12 Operateur KONV Voir aussi : NAVI -------------- DESCRIPTION : I Finite Volume Formulation (OPTI VF) : ______________________________________ Discretizes the convection operator by finite volume diagrams. It calculates a FACE field by point which stands for the flux of each edge of the mesh, according to 3 diagrams. The flux is written in the KIZG increment. SYNTAX 1 : KONV VNF VNC option; VNF = U calculated at vertexes (by ksof) VNC = U calculated at centres (by knol) Option = 'upwind' | 'quick' | 'muscl' SYNTAX 2 : using EQEX RV = EQEX TABDOM ALFA .. ITMA .. 'ZONE' MOD1 'OPER' 'KONV' VNF VNC 'INCO' 'TN' CLIM 'TN' TIMP ENTREE ... ; the option is stored in klop : klop ind rv 'option' ; Possible error in the calculation of DT, if VN is small, change EPSILON COMMENTS : The flux is estimated on each mesh by : FI = VNF TK LGR in which TK is the temperature on K side calculated in different ways depending on the diagrams from the temperatures on the connected meshes: TIM ,TI ET TIP. (See the report for selecting these three temperatures) -UPWIND diagram: TK = TI -QUICK diagram: TK = (TI+TIP)/2 + (TIM+TIP-2*TI)/8 -MUSCL diagram: TK = TI + DELTA_I/2 in which DELTA_I is the slope between two meshes : GAMMA_I = SIGNE (TIP-TI) DELTA_I = GAMMA_I * MAX (0,MIN(GAMMA_I*(TIP-TI),GAMMA_I*(TI-TIM))) The result of the previous fluxes is computed in the AVCT operator. II Finite Element Formulation (OPTI EF ou EFM1) : ________________________________________________ Discretizes the convection operator by finite element method. According to the option the operator is discretized in a conservative or non conservative form. SYNTAX - EQEX Cf operator EQEX ______________ 'OPER' 'KONV' ROC UN LAM 'INCO' 'TN' : 1/ non conservative form roc ( u Grad T ) 2/ conservative form Div ( roc u T ) Comments : __________ roc heat capacity (J/M**3/°C) FLOTTANT or CHPOINT SCAL CENTRE or CHPOINT SCAL SOMMET or MOT lam thermal conductivity (W/M/°C) this data is necessary for evaluating the local Peclet number. Usually it's the coefficient of the LAPN operator. If not set lam=0. FLOTTANT or CHPOINT SCAL CENTRE or CHPOINT SCAL SOMMET or MOT un Convective velocity field CHPOINT VECT SOMMET ou MOT tn Temperature field CHPOINT SCAL SOMMET ou MOT When a key word is put instead of a coefficient, the operator look for data in INCO table at the index 'key word'. Options : (EQEX) _________ The discretization of the convective term can be : centree OPTION CENTREE upwind OPTION SUPG upwind with discontinuity capturing OPTION SUPGCC Default Option Crank Nicholson generalized OPTION CNG (fourth order in time) Non conservative Formulation OPTION NOCONS Default Option Conservative Formulation OPTION CONS Finite Element Formulation OPTION EF III Numerical discretisation of the Euler Equations ___________________________________________________ IIIa : perfect mono-component polytropic gas ________________________________________________ Finite-Volume "cell-centered" discretisation of the Euler equations of gas dynamics for perfect mono-component polytropic gas Unknowns: -------- density, momentum, total energy per unit volume (conserved variables) or density, velocity, pressure (primitive variables) One can compute: IIIa.1. Numerical flux IIIa.2 Residual IIIa.3 Jacobian matrix of the residual with respect to the conserved variables IIIa.4 Jacobian matrix of the residual with respect to the primitive variables IIIa.5 Preconditioning matrix for low Mach number flow with respect to the conserved variables IIIa.6 Preconditioning matrix for low Mach number flow with respect to the primitive variables IIIa.7 Contribution of some boundary condition to the residuum and to the Jacobian matrix. IIIa.1 et IIIa.2 The numerical flux and the Residual ________________ RCHPO1 RFLOT1 = 'KONV' 'VF' 'PERFMONO' MOT1 MOT2 MOD1 LMOT1 MCHAM1 MCHAM2 MCHAM3 MCHAM4 (CHPO5 CHPO6) (MAIL1) ; ARGUMENTS --------- MOT1 : object of the type MOT Use 'RESI' if one wants to compute the Residual Use 'FLUX' if one wants to compute the numerical Flux MOT2 : object of the type MOT It indicates the numerical method: 'GODUNOV' = exact Riemann solver 'VANLEER' = solver of van Leer 'VLH' = solver of van Leer Hanel 'HUSVL' = HUS (van Leer + Osher) 'HUSVLH' = HUS (van Leer Hanel + Osher) 'AUSMPLUS' = AUSM+ 'ROE' = solver of Roe 'SS' = solver "shock-shock" 'AUSMPLM' = AUSM+ low Mach 'RUSANOV' = solver of Rusanov 'RUSANOLM' = solver of Rusanov for low Mach 'CENTERED' = centered scheme 'ROELM' = solver of Roe-Turkel for low-Mach 'HLLC' = solver HLLC 'HLLCLM' = solver HLLC-Turkel for low-Mach 'AUSMPUP' = solver AUSM+up low Mach LMOT1 : object of the type LISTMOTS Names of the components of the resultant vector (RCHPO1) They are named in the following order: name of the density, name of the momentum, name of the total energy per unit volume MOD1 : MODELE object. MCHAM1 : MCHAML containing the density, and it has as SPG (geometric support) 'DOMA' MOD1 'FACEL' (one component, 'SCAL') (see the description of the operator PRET) MCHAM2 : MCHAML containing the velocity components and the components of the local basis (n,t) with respect to the global basis (x,y) (in the 2D case there are 6 components: * 'UN' = normal component of velocity (SPG = 'DOMA' MOD1 'FACEL') * 'UT' = tangential component of velocity (SPG = 'DOMA' MOD1 FACEL') * 'NX' = n.x (SPG = 'FACE') * 'NY' = n.y (SPG = 'FACE') * 'TX' = t.x (SPG = 'FACE') * 'TY' = t.y (SPG = 'FACE')). (see the description of the operator PRET) MCHAM3 : MCHAML (SPG = 'DOMA' MOD1 'FACEL') containing the pressure of the gas (single component, 'SCAL'). (see the description of the operator PRET) MCHAM4 : MCHAML (SPG = 'DOMA' MOD1 'FACEL') containing the "gamma" of the gas (single component, 'SCAL'). (see the description of the operator PRET) CHPO5 : CHPOINT containing the cut-off velocity (SPG = 'DOMA' MOD1 'CENTRE', single component, 'SCAL'). To specify in the case of the low Mach number flows CHPO6 : CHPOINT containing the second cut-off velocity (SPG = 'DOMA' MOD1 'CENTRE', single component, 'SCAL'). To specify in the case of the low Mach number flows (MAIL1) : MAILLAGE of POI1 or, if appeared in ('DOMA' MOD1 'FACE'), one doesn't compute the contribution to the numerical flux or the residual. RESULTS ------- RCHPO1 : object of the type CHPOINT (components = LMOT1) Residual if MOT2 = 'RESI' (SPG = 'DOMA' MOD1 'CENTRE') Flux if MOT2 = 'FLUX' (SPG = 'DOMA' MOD1 'FACE') RFLOT1 : object of the type FLOTTANT It is the characteristic time associated with the fastest wave (even in the case of low Mach flow, one considers the non-preconditioned system) Remark -------- RCHPO1 is equal to: * the time derivative of the unknowns if the option 'RESI' is used * the projection of the flux on ('DOMA' MOD1 'XXNORMAF') if the option 'FLUX' is used IIIa.3 The Jacobian matrix of the residual with respect to the _____ conserved variables RMAT1 = 'KONV' 'VF' 'PERFMONO' 'JACOCONS' MOD1 LMOT1 (MAIL1) MOT1 CHPO1 CHPO2 CHPO3 CHPO4 (CHPO5 CHPO6) ; ARGUMENTS --------- MOT1 : object of the type MOT 'VLH' : Jacobian of the residual for the method VLH 'AUSMPLUS' : Jacobian of the residual for the method AUSM+ 'AUSMPLM' : Jacobian of the residual for the method AUSM+ (low Mach) 'RUSANOLM' : Jacobian of the residual for the Rusanov scheme (low Mach) 'CENTERED' centered scheme LMOT1 : object of the type LISTMOTS Names of the conserved variables They are named in the following order: the name of the density, the momentum, the total energy per unit volume MOD1 : MODELE object. CHPO1 : CHPOINT containing the density (SPG = 'DOMA' MOD1 'CENTRE', single component, 'SCAL'). CHPO2 : CHPOINT containing the components of the velocity (SPG = 'DOMA' MOD1 'CENTRE', two/three components 'UX', 'UY', 'UZ') CHPO3 : CHPOINT containing the gas pressure (SPG = 'DOMA' MOD1 'CENTRE', single component, 'SCAL'). CHPO4 : CHPOINT containing the "gamma" of the gas (SPG = 'DOMA' MOD1 'CENTRE', single component, 'SCAL'). CHPO5 : CHPOINT containing the cut-off velocity (SPG = 'DOMA' MOD1 'CENTRE', single component, 'SCAL'). To specify in the case of the low Mach number flows CHPO6 : CHPOINT containing the second cut-off velocity (SPG = 'DOMA' MOD1 'CENTRE', single component, 'SCAL'). To specify in the case of the low Mach number flows (MAIL1) : MAILLAGE of the POI1 or, if appeared in ('DOMA' MOD1 'FACE'), one doesn't compute the contribution to the Jacobian. RESULTS ------- RMAT1 : object of the type MATRIK (SPG = 'DOMA' MOD1 'CENTRE') (primal unknowns = dual unknowns = LMOT1) It contains the Jacobian matrix of the Residual with respect to the conserved variables. IIIa.4 The Jacobian matrix of the residual with respect to the ______ primitive variables RMAT1 = 'KONV' 'VF' 'PERFMONO' 'JACOPRIM' MOD1 LMOT1 LMOT2 (MAIL1) MOT1 CHPO1 CHPO2 CHPO3 CHPO4 (CHPO5 CHPO6) ; ENTREES MOT1 : object of the type MOT 'VLH' : Jacobian of the residual for the method VLH 'AUSMPLUS' : Jacobian of the residual for the method AUSM+ 'AUSMPLM' : Jacobian of the residual for the method AUSM+ low Mach LMOT1 : object of the type LISTMOTS Names of the conserved variables They are named in the following order: the name of the density, the momentum, the total energy per unit volume LMOT2 : object of the type LISTMOTS Names of the primitive variables They are named in the following order: the name of the density, of the velocity, of the pressure MOD1 : MODELE object. CHPO1 : CHPOINT containing the density (SPG = 'DOMA' MOD1 'CENTRE', single component, 'SCAL'). CHPO2 : CHPOINT containing the velocity components (SPG = 'DOMA' MOD1 'CENTRE', two/three components 'UX', 'UY', 'UZ') CHPO3 : CHPOINT containing the gas pressure (SPG = 'DOMA' MOD1 'CENTRE', single component, 'SCAL'). CHPO4 : CHPOINT containing the "gamma" of the gas (SPG = 'DOMA' MOD1 'CENTRE', single component, 'SCAL'). CHPO5 : CHPOINT containing the cut-off velocity (SPG = 'DOMA' MOD1 'CENTRE', single component, 'SCAL'). To specify in the case of the low Mach number flows CHPO6 : CHPOINT containing the second cut-off velocity (SPG = 'DOMA' MOD1 'CENTRE', single component, 'SCAL'). To specify in the case of the low Mach number flows (MAIL1) : MAILLAGE of the POI1 or, if appeared in ('DOMA' MOD1 'FACE'), one doesn't compute the contribution to the Jacobian. RESULTS ------- RMAT1 : object of the type MATRIK (SPG = 'DOMA' MOD1 'CENTRE') (primal variables = primitive variables = LMOT2) (dual variables = conserved variables = LMOT1) It contains the Jacobian of the residual with respect to the primitive variables. IIIa.5 Preconditioning matrix for low Mach number flows with ______ respect to the conserved variables (divided by the local time step; the time step is computed for the preconditioned system) RMAT1 = 'KONV' 'VF' 'PERFMONO' 'GAMMCONS' MAIL1 LMOT1 CHPO1 CHPO2 CHPO3 CHPO4 CHPO5 CHPO6 ; LMOT1 : object of the type LISTMOTS Names of the conserved variables. They are named in the following order: the name of the density, the momentum, the total energy per unit volume MAIL1 : SPG of the CHPOINTs CHPO0 : CHPOINT containing the diameters of the elements (single component, 'SCAL'). CHPO1 : CHPOINT containing the density (single component, 'SCAL'). CHPO2 : CHPOINT containing the velocity components (two/three components 'UX', 'UY', 'UZ') CHPO3 : CHPOINT containing the gas pressure (single component, 'SCAL'). CHPO4 : CHPOINT containing the "gamma" of the gas (single component, 'SCAL'). CHPO5 : CHPOINT containing the cut-off velocity (SPG = 'CENTRE', single component, 'SCAL'). To specify in the case of the low Mach number flows CHPO6 : CHPOINT containing the second cut-off velocity (SPG = 'CENTRE', single component, 'SCAL'). To specify in the case of the low Mach number flows RMAT1 : object of the type MATRIK (SPG = MAIL1) (primal unknowns = dual variables = LMOT1) IIIa.6 Preconditioning matrix for low Mach number flows with ______ respect to the primitive variables (divided by the local time step; the time step is computed for the preconditioned system) RMAT1 = 'KONV' 'VF' 'PERFMONO' 'GAMMPRIM' MAIL1 LMOT1 LMOT2 CHPO1 CHPO2 CHPO3 CHPO4 CHPO5 CHPO6 ; LMOT1 : object of the type LISTMOTS Names of the conserved variables. They are named in the following order: the name of the density, the momentum, the total energy per unit volume LMOT2 : object of the type LISTMOTS Names of the primitive variables They are named in the following order: the name of the density, of the velocity, of the pressure. MAIL1 : SPG of the CHPOINTs CHPO0 : CHPOINT containing the diameter of the element (single component, 'SCAL'). CHPO1 : CHPOINT containing the density (single component, 'SCAL'). CHPO2 : CHPOINT containing the velocity components (two/three components 'UX', 'UY', 'UZ') CHPO3 : CHPOINT containing the gas pressure (single component, 'SCAL'). CHPO4 : CHPOINT containing the "gamma" of the gas (single component, 'SCAL'). CHPO5 : CHPOINT containing the cut-off velocity (SPG = 'CENTRE', single component, 'SCAL'). To specify in the case of the low Mach number flows CHPO6 : CHPOINT containing the second cut-off velocity (SPG = 'CENTRE', single component, 'SCAL'). To specify in the case of the low Mach number flows RMAT1 : object of the type MATRIK (SPG = 'CENTRE') (primal unknowns = primitive variables = LMOT2) (dual unknowns = conserved variables = LMOT1) IIIa.7 Contribution of some boundary condition to the residuum and to the Jacobian matrix. RCHPLI RCHPRE = 'KONV' 'VF' 'PERFMONO' 'CLIM' 'RESI' $MOD1 $MOD2 LMOTC LMOTP CHPRN CHPVN CHPPN CHPGN MOT1 CHPLI ; or RJACO = 'KONV' 'VF' 'PERFMONO' 'CLIM' 'JACOCONS' $MOD1 $MOD2 LMOTC LMOTP CHPRN CHPVN CHPPN CHPGN MOT1 CHPLI ; RJACO = 'KONV' 'VF' 'PERFMONO' 'CLIM' 'JACOPRIM' $MOD1 $MOD2 LMOTC LMOTP CHPRN CHPVN CHPPN CHPGN MOT1 CHPLI ; $MOD1 : model objet of the total domain $MOD2 : model objet of the border domain LMOTC : LISTMOTS, names of the conserved variables LMOTP : LISTMOTS, names of the primitive variables CHPRN : density (SPG ='DOMA' $MOD1 'CENTRE', one component, 'SCAL') CHPVN : velocity (SPG ='DOMA' $MOD1 'CENTRE', components: 'UX', 'UY', ('UZ')) CHPPN : pressure (SPG ='DOMA' $MOD1 'CENTRE', one component, composante, 'SCAL') CHPGN : gamma (SPG ='DOMA' $MOD1 'CENTRE', one component, 'SCAL') MOT1 : MOT, type of the boundary condition: 'INRI' : subsonic inlet. We use the Riemann invariants. We specify density 'RN', speed 'UX' 'UY' ('UZ'), pressure 'PN'. 'INSU' : subsonic inlet. We specift the total enthalpy 'HT' (per unit mass), the entropy 'S' (pressure divided by density power gamma). We impose that the tangential velocity is zero. We recover pressure from inside. The contribution to residuum and to Jacobian matrix are computed via 'AUSMPLUS'. 'OUTRI': subsonic outlet. We use the Riemann invariants. We specify density 'RN', speed 'UX' 'UY' ('UZ'), pressure 'PN'.sortie subsonique. 'OUTP' : subsonic outlet. We specify pressure 'PN', and we recover speed and density from inside. The contribution to residuum and to Jacobian matrix are computed via 'AUSMPLUS'. 'INSS' : supersonic inlet. We specify density 'RN', speed 'UX' 'UY' ('UX'), pressure 'PN'. 'OUTSS': supersonic outlet. The boundary condition CHPOINT is empty. 'INJE' : boundary condition of a compressible injection. We specify the mass flux 'MOME' and 'RT' (temperature time the gas constant); we impose on impose that the tangential velocity is zero. We recover pressure from inside. 'INJELM': boundary condition of Low Mach number injection. We specify the mass flux 'MOME' and 'RT' (temperature time the gas constant); we impose on impose that the tangential velocity is zero. We recover pressure from inside. CHPLI : boundary condition CHPOINT (SPG ='DOMA' $MOD2 'CENTRE') Its components names depends on MOT1 Results RCHPLI : CHPOINT which contains density, speed, pressure on the boundary. (SPG ='DOMA' $MOD2 'CENTRE', components = LMOTP) RCHPRE : CHPOINT which contains the contribution to residuum. (SPG in 'DOMA' $MOD1 'CENTRE', components = LMOTC) RJACO : MATRIK which contains the contribution to the Jacobian matrix of the residuum. IIIb : gas "thermally perfect" ____ VF "cell-centered" discretization of the Euler equations Unknowns : total density, momentum, total energy per volume unity, densities of the gas components (in the multicomponent case), passive scalars (multiplied by the total density) RCHPO1 RFLOT1 = 'KONV' 'VF' 'PERFTEMP' MOT1 MOT2 LMOT1 MOD1 TAB2 MCHAM1 MCHAM2 MCHAM3 (MCHAM4) (MCHAM5) ; INPUTS MOT1 : MOT object 'RESI' if we want to compute the residuum 'FLUX' if we want to compute the flux MOT2 : MOT object It refers to the used upwind scheme 'VLH' = van Leer Hanel Flux Vector Splitting 'SS' = shock-shock Flux Difference Splitting MOD1 : MODELE object. TAB2 : TABLE object that contains: * the name of the species non-explicitly treated in Euler's Equations in TAB2 . 'ESPNEULE' (MOT object); * the names of the species explicitly treated in TAB2 . 'ESPEULE' (LISTMOTS object; to specify in the multicomponent case only); * the degree of the polynomial cv=cv(T), in TAB2 . 'NORD' (ENTIER object, >= 0) * the properties of each gas 'ESPI', in TAB2 . 'ESPI' (TABLE object): - TAB2 . 'ESPI' . 'A' (LISTREEL object) which contains the (TAB2.'NORD')+1 coefficients of cv(T), (A0,A1,...); cv are expressed in J/kg/K; - TAB2 . 'ESPI' . 'R' (FLOTTANT object, J/kg/K) the constant of the gas - TAB2 . 'ESPI' . 'H0K', (J/kg, FLOTTANT object) the enthalpy of formation at 0K * TAB2 . 'SCALPASS' = if existing, the names of the transported passive scalars LMOT1 : LISTMOTS object It contains the components names of RCHPO1 in the following order: density, momentum, total energy, densities of the gas components (in TAB2 . 'ESPEULE'), the passive scalars (in TAB2 . 'SCALPASS') times the total density MCHAM1: MCHAML object which contains the density and has as geometrical support (SPG) 'DOMA' MOD1 'FACEL' (one component, 'SCAL') (see 'PRET' operator) MCHAM2: MCHAML object containing the velocity and the director cosines of the local frame (n,t) with respect to the global one (x,y) (in 2D, 6 components: * 'UN' = normal velocity (SPG = 'DOMA' MOD1 'FACEL') * 'UT' = tangential velocity (SPG = 'DOMA' MOD1 FACEL') * 'NX' = n.x (SPG = 'FACE') * 'NY' = n.y (SPG = 'FACE') * 'TX' = t.x (SPG = 'FACE') * 'TY' = t.y (SPG = 'FACE')). (see 'PRET' operator) MCHAM3: MCHAML (SPG = 'DOMA' MOD1 'FACEL') containing the pressure (one component, 'SCAL'). (see 'PRET' operator) (MCHAM4):MCHAML (SPG = 'DOMA' MOD1 'FACEL') containing the mass fractions of the single gas component (see TAB2 . 'ESPEULE') (see 'PRET' operator) (MCHAM5):MCHAML (SPG = 'DOMA' MOD1 'FACEL') containing the passive scalars (see TAB2 . 'ESPEULE') (see 'PRET' operator) OUTPUTS RCHPO1: CHPOINT object (components into LMOT1) Residuum if MOT1 = 'RESI' (SPG = 'DOMA' MOD1 'CENTRE') Flux if MOT1 = 'FLUX' (SPG = 'DOMA' MOD1 'FACE') RFLOT1: FLOTTANT object It is the characteristic time of the fastest wave Remark ------ RCHPO1 contains : * the temporal derivatives of the unknowns, if MOT1 = 'RESI' * the projection of the convective flux on the faces normals ('DOMA' MOD1 'XXNORMAF'), if MOT1 = 'FLUX' IIIc : perfect gas, "Free matrix method" ____ VF "cell-centered" discretization of the Euler equations Unknowns : U (density, momentum, total energy per volume unity (conservative variables)) Free matrix method implicitation. In the i-th cell we have to compute (U_i^{n+1} - U_i^{n}) * AN_i(U^{n}) = RES_i(U^{n}) + BN_i(U^{n}) - BN_i(U_i^{n+1}) where AN_i contains the contributions linked to inverse of the local time step and to the interfacial Rusanov diffusivities; RES_i is the residuum computed with any numerical scheme (see KONV operator, option IIIa). BN_i contains the interfacial contributions linked to the centered flux and to the Rusanov diffusivity multiplied by the neighboring state. We emphasize that at the stationary state we have RES_i(U)= 0 To compute the CHPOINT RES, we use the KONV operator, option IIIa. Here we compute the CHPOINTs AN and BN. AN = 'KONV' 'VF' 'PMONOFMM' 'AN' LMOT1 MOD1 CHPO1 CHPO2 CHPO3 CHPO4 FLOT1 ('CLIM' LMOT2 CHPO5) ; BN = 'KONV' 'VF' 'PMONOFMM' 'BN' LMOT1 MOD1 CHPO1 CHPO2 CHPO3 CHPO4 ('CLIM' LMOT2 CHPO5) ; INPUT MOD1 : MODELE object 'EULER' LMOT1 : LISTMOTS object. Names of the components of the result (RCHPO1). It contains the names of: density, momentum, total energy per unit volume. CHPO1 : CHPOINT object that contains the total mass density (kg/m3; the name of its component is 'SCAL'). CHPO2 : CHPOINT object that contains the momentum (kg/s/m2; two components in 2D, 'UX ','UY ', three components in 3D, 'UX ','UY ','UZ '). CHPO3 : CHPOINT object that contains the total volumic energy (J/m3; one component, 'SCAL'). CHPO4 : CHPOINT object that contains the gas gamma (one component, 'SCAL'). FLOT1 : real object (the CFL time 2) LMOT2 : LISTMOTS object. Names of the components of the boundary conditions (CHPO5). It contains the names of: density, speed, pressure. CHPO5 : CHPOINT, boundary conditions (density, speed and pressure on the border). OUTPUTs AN : CHPOINT object (SPG = 'DOMA' MOD1 'CENTRE', 1 component, 'SCAL') BN : CHPOINT object (SPG = 'DOMA' MOD1 'CENTRE', components = LMOT1) IIId : perfect gas, "Free matrix method", Euler/NS for low mach flows ____ VF "cell-centered" discretization of the Euler equations Unknowns : U (density, momentum, total energy per volume unity (conservative variables)) Free matrix method implicitation. In the i-th cell we have to compute (U_i^{n+1} - U_i^{n}) = DUN Syntax: DUN IPRO = 'KONV' 'VF' 'PMON1FMM' MOT1 LMOT1 MOD1 CHPORE CHPO1 CHPO2 CHPO3 CHPO4 CHPO5 FLOT1 FLOT2 NJAC 'CLIM' LMOT2 CHPO6 CHPO7 ; INPUT MOT1 : MOT object, inversion method ('PJACO', point jacobi, 'LJACOF', 'LJACOB', 'LJACOFB' Gauss-Seidel Forward, Backward and Symmetric) LMOT1 : LISTMOTS object. Names of the components of the result (RCHPO1). It contains the names of: density, momentum, total energy per unit volume. MOD1 : objet MODELE 'EULER' CHPORE: CHPOINT, explicit residual (Euler/NS) CHPO1 : CHPOINT object that contains the total mass density (kg/m3; the name of its component is 'SCAL'). CHPO2 : CHPOINT object that contains the momentum (kg/s/m2; two components in 2D, 'UX ','UY ', three components in 3D, 'UX ','UY ','UZ '). CHPO3 : CHPOINT object that contains the total volumic energy (J/m3; one component, 'SCAL'). CHPO4 : CHPOINT object that contains the gas gamma (one component, 'SCAL'). CHPO5 : CHPOINT, cut-off speed, (one component, 'SCAL'). FLOT1 : flottant, physical time step FLOT2 : flottant, twice of the CFL for the dual time step LMOT2 : objet de type LISTMOTS Noms de composantes de conditions aux bords (CHPO6) Names of the components of the boundary conditions (CHPO5). It contains the names of: density, speed, pressure. CHPO6 : CHPOINT, boundary conditions (density, speed and pressure on the border). CHPO7 : CHPOINT, viscous spectral radious (one component, 'SCAL'). OUTPUT DUN : CHPOINT object, (SPG = 'DOMA' MOD1 'CENTRE', components = LMOT1). IPRO : INTEGER, 0 if always is OK IIIg. Gas perfect multi-component ___________________________________ IIId.1 The residual ____________________ RESIDU DELTAT = 'KONV' 'VF' 'PERFMULT' 'RESI' MOT1 LMOT1 MOD1 MCHAM1 MCHAM2 MCHAM3 MCHAM4 MCHAM5 TABGAS (CHPO6) (CHPO7) (MAIL1) ; ENTRÉES MOT1 : object of the type MOT One can chose from the list: 'GODUNOV' = exact solver 'VANLEER' = Van Leer's solver 'VLH' = Van Leer Hanel's solver 'HUSVL' = HUS (van Leer + Osher) 'HUSVLH' = HUS (van Leer Hanel + Osher) 'AUSMPLUS' = AUSM+ 'ROE' = Roe' solver 'SS' = shock-shock solver 'AUSMPLM' = AUSM+ low Mach solver 'RUSANOV' = Rusanov scheme 'RUSANOLM' = Rusanov scheme for low-Mach 'CENTERED' = Centered scheme 'ROELM' = Roe-Turkel scheme for low-Mach 'HLLC' = solver HLLC 'HLLCLM' = solver HLLC-Turkel for low-Mach 'AUSMPUP' = solver AUSM+up low Mach LMOT1 : object of the type LISTMOTS Names of the components of the resultant vector (RCHPO1) They are named in the following order: name of the density, name of the momentum, name of the total energy per unit volume names of the species (which are in TABGAS.'ESPEULE') MOD1 : MODELE object. MCHAM1 : MCHAML containing the density, and it has as SPG (geometric support) 'DOMA' MOD1 'FACEL' (one component, 'SCAL') (see the description of the operator PRET) MCHAM2 : MCHAML containing the velocity components and the components of the local basis (n,t) with respect to the global basis (x,y) (in the 2D case there are 6 components: * 'UN' = normal component of velocity (SPG = 'DOMA' MOD1 'FACEL') * 'UT' = tangential component of velocity (SPG = 'DOMA' MOD1 FACEL') * 'NX' = n.x (SPG = 'FACE') * 'NY' = n.y (SPG = 'FACE') * 'TX' = t.x (SPG = 'FACE') * 'TY' = t.y (SPG = 'FACE')). (see the description of the operator PRET) MCHAM3 : MCHAML (SPG = 'DOMA' MOD1 'FACEL') containing the pressure of the gas (single component, 'SCAL'). (see the description of the operator PRET) MCHAM4 : MCHAML (SPG = 'DOMA' MOD1 'FACEL') containing the "gamma" of the gas (single component, 'SCAL'). (see the description of the operator PRET) MCHAM5 : MCHAML (SPG = 'DOMA' MOD1 'FACEL') contenant les fractions massiques (nombre des composants egal celui dans TABGAS.'ESPEULE') TABGAS : la table contenant les properties de gas (voir PRET ou PRIM) CHPO6 : CHPOINT containing the cut-off velocity (SPG = 'DOMA' MOD1 'CENTRE', single component, 'SCAL'). To specify in the case of the low Mach number flows CHPO7 : CHPOINT containing the second cut-off velocity (SPG = 'DOMA' MOD1 'CENTRE', single component, 'SCAL'). To specify in the case of the low Mach number flows (MAIL1) : MAILLAGE of POI1 or, if appeared in ('DOMA' MOD1 'FACE'), one doesn't compute the contribution to the numerical flux or the residual. RESULTS ------- RCHPO1 : object of the type CHPOINT (components = LMOT1) Residual if MOT2 = 'RESI' (SPG = 'DOMA' MOD1 'CENTRE') Flux if MOT2 = 'FLUX' (SPG = 'DOMA' MOD1 'FACE') RFLOT1 : object of the type FLOTTANT It is the characteristic time associated with the fastest wave (even in the case of low Mach flow, one considers the non-preconditioned system) Remark -------- RCHPO1 is equal to: * the time derivative of the unknowns if the option 'RESI' is used IIIg.2 The jacobian matrix of the residual with respect to the conservative variables ___________________________________________________________ RMAT1 = 'KONV' 'VF' 'PERFMULT' 'JACOCONS' MOT1 MOD1 TABGAS LMOT1 (MAIL1) CHPO1 CHPO2 CHPO3 CHPO4 (CHPO5 CHPO6) ; ARGUMENTS --------- MOT1 : object of the type MOT 'VLH' : Jacobian of the residual for the method VLH 'AUSMPLUS' : Jacobian of the residual for the method AUSM+ 'AUSMPLM' : Jacobian of the residual for the method AUSM+ low Mach TABGAS : the table containing the gas properties (see PRET or PRIM) LMOT1 : object of the type LISTMOTS Names of the conserved variables They are named in the following order: the name of the density, the momentum, the total energy per unit volume, the species which are in TABGAS.'ESPEULE'. MOD1 : MODELE object. CHPO1 : CHPOINT containing the density (SPG = 'DOMA' MOD1 'CENTRE', single component, 'SCAL'). CHPO2 : CHPOINT containing the components of the velocity (SPG = 'DOMA' MOD1 'CENTRE', two/three components 'UX', 'UY', 'UZ') CHPO3 : CHPOINT containing the gas pressure (SPG = 'DOMA' MOD1 'CENTRE', single component, 'SCAL'). CHPO4 : CHPOINT containing the mass fractions of the species (SPG = 'DOMA' MOD1 'CENTRE', number of components is equal to one in TABGAS.'ESPEULE') CHPO5 : CHPOINT containing the cut-off velocity (SPG = 'DOMA' MOD1 'CENTRE', single component, 'SCAL'). To specify in the case of the low Mach number flows CHPO6 : CHPOINT containing the second cut-off velocity (SPG = 'DOMA' MOD1 'CENTRE', single component, 'SCAL'). To specify in the case of the low Mach number flows (MAIL1) : MAILLAGE of the POI1 or, if appeared in ('DOMA' MOD1 'FACE'), one doesn't compute the contribution to the Jacobian. RESULTS ------- RMAT1 : object of the type MATRIK (SPG = 'DOMA' MOD1 'CENTRE') (primal unknowns = dual unknowns = LMOT1) It contains the Jacobian matrix of the Residual with respect to the conserved variables. IIIg.3 The contribution of the some boundary conditions _______ to the residual and the jacobian matrix RCHPLI RCHPRE = 'KONV' 'VF' 'PERFMULT' 'CLIM' 'RESI' $MOD1 $MOD2 TABGAS LMOTC LMOTP CHPRN CHPVN CHPPN CHPYN CHPLI MOT1 ; or RJACO = 'KONV' 'VF' 'PERFMULT' 'CLIM' 'JACOCONS' $MOD1 $MOD2 TABGAS LMOTC LMOTP CHPRN CHPVN CHPPN CHPYN CHPLI MOT1 ; $MOD1 : model object of the total domain $MOD2 : model object of the border domain TABGAS : the table containing the gas properties (see PRET or PRIM) LMOTC : LISTMOTS, names of the conserved variables LMOTP : LISTMOTS, names of the primitive variables CHPRN : density (SPG ='DOMA' $MOD1 'CENTRE', one component, 'SCAL') CHPVN : velocity (SPG ='DOMA' $MOD1 'CENTRE', components: 'UX', 'UY', ('UZ')) CHPPN : pressure (SPG ='DOMA' $MOD1 'CENTRE', one component, composante, 'SCAL') CHPYN : mass fraction of the species (SPG ='DOMA' $MOD1 'CENTRE', number of components is equal to one in TABGAS.'ESPEULE') MOT1 : MOT, type of the boundary condition: 'INRI' : subsonic inlet. We use the Riemann invariants. We specify density 'RN', speed 'UX' 'UY' ('UZ'), pressure 'PN' and the mass fractions 'INSU' : subsonic inlet. We specift the total enthalpy 'HT' (per unit mass), the entropy 'S' (pressure divided by density power gamma) and the mass fractions We impose that the tangential velocity is zero. We recover pressure from inside. The contribution to residuum and to Jacobian matrix are computed via 'AUSMPLUS'. 'OUTP' : subsonic outlet. We specify pressure 'PN', and we recover speed, density and mass fractions from inside. The contribution to residuum and to Jacobian matrix are computed via 'AUSMPLUS'. 'INJE' : boundary condition of a compressible injection. We specify the mass flux 'MOME', 'RT' (temperature times the gas constant) and mass fractions; we impose that the tangential velocity is zero. We recover pressure from inside. 'INSS': supersonic inlet. We specify the density, velocity, pressure and mass fractions at the inlet. The flux at the inlet is imposed using these values. 'OUTSS': supersonic outlet. We impose Champ par point empty (vide). All information is taken from inside the domain. 'RESE' : reservoir boundary condition. We specify the pressure 'PN', the density 'RN' and the mass fractions; we impose that the tangential velocity is zero. Following the value of the internal pressure, we impose the sonic or subsonic throat conditions. CHPLI : boundary condition CHPOINT (SPG ='DOMA' $MOD2 'CENTRE') Its components names depends on MOT1 Results RCHPLI : CHPOINT which contains density, speed, pressure and mass fractions on the boundary. (SPG ='DOMA' $MOD2 'CENTRE', components = LMOTP) RCHPRE : CHPOINT which contains the contribution to residuum. (SPG in 'DOMA' $MOD1 'CENTRE', components = LMOTC) RJACO : MATRIK which contains the contribution to the Jacobian matrix of the residuum. IV Scalar Transport ___________________ FV "cell-centered" discretization of --> --> d/dt S + div . (u S) = 0 RCHPO1 RFLOT1 = 'KONV' 'VF' 'CLAUDEIS' 'FACE' MOT1 MOT2 MOD1 CHPO1 MCHAM1 ; or RMAT1 = 'KONV' 'VF' 'CLAUDEIS' 'FACE' 'JACO' MOT2 MOD1 CHPO1 MCHAM1 ; MOT1 : MOT object 'RESI' if we want to compute the residuum; 'FLUX' sif we want to compute the interfacial flux MOT2 : MOT object It refers to the method to compute the flux/residuum: 'UPWIND' 'CENTERED' MOD1 : MODELE object CHPO1 : CHPOINT object containing the velocity (geometrical support SPG = 'DOMA' DOM1 'FACE') 2/3 components, 'UX', 'UY', 'UZ' MCHAM1 : MCHAML object containing the scalars to transport (SPG = 'DOMA' DOM1 'FACEL') RCHPO1 : CHPOINT object (same components as MCHAM1) Residuum if MOT2 = 'RESI' (SPG = 'DOMA' DOM1 'CENTRE') Flux if MOT2 = 'FLUX' (SPG = 'DOMA' DOM1 'FACE') RFLOT1 : FLOTTANT object It is the characteristic time associated to the fastes wave RMAT1 : MATRIK object (SPG = 'DOMA' DOM1 'CENTRE') (primal variables = dual variables; same components as MCHAM1) V Two-fluid flow ___________________________________________________ Finite-Volume "cell-centered" discretisation of the one-pressure six-equation two-fluid model, only for water and air mixtures Unknowns: -------- mass flow rate, momentum and total energy per unit volume of each fluid (conserved variables) or void fraction, gas and liquid velocities, pressure, gas and liquid temperatures (primitive variables) One can compute the numerical flux and the residual RCHPO2 RCHPO1 RFLOT1 = 'KONV' 'VF' 'TWOFLUID' MOT1 MOT2 MOD1 LMOT1 MCHAM1 MCHAM2 MCHAM3 MCHAM4 MCHAM5 MCHAM6 MCHAM7 MCHAM8; ARGUMENTS --------- MOT1 : Use 'RESI' if one wants to compute the residual and 'FLUX' to compute the numerical flux MOT2 : object of the type MOT It indicates the numerical method: 'AUSMP1' = AUSM+ 'AUSMP2' = Preconditioned AUSM+ 'AUSMDV1' = AUSMDV 'AUSMDV2' = Preconditioned AUSMDV LMOT1 : object of the type LISTMOTS Names of the components of the resultant vector (RCHPO1) They are named in the following order: name of the gas flow rate, name of the liquid mass flow rate, name of the gas momentum, name of the liquid momentum, name of the gas total energy per unit volume name of the liquid total energy per unit volume MOD1 : MODELE object. MCHAM1 : MCHAML containing the void fraction, and it has as SPG (geometric support) 'DOMA' MOD1 'FACEL' (one component, 'SCAL') (see the description of the operator PRET) MCHAM2 : MCHAML containing the gas velocity components and the components of the local basis (n,t) with respect to the global basis (x,y) (in the 2D case there are 6 components: * 'UN' = normal component of velocity (SPG = 'DOMA' MOD1 'FACEL') * 'UT' = tangential component of velocity (SPG = 'DOMA' MOD1 FACEL') * 'NX' = n.x (SPG = 'FACE') * 'NY' = n.y (SPG = 'FACE') * 'TX' = t.x (SPG = 'FACE') * 'TY' = t.y (SPG = 'FACE')). (see the description of the operator PRET) MCHAM3 : MCHAML containing the liquid velocity components and the components of the local basis (n,t) with respect to the global basis (x,y) (in the 2D case there are 6 components: * 'UN' = normal component of velocity (SPG = 'DOMA' MOD1 'FACEL') * 'UT' = tangential component of velocity (SPG = 'DOMA' MOD1 FACEL') * 'NX' = n.x (SPG = 'FACE') * 'NY' = n.y (SPG = 'FACE') * 'TX' = t.x (SPG = 'FACE') * 'TY' = t.y (SPG = 'FACE')). (see the description of the operator PRET) MCHAM4 : MCHAML (SPG = 'DOMA' MOD1 'FACEL') containing the pressure (single component, 'SCAL'). (see the description of the operator PRET) MCHAM5 : MCHAML (SPG = 'DOMA' MOD1 'FACEL') containing the gas temperature (single component, 'SCAL'). (see the description of the operator PRET) MCHAM6 : MCHAML (SPG = 'DOMA' MOD1 'FACEL') containing the liquid temperature (single component, 'SCAL'). (see the description of the operator PRET) MCHAM7 : MCHAML (SPG = 'DOMA' MOD1 'FACEL') containing the gas density (single component, 'SCAL'). (see the description of the operator PRET) MCHAM8 : MCHAML (SPG = 'DOMA' MOD1 'FACEL') containing the liquid density (single component, 'SCAL'). (see the description of the operator PRET) RESULTS ------- RCHPO1 : object of the type CHPOINT (components = LMOT1) Residual if MOT2 = 'RESI' or flux if MOT2 = 'FLUX' (SPG = 'DOMA' MOD1 'CENTRE') RCHPO2 : object of the type CHPOINT (components = LMOT1) Flux if (SPG = 'DOMA' MOD1 'CENTRE') RFLOT1 : object of the type FLOTTANT It is the characteristic time associated with the fastest wave Vl Reactive Flow with "Discrete Equation Method" resolution ____________________________________________________________ Finite-Volume discretisation of Euler equation describing flow of multi-component thermally perfect gas. Discrete Equation Method is used to determine the flux. RCHPO1 RFLOT1 = 'KONV' 'VF' 'DEM' MOT1 MOT2 MOT3 MOD1 TABG LMOT1 CHPA1 CHPA2 MCHAA1 MCHAA2 MCHAR1 MCHAR2 MCHAV1 MCHAV2 MCHAP1 MCHAP2 GRALP1 K0 EPS MAILLIM (CHPV1 CHPV2) ; ARGUMENTS : ---------- MOT1 : object of the type MOT it is equal to 'RESI' if we would like to compute the residual MOT2 : object of the type MOT It indicates the non-reactive upwinding method 'SS' = shock-shock solver 'VLH' = Van Leer Hanel's solver 'AUSMPUP' = AUSM+up solver (low Mach) MOT3 : object of the type MOT 'CONS' = the fundamental velocity is constant (REEL object) 'VARI' = the fundamental velocity is variable (CHAMPOINT object) MOD1 : model of the object, type EULER TABG : object of the type TABLE; it contains information on the properties of the gas. For complete description please see the notice of 'PRIM' operator LMOT1 : object of type LISTMOTS Names of the components of the resulting vector (RCHPO1) They are given in the following order: names of alpha, of density, of velocity, of the total specific energy. CHPA1 : CHPOINT, contains the volume fraction \alpha of the phase 1, which has as a SPG (geometric support) index the index 'CENTRE' of the table MOD1 (one component, 'SCAL') CHPA2 : CHPOINT, contains the volume fraction \alpha of the phase 1, which has as a SPG (geometric support) index the index 'CENTRE' of the table MOD1 (one component, 'SCAL') MCHAA1 : MCHAML contains the volume fraction \alpha of the phase 1, which has as a SPG (geometric support) index the index 'FACEL' of the table MOD1 (one component, 'SCAL') MCHAA2 : MCHAML contains the volume fraction \alpha of the phase 2, same SPG as MCHAA1, (one component, 'SCAL') MCHAR1 : MCHAML contains density of the phase 1, same SPG as MCHAA1, (one component, 'SCAL') MCHAR2 : MCHAML contains density of the phase 2, same SPG as MCHAA1, (one component, 'SCAL') MCHAV1 : MCHAML contains velocity of the phase 1 and the vector components of the local system of coordinates (n,t) with respect to the global system of coordinates (x,y), same SPG as MCHAA1, (in the 2D case, we have 6 components: * 'UN' = normal component of velocity (SPG =('DOMA' MOD1 'FACEL')) * 'UT' = tangential component of velocity (SPG =('DOMA' MOD1 'FACEL * 'NX' = n.x (SPG = 'FACE') * 'NY' = n.y (SPG = 'FACE') * 'TX' = t.x (SPG = 'FACE') * 'TY' = t.y (SPG = 'FACE')). MCHAV2 : MCHAML contains velocity of the phase 2 and the vector components of the local system of coordinates (n,t) with respect to the global system of coordinates (x,y), same SPG as MCHAA1. (same structure as above) MCHAP1 : MCHAML (SPG =('DOMA' MOD1 'FACEL')) contains the pressure of the phase 1 (one component, 'SCAL'). MCHAP2 : MCHAML (SPG =('DOMA' MOD1 'FACEL')) contains the pressure of the phase 2 (one component, 'SCAL'). K0 : FLOTTANT/CHAMPOINT (see MOT3), fundamental flame speed GRALP1 : CHPOINT, grad(alp1)/|grad(alp1)| EPSILON : FLOTTANT t.q. a < EPSILON => a = 0 MAILLIM : MAILLAGE -- describes the mesh where the flux is not determined; it will be found by using the subroutins for the Boundary Conditions CHPV1 : CHPOINT, cut-off speed in the AUSM+up method, for the phase 1 CHPV2 : CHPOINT, cut-off speed in the AUSM+up method, for the phase 2 RESULTS : ----------- RCHPO1 : object of type CHPOINT (components are in LMOT1) Residual vector if MOT2 = 'RESI' (SPG =('DOMA' MOD1 'CENTRE')) RFLOT1 : object of the type FLOTTANT It is the characteristic time associated with the fastest wave. VII Ghost fluid method for the poor. ___________________________________________________ VF "cell-centered" discetisation of two fluid Euler Equations for interface transport. Unknowns: phi, density, momentum, total energy per unit volume, densities and volume fractions of the components. RCHPO1 RFLOT1 = 'KONV' 'VF' 'GFMP' MOT1 MOT2 MOD1 TABG LMOT1 MCHAPH MCHAR MCHAV MCHAP (MCHAY MCHAA) MCHPPH LOG1 MAILLIM ; INPUT MOT1 : MOT object ('RESI'). MOT2 : MOT object. 'GODUNOV' (stands for Godunov method)/ MOD1 : Euler model object. TABG : TABLE object that contains the gas properties (see PRIM operator). LMOT1 : LISTMOTS object. It contains the name of the components of RCHPO1, i.e. the name of phi, total density, velocity, total energy per unit volume, densities and volume fractions of the single species. MCHAPH : MCHAML object which contains phi and has as geometrical support (SPG) 'DOMA' MOD1 'FACEL' (one component, 'SCAL') (see 'PRET' operator) MCHAR : MCHAML object which contains the density and has as geometrical support (SPG) 'DOMA' MOD1 'FACEL' (one component, 'SCAL') (see 'PRET' operator) MCHAV : MCHAML object containing the velocity and the director cosines of the local frame (n,t) with respect to the global one (x,y) (in 2D, 6 components: * 'UN' = normal velocity (SPG = 'DOMA' MOD1 'FACEL') * 'UT' = tangential velocity (SPG = 'DOMA' MOD1 FACEL') * 'NX' = n.x (SPG = 'FACE') * 'NY' = n.y (SPG = 'FACE') * 'TX' = t.x (SPG = 'FACE') * 'TY' = t.y (SPG = 'FACE')). (see 'PRET' operator) MCHAP : MCHAML (SPG = 'DOMA' MOD1 'FACEL') containing the pressure (one component, 'SCAL'). (see 'PRET' operator) MCHAY : MCHAML (SPG = 'DOMA' MOD1 'FACEL') containing the mass fractions of the single gas component (see TAB2 . 'ESPEULE') (see 'PRET' operator) MCHAA : MCHAML (SPG = 'DOMA' MOD1 'FACEL') containing the volume fractions of the single gas component (see TAB2 . 'ESPEULE') (see 'PRET' operator) MCHPPH : CHPOINT (SPG = 'DOMA' MOD1 'CENTRE') containing phi, LOG1 : LOGIQUE, if VRAI phi and the volume fractions are computed with a conservative approach. MAILLIM : MAILLAGE -- FACE points in which the flux is not computed. OUTPUT RCHPO1: CHPOINT object (components into LMOT1) Residuum if MOT1 = 'RESI' (SPG = 'DOMA' MOD1 'CENTRE') RFLOT1: FLOTTANT object It is the characteristic time of the fastest wave
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