$$$$ LAPN NOTICE CHAT 11/09/12 21:16:52 7124 DATE 11/09/12 Operateur LAPN Voir aussi : I Finite Elements Formulation: ______________________________ Syntax EQEX (see EQEX) : ... 'EQEX' ... 'OPTI' MOT1 MOT2 'ZONE' MOD1 'OPER' 'LAPN' OBJ1 'INCO' MOT3 (MOT4) Description : _____________ LAPN operator deals with the discretisation of diffusive terms in scalar or vectorial equations. For vectorial equation, equation of momentum conservation for incompressible flows is considered. For a scalar equation as the heath equation dT/dt = div(alpha grad T) this operator treats the div(alpha grad T) term, where alpha is the diffusivity (alpha in m2/s [SI]). For the momentum equation, this operator deals with the divergence of viscous stress tensor in incompressible form -> -> t -> dU/dt + ... = div(nu (grad U + grad U)) so we have to consider div(nu (grad U + tgrad U)) where nu is the cinematic viscosity (nu in m2/s [SI]). For a system, the discretised term is of the generalised form div(d grad T) in an equation dealing with the evolution of an unknown named V. T is called the primal unknown as V is the dual unknown. Sign convention is the following: when the coefficient of diffusion is greater then zero, the maximum of the scalar or vectorial unknown decreases. Transient procedure EXEC use this operator with data constructed with EQEX operator with the syntax done. Contents : __________ 'OPTI' : Key word introducing numerical options MOT1 : Discretization in space ('EF', 'VF' or 'EFM1') MOT2 : Discretization in time ('EXPL' or 'IMPL') Actually, VF and EF are treated in IMPL ; EFM1 in EXPL. 'ZONE' : Key word introducing geometric informations MOD1 : MODELE object ; contains geometric data associated to the region where exchange is located 'OPER' : Key word introducing operator's name and physical data 'LAPN' : Operator's name treated by EQEX OBJ1 : Coeff of diffusion d (CHPO SCAL CENTRE, FLOTTANT or MOT) 'INCO' : Key word introducing primal and dual unknowns' name MOT3 : Primal unknown's name (T) MOT4 : Dual unknown's name (V) When primal and dual names are the same, only one is mandatory. Note that dual and primal unknowns are always the same when explicit formulation is used. Results : _________ Explicit formulation : - The tight hand side is stored in a CHPO and set in order in the table KIZG at the index MOT3. Implicit formulation : - The matrix is stored in a MATRIK and set in order in the table TAB1 at the index of type MOT MATELM. - The tight hand side is stored in a CHPO and assembled with the other's stored in EQEX table at the index of type MOT SMBR. CHPO component's nane of the LAPN's contribution is MOT4. Remarks : ___________ 1) When OBJ1 is of type MOT, we look for data in INCO table at the index OBJ1. 2) Geometric support (spg) of CHPOINT contains one of those of the table of subtype DOMAINE. Some compatibilities are verified : - For EF or EFM1 formulation, dual unknown's spg contains SOMMET - For VF formulation, dual unknown's spg contains CENTRE - In implicit formulation, when primal and dual unknowns are not the same, spg are to be the same - Exchange coefficient spg is always CENTRE 3) Graduate user who develops his own transient procedure calls the LAPN operator with the following syntax : LAPN TAB1 ; with TAB1 : Table of subtype EQEX ; contains physical and numerical informations ; created by the EQEX operator. II Finite Volume Formulation: _____________________________ IIa : Mono-component perfect gas (constant volume specific heat) ___ Diffusive terms discretization of the compressible Navier-Stokes equations for a calorically perfect gas. SYNTAX: RMAT1 RCHP1 DELTAT = 'LAPN' 'VF' 'PROPCOST' MOT1 MOT2 MOD1 FLOT1 FLOT2 FLOT3 CHPO1 CHPO2 CHPO3 CHPO4 CHPO5 (CHAM1 CHAM2 si MOT2 = 'IMPL') ('VIMP' CHPO6) ('TAUI' CHPO7) ('QIMP' CHPO8) ('MIXT' CHP10) ('TIMP' CHPO9) LMOT ('CLAUDEIS'); MOT1 : MOT object 'RESI' if we want to compute the residuum 'FLUX' if we want to compute the flux MOT2 : MOT object 'IMPL' if we want to compute the residuum jacobian RMAT1 'EXPL' if we don't want to compute RMAT1 MOD1 : MODELE object. FLOT1 : 'FLOTTANT' object (dynamic viscosity) FLOT2 : 'FLOTTANT' object (thermal conductivity) FLOT3 : 'FLOTTANT' object (constant volume specific heat) CHPO1 : 'CHPOINT' 'CENTRE' (mass density, 1 component, 'SCAL') CHPO2 : 'CHPOINT' 'CENTRE' (velocity, 2/3 components 'UX','UY', ('UZ')) CHPO3 : 'CHPOINT' 'CENTRE' (temperature, 1 component, 'SCAL') CHPO4 : 'CHPOINT' 'FACE' (velocity gradient 4/9 components, 'P1DX', 'P1DY',('P1DZ'),'P2DX','P2DY',('P2DZ'), ('P3DX','P3DY','P3DZ')) CHPO5 : 'CHPOINT' 'FACE' (temperature gradient, 2/3 components, 'P1DX','P1DY',('P1DZ')) CHAM1 : 'MCHAML' (coefficients used for velocity gradient computation (see 'PENT' operator)) CHAM2 : 'MCHAML' (coefficients used for temperature gradient computation (see 'PENT' operator)) CHPO6 : 'CHPOINT' 'FACE' (imposed velocity, 2/3 components, 'UX','UY',('UZ')) CHPO7 : 'CHPOINT' 'FACE' (imposed viscous stress tensor, 3/6 components 'TXX','TYY','TXY',('TXZ''TYZ','TZZ')) CHPO8 : 'CHPOINT' 'FACE' (imposed heat flux, 2/3 components, 'UX','UY',('UZ')) CHPO9 : 'CHPOINT' 'FACE' (imposed temperature, 1 component 'SCAL') CHP10 : 'CHPOINT' 'FACE' (4 components, lambda1,lmabda2,qlimx,qlimy ) (imposed mixed condition) lambda1 (d grad T . n) + lambda2 T = (qlimx*nx) + (qlim*ny) LMOT1 : LISTMOTS object It contains the components names of RCHPO1 in the following order: density, momentum, total energy RMAT1 : MATRIK object (SPG = 'DOMA' MOD1 'CENTRE') (primal unknowns = dual unknowns; their names are into LMOT1) In the implicit case, it contains the Jacobian of the residuum with respect to the conservative variables. Conversely, it is an empty MATRIK 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 stability time step for the explicit Euler scheme. CLAUDEIS : Option to take into account thermal part of the Jacobian of the residuum IIb : Multi-component perfect gas (constant volume specific heat ___ for the species) Diffusive terms discretization of the compressible Navier-Stokes equations for a mixture of calorically perfect gases. Unknowns : mass density (of the mixture), momentum, total energy per unit volume, species density SYNTAX: RMAT1 RCHP1 DELTAT = 'LAPN' 'VF' 'PERFMULT' MOT1 MOT2 MOD1 TAB2 CHPO1 CHPO2 CHPO3 CHPO4 CHPO5 CHPO6 CHPO7 CHPO8 (CHAM1 CHAM2 when MOT2 = 'IMPL') ('VIMP' CHPO9) ('TAUI' CHP10) ('QIMP' CHP11) ('TIMP' CHP12) ('RIMP' CHP12) LMOT ; MOT1 : MOT object 'RESI' if we want to compute the residuum 'FLUX' if we want to compute the flux MOT2 : MOT object 'IMPL' if we want to compute the residuum jacobian RMAT1 'EXPL' if we don't want to compute RMAT1 MOD1 : MODELE object. TAB2 : TABLE object with the species properties : * name of the specie not in the Euler equation system : TAB2 . 'ESPNEULE' (MOT) ; * name of the species explicitly part of the Euler equ. system in TAB2 . 'ESPEULE' (LISTMOTS) ; * degree of polynomial for cv_i=cv_i(T), in TAB2 . 'NORD' (it must be 0) * properties of each gaz 'ESPI', in table TAB2 . 'ESPI': - TAB2 . 'ESPI' . 'A' (LISTREEL) the (TAB2.'NORD')+1 coefficients of the polynomial cv(T) - TAB2 . 'ESPI' . 'R' (J/kg/K in SI system, FLOTTANT) perfect gaz constant - TAB2 . 'ESPI' . 'H0K' (J/kg, FLOTTANT) mass formation enthalpy - TAB2 . 'ESPI' . 'CDIFF' (FLOTTANT) : diffusion coefficient of the specie into the mixture - TAB2 . 'ESPI' . 'CLYK' : 'CHPOINT' 'FACE' (Dirichlet BC for the specie density, 1 component, 'SCAL') - TAB2 . 'ESPI' . 'YK' : 'CHPOINT' 'FACE' (specie density , 1 component, 'SCAL') - TAB2 . 'ESPI' . 'CGRYK' : 'MCHAML' (coefficient used for the computation of the gradient of the specie density) - TAB2 . 'ESPI' . 'GRADYK' : 'CHPOINT' 'FACE' (gradient of the specie density, 2/3 components, 'P1DX','P1DY',('P1DZ')) CHPO1 : 'FLOTTANT' object (dynamic viscosity of the mixture) CHPO2 : 'FLOTTANT' object (thermal conductivity of the mixture) CHPO3 : 'FLOTTANT' object (constant volume specific heat of the mixture) CHPO4 : 'CHPOINT' 'CENTRE' (mass density, 1 component, 'SCAL') CHPO5 : 'CHPOINT' 'CENTRE' (velocity, 2/3 components 'UX','UY', ('UZ')) CHPO6 : 'CHPOINT' 'CENTRE' (temperature, 1 component, 'SCAL') CHPO7 : 'CHPOINT' 'FACE' (velocity gradient 4/9 components, 'P1DX', 'P1DY',('P1DZ'),'P2DX','P2DY',('P2DZ'), ('P3DX','P3DY','P3DZ')) CHPO8 : 'CHPOINT' 'FACE' (temperature gradient, 2/3 components, 'P1DX','P1DY',('P1DZ')) CHAM1 : 'MCHAML' (coefficients used for velocity gradient computation (see 'PENT' operator)) CHAM2 : 'MCHAML' (coefficients used for temperature gradient computation (see 'PENT' operator)) CHPO9 : 'CHPOINT' 'FACE' (imposed velocity, 2/3 components, 'UX','UY',('UZ')) CHP10 : 'CHPOINT' 'FACE' (imposed viscous stress tensor, 3/6 components 'TXX','TYY','TXY',('TXZ''TYZ','TZZ')) CHP11 : 'CHPOINT' 'FACE' (imposed heat flux, 2/3 components, 'UX','UY',('UZ')) CHP12 : 'CHPOINT' 'FACE' (imposed temperature, 1 component 'SCAL') CHP13 : 'CHPOINT' 'FACE' (imposed mass density, 1 component 'SCAL') LMOT1 : LISTMOTS object It contains the components names of RCHPO1 in the following order: density, momentum, total energy, specie mass density. RMAT1 : MATRIK object (SPG = 'DOMA' MOD1 'CENTRE') (primal unknowns = dual unknowns; their names are into LMOT1) In the implicit case, it contains the Jacobian of the residuum with respect to the conservative variables. Conversely, it is an empty MATRIK 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 stability time step for the explicit Euler scheme. IIc : Laplacian discretisation in porous media or on heat equation ___ SYNTAXE: RMAT1 RCHP1 DELTAT = 'LAPN' 'VF' 'CLAUDEIS' MOT2 MOD1 CHPO3 CHPO5 (CHAM1 si MOT2 = 'IMPL') ('QIMP' CHPO8) ('MIXT' CHP10) ('TIMP' CHPO9) ; MOT2 : MOT object 'IMPL' if we want to compute the residuum jacobian RMAT1 'EXPL' if we don't want to compute RMAT1 MOD1 : MODELE object CHPO3 : 'CHPOINT' 'CENTRE' (temperature, 1 component, 'SCAL') CHPO5 : 'CHPOINT' 'FACE' (temperature gradient, 2/3 components, 'P1DX','P1DY',('P1DZ')) CHAM1 : 'MCHAML' (coefficients used for temperature gradient computation (see 'PENT' operator)) CHPO8 : 'CHPOINT' 'FACE' (imposed heat flux, 1 component, 'FLUX') CHPO9 : 'CHPOINT' 'FACE' (imposed temperature, 1 component ,'SCAL') CHP10 : 'CHPOINT' 'FACE' (3 components, lambda1,lmabda2,qlim) (imposed mixed condition) lambda1 (d grad T . n) + lambda2 T = qlim
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