$$$$ PRET NOTICE CHAT 11/09/12 21:17:43 7124 DATE 11/09/12 Operateur PRET Voir aussi : PRIM -------------- KONV I) COMPRESSIBLE FLOW, EULER EQUATIONS __________________________________ Evaluation of the primitive variables at the interfaces in the modelling of the Euler Equations in the "cell-centred" Finite Volume formulation. ----------------- | 1st model | ----------------- Calorically perfect gas; specific heats cp and cv do not depend on temperature. Case a: first order in space, first order in time. ______ MCHAM1 MCHAM2 MCHAM3 MCHAM4 = 'PRET' MCLE1 ENTI1 ENTI2 MOD1 CHPO1 CHPO2 CHPO3 CHPO4 ; Contents : _________ MCLE1 : MOT object; 'PERFMONO'. ENTI1 : ENTIER object; space order (=1). ENTI2 : ENTIER object; time order (=1). MOD1 : MODELE Object. CHPO1 : CHPOINT "CENTRE" that contains the total mass density (kg/m^3; the name of its component is 'SCAL'). CHPO2 : CHPOINT "CENTRE" that contains the velocity (m/s; two components in 2D, 'UX ','UY '). CHPO3 : CHPOINT "CENTRE" that contains the pressure (Pa; one component, 'SCAL'). CHPO4 : CHPOINT "CENTRE" that contains the "gamma" of the gas (one component, 'SCAL'). MCHAM1 : MCHAML that contains the total mass density and has as underlying space (SPG) 'DOMA' MOD1 'FACEL' (kg/m^3; one component, 'SCAL'). MCHAM2 : MCHAML that contains the velocity (m/s) and the direction cosines of the local frame (n,t) in the global frame (x,y) (in 2D it has 6 components: * 'UN' = normal velocity (SPG = 'FACEL') * 'UT' = tangential velocity (SPG = 'FACEL') * 'NX' = n.x (SPG = 'FACE') * 'NY' = n.y (SPG = 'FACE') * 'TX' = t.x (SPG = 'FACE') * 'TY' = t.y (SPG = 'FACE')). MCHAM3 : MCHAML (SPG = "FACEL") that contains the pressure of the gas (Pa, one component, 'SCAL'). MCHAM4 : MCHAML (SPG = "FACEL") that contains the "gamma" of the gas (one component, 'SCAL'). Case b : second order in space, first or second order in time ______ MCHAM1 MCHAM2 MCHAM3 MCHAM4 = 'PRET' MCLE1 ENTI1 ENTI2 MOD1 CHPO1 CHPO2 CHPO3 CHPO4 CHPO5 CHPO6 CHPO7 CHPO8 CHPO9 CHPO10 (FLOT1) ; Contents : _________ MCLE1 : MOT object; 'PERFMONO' ENTI1 : ENTIER object; space order (=2) ENTI2 : ENTIER object; time order (=1 or 2) MOD1 : MODELE Object. CHPO1 : CHPOINT "CENTRE" that contains the total mass density (kg/m^3; the name of its component is 'SCAL'). CHPO2 : CHPOINT "CENTRE" that contains the gradient of the mass density (kg/m^4; 2 components in 2D, 'P1DX', 'P1DY'). CHPO3 : CHPOINT "CENTRE" that contains the limiter of mass density gradient (one component, 'P1 ') CHPO4 : CHPOINT "CENTRE" that contains the velocity (m/s; two components in 2D, 'UX ','UY '). CHPO5 : CHPOINT "CENTRE" that contains the velocity gradient (s^-1; 4 components in 2D, 'P1DX', 'P1DY', 'P2DX', 'P2DY'). CHPO6 : CHPOINT "CENTRE" that contains the limiter of the velocity gradient (2 component in 2D, 'P1', 'P2'). CHPO7 : CHPOINT "CENTRE" that contains the pressure of the gas (Pa; one component, 'SCAL'). CHPO8 : CHPOINT "CENTRE" that contains the pressure gradient (Pa/m; 2 components in 2D, 'P1DX', 'P1DY'). CHPO9 : CHPOINT "CENTRE" that contains the limiter of the pressure gradient (one component, 'P1' ). CHPO10 : CHPOINT "CENTRE" that contains the "gamma" of the gas (one component, 'SCAL'). FLOT1 : FLOTTANT (in the case ENTI2 = 2) that contains the time increment (s) for the prediction step (suggested value = Dt / 2); MCHAM1 : MCHAML that contains the total mass density and has as underlying space (SPG) 'DOMA' MOD1 'FACEL' (kg/m^3; one component, 'SCAL'). MCHAM2 : MCHAML that contains the velocity (m/s) and the direction cosines of the local frame (n,t) in the global frame (x,y) (in 2D it has 6 components: * 'UN' = normal velocity (SPG = 'FACEL') * 'UT' = tangential velocity (SPG = 'FACEL') * 'NX' = n.x (SPG = 'FACE') * 'NY' = n.y (SPG = 'FACE') * 'TX' = t.x (SPG = 'FACE') * 'TY' = t.y (SPG = 'FACE')). MCHAM3 : MCHAML (SPG = "FACEL") that contains the pressure of the gas (Pa, one component, 'SCAL'). MCHAM4 : MCHAML (SPG = "FACEL") that contains the "gamma" of the gas (one component, 'SCAL'). ----------------- | 2nd model | ----------------- Mixture of perfect gases (cp and cv are temperature independents) Case a: first order in space, first order in time ______ MCHAM1 MCHAM2 MCHAM3 MCHAM4 MCHAM5 = 'PRET' MCLE1 ENTI1 ENTI2 MOD1 CHPO1 CHPO2 CHPO3 CHPO4 CHPO5 ; Contents : __________ MCLE1 : MOT object; 'PERFMULT'. ENTI1 : ENTIER object; space order (=1). ENTI2 : ENTIER object; time order (=1). MOD1 : MODELE Object. CHPO1 : CHPOINT "CENTRE" that contains the total mass density (kg/m^3; the name of its component is 'SCAL'). CHPO2 : CHPOINT "CENTRE" that contains the velocity (m/s; two components in 2D, 'UX ','UY '). CHPO3 : CHPOINT "CENTRE" that contains the pressure (Pa; one component, 'SCAL'). CHPO4 : CHPOINT "CENTRE" that contains the mass fractions of the different species (one or more components). CHPO5 : CHPOINT "CENTRE" that contains the "gamma" of the gas (one component, 'SCAL'). MCHAM1 : MCHAML that contains the total mass density and has as underlying space (SPG) 'DOMA' MOD1 'FACEL' (kg/m^3; one component, 'SCAL'). MCHAM2 : MCHAML that contains the velocity (m/s) and the direction cosines of the local frame (n,t) in the global frame (x,y) (in 2D it has 6 components: * 'UN' = normal velocity (SPG = 'FACEL') * 'UT' = tangential velocity (SPG = 'FACEL') * 'NX' = n.x (SPG = 'FACE') * 'NY' = n.y (SPG = 'FACE') * 'TX' = t.x (SPG = 'FACE') * 'TY' = t.y (SPG = 'FACE')). MCHAM3 : MCHAML (SPG = "FACEL") that contains the pressure of the gas (Pa, one component, 'SCAL'). MCHAM4 : MCHAML (SPG = "FACEL") that contains the mass fractions of each species (the same components as CHPO4). MCHAM5 : MCHAML (SPG = "FACEL") that contains the "gamma" of the gas (one component, 'SCAL'). Case b : second order in space, first or second order in time ______ MCHAM1 MCHAM2 MCHAM3 MCHAM4 MCHAM5 = 'PRET' MCLE1 ENTI1 ENTI2 MOD1 TAB2 CHPO1 CHPO2 CHPO3 CHPO4 CHPO5 CHPO6 CHPO7 CHPO8 CHPO9 CHPO10 CHPO11 CHPO12 CHPO13 (FLOT1) ; Contents : __________ MCLE1 : MOT object; 'PERFMULT'. ENTI1 : ENTIER object; space order (= 2). ENTI2 : ENTIER object; time order (= 1 or 2). MOD1 : MODELE Object. TAB2 : TABLE object that contains the physical properties of the gas (see operator PRIM). CHPO1 : CHPOINT "CENTRE" that contains the total mass density (kg/m^3; the name of its component is 'SCAL'). CHPO2 : CHPOINT "CENTRE" that contains the gradient of the mass density (kg/m^4; 2 components in 2D, 'P1DX', 'P1DY'). CHPO3 : CHPOINT "CENTRE" that contains the limiter of mass density gradient (one component, 'P1 ') CHPO4 : CHPOINT "CENTRE" that contains the velocity (m/s; two components in 2D, 'UX ','UY '). CHPO5 : CHPOINT "CENTRE" that contains the velocity gradient (s^-1; 4 components in 2D, 'P1DX', 'P1DY', 'P2DX', 'P2DY'). CHPO6 : CHPOINT "CENTRE" that contains the limiter of the velocity gradient (2 component in 2D, 'P1', 'P2'). CHPO7 : CHPOINT "CENTRE" that contains the pressure of the gas (Pa; one component, 'SCAL'). CHPO8 : CHPOINT "CENTRE" that contains the pressure gradient (Pa/m; 2 components in 2D, 'P1DX', 'P1DY'). CHPO9 : CHPOINT "CENTRE" that contains the limiter of the pressure gradient (one component, 'P1' ). CHPO10 : CHPOINT "CENTRE" that contains the mass fractions of the different species (n components, n >= 1; their names are in the object (TAB2 . 'ESPEULE')). CHPO11 : CHPOINT "CENTRE" that contains the gradient of the mass fractions (m^-1, 2n components in 2D). CHPO12 : CHPOINT "CENTRE" that contains the limiter of the gradient of the mass fractions (n components). CHPO13 : CHPOINT "CENTRE" containing the "gamma" of the gas (une composante, 'SCAL'). FLOT1 : FLOTTANT (in the case ENTI2 = 2) that contains the time increment (s) for the prediction step (suggested value = Dt / 2); MCHAM1 : MCHAML that contains the total mass density and has as underlying space (SPG) 'DOMA' DOM1 'FACEL' (kg/m^3; one component, 'SCAL'). MCHAM2 : MCHAML that contains the velocity (m/s) and the direction cosines of the local frame (n,t) in the global frame (x,y) (in 2D it has 6 components: * 'UN' = normal velocity (SPG = 'FACEL') * 'UT' = tangential velocity (SPG = 'FACEL') * 'NX' = n.x (SPG = 'FACE') * 'NY' = n.y (SPG = 'FACE') * 'TX' = t.x (SPG = 'FACE') * 'TY' = t.y (SPG = 'FACE')). MCHAM3 : MCHAML (SPG = "FACEL") that contains the pressure of the gas (Pa, one component, 'SCAL'). MCHAM4 : MCHAML (SPG = "FACEL") that contains the mass fractions of each species (the same components as CHPO4). MCHAM5 : MCHAML (SPG = "FACEL") that contains the "gamma" of the gas (one component, 'SCAL'). ----------------- | 3rd model | ----------------- Perfect gas / mixture of perfect gases (cv are temperature dependent) Case a: first order in space, first order in time ______ MCHAM1 MCHAM2 MCHAM3 (MCHAM4) (MCHAM5) = 'PRET' MCLE1 ENTI1 ENTI2 MOD1 TAB2 CHPO1 CHPO2 CHPO3 (CHPO4) (CHPO5) ; Contents : __________ MCLE1 : MOT object; 'PERFTEMP'. ENTI1 : ENTIER object; space order (=1). ENTI2 : ENTIER object; time order (=1). MOD1 : MODELE Object. TAB2 : TABLE object that contains the physical properties of the gas (see operator PRIM). CHPO1 : CHPOINT "CENTRE" that contains the total mass density (kg/m^3; the name of its component is 'SCAL'). CHPO2 : CHPOINT "CENTRE" that contains the velocity (m/s; two components in 2D, 'UX ','UY '). CHPO3 : CHPOINT "CENTRE" that contains the pressure (Pa; one component, 'SCAL'). (CHPO4) : CHPOINT "CENTRE" that contains the mass fractions of the different species (only in the case of a mixture; its components are also in the object (TAB2. 'ESPEULE')). (CHPO5) : CHPOINT "CENTRE" that contains the transported passive scalars (of course, only in the case of transport of passive scalars; its components are in the object (TAB2. 'SCALPASS')). MCHAM1 : MCHAML that contains the total mass density and has as underlying space (SPG) 'DOMA' MOD1 'FACEL' (kg/m^3; one component, 'SCAL'). MCHAM2 : MCHAML that contains the velocity (m/s) and the direction cosines of the local frame (n,t) in the global frame (x,y) (in 2D it has 6 components: * 'UN' = normal velocity (SPG = 'FACEL') * 'UT' = tangential velocity (SPG = 'FACEL') * 'NX' = n.x (SPG = 'FACE') * 'NY' = n.y (SPG = 'FACE') * 'TX' = t.x (SPG = 'FACE') * 'TY' = t.y (SPG = 'FACE')). MCHAM3 : MCHAML (SPG = "FACEL") that contains the pressure of the gas (Pa, one component, 'SCAL'). MCHAM4 : MCHAML (SPG = "FACEL") that contains the mass fractions of each species (only in the case of a mixture; the same components as CHPO4). (MCHAM5): MCHAML (SPG = "FACEL") that contains the transported passive scalars (of course, only in the case of transport of passive scalars). Case b : second order in space, first or second order in time ______ First order in time MCHAM1 MCHAM2 MCHAM3 (MCHAM4)(MCHAM5)= 'PRET' MCLE1 ENTI1 ENTI2 MOD1 TAB2 CHPO1 CHPO2 CHPO3 CHPO4 CHPO5 CHPO6 CHPO7 CHPO8 CHPO9 (CHPO10 CHPO11 CHPO12) (CHPO13 CHPO14 CHPO15) ; Second order in time MCHAM1 MCHAM2 MCHAM3 (MCHAM4)(MCHAM5)= 'PRET' MCLE1 ENTI1 ENTI2 MOD1 TAB2 CHPO1 CHPO2 CHPO3 CHPO4 CHPO5 CHPO6 CHPO7 CHPO8 CHPO9 (CHPO10 CHPO11 CHPO12) (CHPO13 CHPO14 CHPO15) CHPO16 FLOT1 ; Contents : __________ MCLE1 : MOT object; 'PERFTEMP'. ENTI1 : ENTIER object; space order (= 2). ENTI2 : ENTIER object; time order (= 1 or 2). MOD1 : MODELE Object. TAB2 : TABLE object that contains the physical properties of the gas (see operator PRIM). CHPO1 : CHPOINT "CENTRE" that contains the total mass density (kg/m^3; the name of its component is 'SCAL'). CHPO2 : CHPOINT "CENTRE" that contains the gradient of the mass density (kg/m^4; 2 components in 2D, 'P1DX', 'P1DY'). CHPO3 : CHPOINT "CENTRE" that contains the limiter of mass density gradient (one component, 'P1 ') CHPO4 : CHPOINT "CENTRE" that contains the velocity (m/s; two components in 2D, 'UX ','UY '). CHPO5 : CHPOINT "CENTRE" that contains the velocity gradient (s^-1; 4 components in 2D, 'P1DX', 'P1DY', 'P2DX', 'P2DY'). CHPO6 : CHPOINT "CENTRE" that contains the limiter of the velocity gradient (2 component in 2D, 'P1', 'P2'). CHPO7 : CHPOINT "CENTRE" that contains the pressure of the gas (Pa; one component, 'SCAL'). CHPO8 : CHPOINT "CENTRE" that contains the pressure gradient (Pa/m; 2 components in 2D, 'P1DX', 'P1DY'). CHPO9 : CHPOINT "CENTRE" that contains the limiter of the pressure gradient (one component, 'P1' ). (CHPO10) : CHPOINT "CENTRE" that contains the mass fractions of the different species (only in the case of a mixture; n components, the same as (TAB2. 'ESPEULE')). (CHPO11) : CHPOINT "CENTRE" that contains the gradient of the mass fractions (m^-1; only in the case of a mixture; 2n components in 2D). (CHPO12) : CHPOINT "CENTRE" that contains the limiter of the gradient of the mass fractions (only in the case of a mixture; n components). (CHPO13) : CHPOINT "CENTRE" that contains the transported passive scalars (of course, only in the case of transport of passive scalars; k components, specified in TAB2 . 'SCALPASS') (CHPO14) : CHPOINT "CENTRE" that contains the gradients of the passive scalars (of course, only in the case of transport of passive scalars; 2k components, in 2D) (CHPO15) : CHPOINT "CENTRE" that contains the limiter of the gradients of the passive scalars (of course, only in the case of transport of passive scalars; k components) CHPO16 : CHPOINT "CENTRE" containing the "gamma" of the gas (one component, 'SCAL'; only in the case ENTI2 = 2). FLOT1 : FLOTTANT object that contains the time increment (s) for the prediction step (only in the case ENTI2 = 2; suggested value: Dt / 2); MCHAM1 : MCHAML that contains the total mass density and has as underlying space (SPG) 'DOMA' MOD1 'FACEL' (kg/m^3; one component, 'SCAL'). MCHAM2 : MCHAML that contains the velocity (m/s) and the direction cosines of the local frame (n,t) in the global frame (x,y) (in 2D it has 6 components: * 'UN' = normal velocity (SPG = 'FACEL') * 'UT' = tangential velocity (SPG = 'FACEL') * 'NX' = n.x (SPG = 'FACE') * 'NY' = n.y (SPG = 'FACE') * 'TX' = t.x (SPG = 'FACE') * 'TY' = t.y (SPG = 'FACE')). MCHAM3 : MCHAML (SPG = "FACEL") that contains the pressure of the gas (Pa, one component, 'SCAL'). (MCHAM4) : MCHAML (SPG = "FACEL") that contains the mass fractions of each species (the same components as CHPO10). (MCHAM5): MCHAML (SPG = "FACEL") that contains the transported passive scalars (of course, only in the case of transport of passive scalars). Remark: _______ The SPG (geometrical support) of MCHAML, that is obtained by 'DOMA' MOD1 'FACEL', is a MAILLAGE object of SEG3. If the face is not on the border, the first and the third point of each SEG3 are the centers of the elements laying on this face (for convention we say that the first point is the center of the left element and the third is the center of the right one), while the second point is the center of the face. MCHAMLs 'FACEL' are defined on the first and on the third point of the SEG3, and they represent the reconstruction of the variables on the left and on the right of each face. For a border face, the first point of the SEG3 contains the reconstructed state of the variables while the third point contains his mirror state (i.e. we impose boundary conditions of "wall" type). II) SCALARS TRANSPORT __________________ We want to solve by FV discretization --> ---> d/dt S + u . grad (S) = 0 --> with div( u ) = 0 This operator computes the variables S at the interfaces starting from their centered values. a) 1st order accuracy in space CHAM1S = 'PRET' 'CLAUDEIS' 'FACE' ENTI1 MOD1 CHPO1 ; ENTI1 : space order = 1 MOD1 : MODELE Object. CHPO1 : CHPOINT containing the scalars to transport (geometrical support SPG = 'DOMA' MOD1 'CENTRE') CHAM1S : MCHAML containing the scalars to transport (SPG = 'DOMA' MOD1 'CENTRE', same components as CHPO1) Remark: _______ The SPG (geometrical support) of MCHAML, that is obtained by 'DOMA' MOD1 'FACEL', is a MAILLAGE object of SEG3. If the face is not on the border, the first and the third point of each SEG3 are the centers of the elements laying on this face (for convention we say that the first point is the center of the left element and the third is the center of the right one), while the second point is the center of the face. MCHAMLs 'FACEL' are defined on the first and on the third point of the SEG3, and they represent the reconstruction of the variables on the left and on the right of each face. For a border face, the first point of the SEG3 contains the reconstructed state of the variables while the third point contains his mirror state. III) COMPRESSIBLE FLOW, TWO-FLUID EQUATIONS ______________________________________ Evaluation of the primitive variables at the interfaces in the modelling of the one-pressure six-equation two-fluid model (only for water and air mixtures) in the "cell-centred" Finite Volume formulation. Case a: first order in space, first order in time. ______ MCHAM8 MCHAM7 MCHAM6 MCHAM5 MCHAM4 MCHAM3 MCHAM2 MCHAM1 = 'PRET' MCLE1 ENTI1 ENTI2 MOD1 CHPO1 CHPO2 CHPO3 CHPO4 CHPO5 CHPO6 CHPO7 CHPO8 ; Contents : _________ MCLE1 : MOT object; 'TWOFLUID'. ENTI1 : ENTIER object; space order (=1). ENTI2 : ENTIER object; time order (=1). MOD1 : MODELE Object. CHPO1 : CHPOINT "CENTRE" that contains the void fraction (the name of its component is 'SCAL'). CHPO2 : CHPOINT "CENTRE" that contains the gas velocity (m/s; two components in 2D, 'UVX ','UVY '). CHPO3 : CHPOINT "CENTRE" that contains the liquid velocity (m/s; two components in 2D, 'ULX ','ULY '). CHPO4 : CHPOINT "CENTRE" that contains the pressure (Pa; one component, 'SCAL'). CHPO5 : CHPOINT "CENTRE" that contains the gas temperature (K; one component, 'SCAL'). CHPO6 : CHPOINT "CENTRE" that contains the liquid temperature (K; one component, 'SCAL'). CHPO7 : CHPOINT "CENTRE" that contains the gas density (kg/m^3; one component, 'SCAL'). CHPO8 : CHPOINT "CENTRE" that contains the liquid density (kg/m^3; one component, 'SCAL'). MCHAM1 : MCHAML that contains the void fraction and has as underlying space (SPG) 'DOMA' MOD1 'FACEL' (one component, 'SCAL'). MCHAM2 : MCHAML that contains the gas velocity (m/s) and the direction cosines of the local frame (n,t) in the global frame (x,y) (in 2D it has 6 components: * 'UN' = normal velocity (SPG = 'FACEL') * 'UT' = tangential velocity (SPG = 'FACEL') * 'NX' = n.x (SPG = 'FACE') * 'NY' = n.y (SPG = 'FACE') * 'TX' = t.x (SPG = 'FACE') * 'TY' = t.y (SPG = 'FACE')). MCHAM3 : MCHAML that contains the liquid velocity (m/s) and the direction cosines of the local frame (n,t) in the global frame (x,y) (in 2D it has 6 components: * 'UN' = normal velocity (SPG = 'FACEL') * 'UT' = tangential velocity (SPG = 'FACEL') * 'NX' = n.x (SPG = 'FACE') * 'NY' = n.y (SPG = 'FACE') * 'TX' = t.x (SPG = 'FACE') * 'TY' = t.y (SPG = 'FACE')). MCHAM4 : MCHAML (SPG = "FACEL") that contains the pressure of the gas (Pa, one component, 'SCAL'). MCHAM5 : MCHAML (SPG = "FACEL") that contains the gas temperature (K; one component, 'SCAL'). MCHAM6 : MCHAML (SPG = "FACEL") that contains the liquid temperature (K; one component, 'SCAL'). MCHAM7 : MCHAML (SPG = "FACEL") that contains the gas density (kg/m^3; one component, 'SCAL'). MCHAM8 : MCHAML (SPG = "FACEL") that contains the liquid density (kg/m^3; one component, 'SCAL'). Case b : second order in space, second order in time ______ MCHAM8 MCHAM7 MCHAM6 MCHAM5 MCHAM4 MCHAM3 MCHAM2 MCHAM1 = 'PRET' MCLE1 ENTI1 ENTI2 MOD1 CHPO1 CHPO2 CHPO3 CHPO4 CHPO5 CHPO6 CHPO7 CHPO8 CHPO9 CHPO10 CHPO11 CHPO12 CHPO13 CHPO14 CHPO15 CHPO16 CHPO17 CHPO18 CHPO19 CHPO20 FLOT1 ; 'PRET' MCLE1 ENTI1 ENTI2 MOD1 CHPO1 CHPO2 CHPO3 CHPO4 CHPO5 CHPO6 CHPO7 CHPO8 ; Contents : _________ MCLE1 : MOT object; 'TWOFLUID' ENTI1 : ENTIER object; space order (= 2) ENTI2 : ENTIER object; time order (= 2) MOD1 : MODELE Object. CHPO1 : CHPOINT "CENTRE" that contains the void fraction (the name of its component is 'SCAL'). CHPO2 : CHPOINT "CENTRE" that contains the gradient of the void fraction (2 components in 2D, 'P1DX', 'P1DY'). CHPO3 : CHPOINT "CENTRE" that contains the limiter of void fraction gradient (one component, 'P1 ') CHPO4 : CHPOINT "CENTRE" that contains the gas velocity (m/s; two components in 2D, 'UVX ','UVY '). CHPO5 : CHPOINT "CENTRE" that contains the gas velocity gradient (s^-1; 4 components in 2D, 'P1DX', 'P1DY', 'P2DX', 'P2DY'). CHPO6 : CHPOINT "CENTRE" that contains the limiter of the gas velocity gradient (2 component in 2D, 'P1', 'P2'). CHPO7 : CHPOINT "CENTRE" that contains the liquid velocity (m/s; two components in 2D, 'UVX ','UVY '). CHPO8 : CHPOINT "CENTRE" that contains the liquid velocity gradient (s^-1; 4 components in 2D, 'P1DX', 'P1DY', 'P2DX', 'P2DY'). CHPO9 : CHPOINT "CENTRE" that contains the limiter of the liquid velocity gradient (2 component in 2D, 'P1', 'P2'). CHPO10 : CHPOINT "CENTRE" that contains the pressure (Pa; one component, 'SCAL'). CHPO11 : CHPOINT "CENTRE" that contains the pressure gradient (Pa/m; 2 components in 2D, 'P1DX', 'P1DY'). CHPO12 : CHPOINT "CENTRE" that contains the limiter of the pressure gradient (one component, 'P1' ). CHPO13 : CHPOINT "CENTRE" that contains the gas temperature (K; one component, 'SCAL'). CHPO14 : CHPOINT "CENTRE" that contains the gas temperature gradient (K/m; 2 components in 2D, 'P1DX', 'P1DY'). CHPO15 : CHPOINT "CENTRE" that contains the limiter of the gas temperature gradient (one component, 'P1' ). CHPO16 : CHPOINT "CENTRE" that contains the liquid temperature (K; one component, 'SCAL'). CHPO17 : CHPOINT "CENTRE" that contains the liquid temperature gradient (K/m; 2 components in 2D, 'P1DX', 'P1DY'). CHPO18 : CHPOINT "CENTRE" that contains the limiter of the liquid temperature gradient (one component, 'P1' ). CHPO19 : CHPOINT "CENTRE" that contains the gas density (kg/m^3; one component, 'SCAL'). CHPO20 : CHPOINT "CENTRE" that contains the liquid density (kg/m^3; one component, 'SCAL'). FLOT1 : FLOTTANT that contains the time increment (s) for the prediction step (suggested value = Dt); MCHAM1 : MCHAML that contains the void fraction and has as underlying space (SPG) 'DOMA' MOD1 'FACEL' (one component, 'SCAL'). MCHAM2 : MCHAML that contains the gas velocity (m/s) and the direction cosines of the local frame (n,t) in the global frame (x,y) (in 2D it has 6 components: * 'UN' = normal velocity (SPG = 'FACEL') * 'UT' = tangential velocity (SPG = 'FACEL') * 'NX' = n.x (SPG = 'FACE') * 'NY' = n.y (SPG = 'FACE') * 'TX' = t.x (SPG = 'FACE') * 'TY' = t.y (SPG = 'FACE')). MCHAM3 : MCHAML that contains the liquid velocity (m/s) and the direction cosines of the local frame (n,t) in the global frame (x,y) (in 2D it has 6 components: * 'UN' = normal velocity (SPG = 'FACEL') * 'UT' = tangential velocity (SPG = 'FACEL') * 'NX' = n.x (SPG = 'FACE') * 'NY' = n.y (SPG = 'FACE') * 'TX' = t.x (SPG = 'FACE') * 'TY' = t.y (SPG = 'FACE')). MCHAM4 : MCHAML (SPG = "FACEL") that contains the pressure of the gas (Pa, one component, 'SCAL'). MCHAM5 : MCHAML (SPG = "FACEL") that contains the gas temperature (K; one component, 'SCAL'). MCHAM6 : MCHAML (SPG = "FACEL") that contains the liquid temperature (K; one component, 'SCAL'). MCHAM7 : MCHAML (SPG = "FACEL") that contains the gas density (kg/m^3; one component, 'SCAL'). MCHAM8 : MCHAML (SPG = "FACEL") that contains the liquid density (kg/m^3; one component, 'SCAL'). IV) COMPRESSIBLE FLOW, REACTIVE DISCRETE EQUATION METHOD ______________________________________ Evaluation of the primitive variables at the interfaces in the modelling of the combustion using the REACTIVE DISCRETE EQUATION METHOD; in the "cell-centred" Finite Volume formulation. For the description of the variables please see the notice of the operator 'PRIM'. a) 2nd order in space (for the 1st order in space please multiply CHPGRA* and CHPLI* by zero) CHAMAL1 CHAMAL2 CHAMRN1 CHAMRN2 CHAMV1 CHAMV2 CHAMP1 CHAMP2 = 'PRET' 'DEM' MOD1 TABPGAS CHPAL1 CHPGRA1 CHPLIA1 CHPAL2 CHPGRA1 CHPLIA1 CHPRN1 CHPGRR1 CHPLIR1 CHPRN2 CHPGRR2 CHPLIR2 CHPVN1 CHPGRV1 CHPLIV1 CHPVN2 CHPGRV2 CHPLIV2 CHPP1 CHPGRP1 CHPLIP1 CHPP2 CHPGRP2 CHPLIP2 EPS ; ARGUMENTS : 'DEM' : key word for "Reactive Discrete Equation Method" MOD1 : OBJET MODELE de TYPE 'EULER' TABPGAS : TABLE of gas properties (see the notice of the operator 'PRIM') CHPAL1 CHPGRA1 CHPLIA1 : CHPOINTs "CENTRE": alpha1, its gradient, its limiter CHPAL2 CHPGRA2 CHPLIA2 : CHPOINTs "CENTRE": alpha2, its gradient, its limiter CHPRN1 CHPGRR1 CHPLIR1 : CHPOINTs "CENTRE": rho1 - density, its gradient, its limiter CHPRN2 CHPGRR2 CHPLIR2 : CHPOINTs "CENTRE": rho2 - density, its gradient, its limiter CHPVN1 CHPGRV1 CHPLIV1 : CHPOINTs "CENTRE": v1 - velocity, its gradient, its limiter CHPVN2 CHPGRV2 CHPLIV2 : CHPOINTs "CENTRE": v2 - velocity, its gradient, its limiter CHPVP1 CHPGRP1 CHPLIP1 : CHPOINTs "CENTRE": p1 - pressure, its gradient, its limiter CHPVP2 CHPGRP2 CHPLIP2 : CHPOINTs "CENTRE": p2 - pressure, its gradient, its limiter EPS : FLOTTANT; alpha_i < eps => no phase_i RESULTS : CHAMAL1 CHAMAL2 CHAMRN1 CHAMRN2 CHAMV1 CHAMV2 CHAMP1 CHAMP2 : MCHAML "FACEL" containing alpha (1 and 2), density (1 and 2) velocity (1 and 2) and pressure (1 and 2) on the left and on the right side of each interface V) COMPRESSIBLE FLOW, GHOST FLUID METHOD FOR THE POOR (GFMP) _______________________________________________________________ Evaluation of the primitive variables at the interfaces in the modelling of the Euler equation via the GFMP, in the "cell-centred" Finite Volume formulation. V.a) 2nd order in space, single species CHAMPH CHAMRN CHAMV CHAMP = 'PRET' 'GFMP' LMOT1 MOD1 CHPPH CHPGRPH CHPLIP CHPRN CHPGRR CHPLIR CHPVN CHPGRV CHPLIV CHPP CHPGRP CHPLIP ; or V.b) 2nd order in space, multispecies CHAMPH CHAMRN CHAMV CHAMP CHAMY CHAMAL = 'PRET' 'GFMP' LMOT1 MOD1 CHPPH CHPGRPH CHPLIP CHPRN CHPGRR CHPLIR CHPVN CHPGRV CHPLIV CHPP CHPGRP CHPLIP CHPYN CHPGRY CHPLIY CHPAN CHPGRA CHPLIA ; INPUT 'GFMP' : MOT OBJECT LMOT1 : LISTMOTS OBJECT, name of the species involved in the Euler equations MOD1 : MODEL OBJECT de TYPE EULER CHPPH CHPGRP CHPLIP : CHPOINTs "CENTRE": phi, its gradient, its limiter CHPRN CHPGRR CHPLIR : CHPOINTs "CENTRE": rho, its gradient, its limiter CHPVN CHPGRV CHPLIV : CHPOINTs "CENTRE": v, its gradient, its limiter CHPVP CHPGRP CHPLIP : CHPOINTs "CENTRE": p its gradient, its limiter CHPYN CHPGRY CHPLIY : CHPOINTs "CENTRE": y, its gradient, its limiter CHPAN CHPGRA CHPLIA : CHPOINTs "CENTRE": alpha, its gradient, its limiter OUTPUT CHAMPH CHAMRN CHAMV CHAMP CHAMY CHAMAL: MCHAML "FACEL" containing phi, density velocity, pressure, mass fractions volume fractions on the left and on the right
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