$$$$ PENT NOTICE CHAT 11/09/12 21:17:35 7124 DATE 11/09/12 Operateur PENT Voir aussi : -------------- Object : _______ Evaluation of the gradient of a field in a cell-centered Finite Volume discretisation. ------------------------------------------------------------ | 1st possibility : creation of a GRADIENT in the CENTERs | ------------------------------------------------------------ RCHPO1 RCHPO2 RCHELEM1 = 'PENT' MOD1 'CENTRE' MCLE1 MCLE2 LMOT1 CHPO1 ('CLIM' CHPO2) ; or RCHPO1 RCHPO2 = 'PENT' MOD1 'CENTRE' MCLE1 MCLE2 LMOT1 CHPO1 ('CLIM' CHPO2) 'GRADGEO' RCHELEM1 ; Contents : _________ MOD1 : MODELE Object. MCLE1 : MOT object; it states how to treat the border elements; four possible choices: * 'BORDNULL': the gradient of CHPOINT is imposed to be zero on the elements next to the border; * 'LINEXACT': the gradient is evaluated on the elements next to the border using a linear interpolation. * 'EULESCAL': the gradient is calculated by using wall boundary conditions on the border for a scalar function (mirror state): Euler equations. * 'EULEVECT': the gradient is calculated by using wall boundary conditions on the border for a vector function (mirror state): Euler equations. MCLE2 : MOT object; it specifies the kind of gradient limiter to compute. Two options: * 'LIMITEUR', Barth-Jespersen limiter * 'NOLIMITE', the limiter coefficients are 1.0 LMOT1 : LISTMOTS, components of CHPO1 (and CHPO2) CHPO1 : CHPOINT 'CENTRE' (i components, 0 < i < 9) of which we want to evaluate the gradient. CHPO2 : CHPOINT 'CENTRE' (the same components as CHPO1) which specifies Dirichlet type boundary conditions on some 'FACE' points RCHELEM1 : CHAMELEM objet; it contains the geometrical coefficients to compute the gradient RCHPO1 : CHPOINT 'CENTRE' (NDIM * i components); the gradient of CHPO1; note that the gradient of the CHPO1 i-th component has as components 'PiDX', 'PiDY' ('PiDZ'). RCHPO2 : CHPOINT 'CENTRE' (i components); the multiplier coefficients that, multiplied by the gradient, give the limited gradient; the name of the i-th component is 'Pi' (same convention as for RCHPO1). Remarks : __________ 1) This gradient reconstruction belongs to 'k-exact reconstruction', family, with k = 1; i.e. if the function is linear the evaluated gradient is exact inside the domain . If option 'LINEXACT' is used, it is also k-exact on the border. 2) Options 'EULESCAL' and 'EULEVECT' consider the border as a wall. They use mirror elements : this is the wall physical condition for the Euler equations. 3) If we use 'EULEVECT' option, CHPO1 (and CHPO2) must have two components in 2D ('UX','UY') and three components in 3D ('UX', 'UY','UZ') ------------------------------------------------------------ | 2nd possibility : creation of a GRADIENT in the FACESs | ------------------------------------------------------------ RCHPO1 RCHELEM1 = 'PENT' MOD1 'FACE' 'DIAMAN2' LMOT1 LMOT2 CHPO1 CHPO2 CHPO3 ; or RCHPO1 = 'PENT' MOD1 'FACE' 'DIAMAN2' LMOT1 LMOT2 CHPO1 CHPO2 CHPO3 'GRADGEO' RCHELEM1 ; Contents : _________ MOD1 : MODELE Object. LMOT1 : LISTMOTS, components of CHPO1 and CHPO2 LMOT2 : LISTMOTS, components of CHPO3 and RCHPO1 CHPO1 : CHPOINT 'CENTRE' (i components, 1 <= i <= 9) of which we want to evaluate the gradient CHPO2 : CHPOINT 'CENTRE' which specifies Dirichlet type boundary conditions on some 'FACE' points CHPO3 : CHPOINT 'CENTRE' which specifies von Neuamnn type boundary conditions on some 'FACE' points RCHELEM1 : CHAMELEM objet; it contains the geometrical coefficients to compute the gradient RCHPO1 : CHPOINT 'FACE' (NDIM * i components) Remarks Von Neumann boundary conditions is taken into account via the scalar product of CHPO3 and the faces normals ------------------------------------------------------------ | 3nd possibility : creation of a GRADIENT in the FACESs | | (2 dimensions) with a symmetric tensor ------------------------------------------------------------ RCHPO1 RCHELEM1 = 'PENT' 'FACE' MCLE1 MOD1 CHPO1 ('DISPDIF CHPO3) ('CLIM' CHPO2) ('NEUM' CHPO4) ('MIXT' CHPO5) ; or RCHPO1 = 'PENT' 'FACE' MCLE1 MOD1 CHPO1 ('DISPDIF CHPO3) ('CLIM' CHPO2) ('NEUM' CHPO4) ('MIXT' CHPO5) 'GRADGEO' RCHELEM1 ; Contents : _________ MOD1 : MODELE Object. MCLE1 : MOT object; it indicates the method used to compute the gradient. Possible choice: 'MPFA' CHPO1 : CHPOINT 'CENTRE' (1 dimension) of which we want to evaluate the gradient CHPO2 : CHPOINT 'FACE' (the same components as CHPO1) which specifies Dirichlet type boundary conditions on some 'FACE' points CHPO4 : CHPOINT 'FACE' (1 component) which specifies flux type boundary conditions on some 'FACE' points CHPO5 : CHPOINT 'FACE' (4 components, lambda1,lambda2,qlimx,qlimy) which specifies mixed type boundary conditions on some 'FACE' points lambda1 (d grad T . n) + lambda2 T = (qlimx*nx) + (qlim*ny) CHPO3 : CHPOINT 'CENTRE' (3 components 'K11','K22','K21') of a tensor (2 dimensions) RCHELEM1 : CHAMELEM objet; it contains the geometrical coefficients to compute the gradient RCHPO1 : CHPOINT 'FACE' : it contains the scalar product of the gradient of CHPO1 with the normal vectors to the faces. It has one component ('FLUX'). -------------------------------------------------------------------- | 4nd possibility : creation of a gradient in the FACEs | with a symmetric tensor following the method described by | Christophe Le Potier in " Finite volume scheme for highly anisotropic dif | operators on unstructured meshes, C. R. Acad. Sci. Ser. I \textbf{340}, | 2005, pp. 921--926". | The obtained scheme is symmetric. | ------------------------------------------------------------------- RCHPO1 RCHELEM1 = 'PENT' 'FACE' MCLE1 MOD1 CHPO1 ('DISPDIF CHPO3) ('CLIM' CHPO2) ('NEUM' CHPO4) ; Contents : _________ MOD1 : MODELE Object. MCLE1 : MOT object; it indicates the method used to compute the gradient. Possible choice: 'VFSYM' CHPO1 : CHPOINT 'CENTRE' (1 dimension) of which we want to evaluate the gradient CHPO2 : CHPOINT 'SOMMET' (the same components as CHPO1) which specifies Dirichlet type boundary conditions on some 'SOMMET' points CHPO4 : CHPOINT 'FACE' (1 component) which specifies flux type boundary conditions on some 'FACE' points (only in 2 dimensions) RCHELEM1 : CHAMELEM objet; it contains the geometrical coefficients to compute the gradient RCHPO1 : CHPOINT 'FACE' : it contains the scalar product of the gradient of CHPO1 with the normal vectors to the faces. It has one component ('FLUX').
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