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opm/core/pressure/mimetic/mimetic.h
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@ -20,78 +20,250 @@
#ifndef OPM_MIMETIC_HEADER_INCLUDED #ifndef OPM_MIMETIC_HEADER_INCLUDED
#define OPM_MIMETIC_HEADER_INCLUDED #define OPM_MIMETIC_HEADER_INCLUDED
/**
* \file
* Routines to assist mimetic discretisations of the flow equation.
*/
#ifdef __cplusplus #ifdef __cplusplus
extern "C" { extern "C" {
#endif #endif
void mim_ip_span_nullspace(int nf, int nconn, int d, /**
double *C, * Form linear operator to span the null space of the normal vectors
double *A, * of a grid cell.
double *X,
double *work, int lwork);
void mim_ip_linpress_exact(int nf, int nconn, int d,
double vol, double *K,
double *N,
double *Binv,
double *work, int lwork);
void mim_ip_simple(int nf, int nconn, int d,
double v, double *K, double *C,
double *A, double *N,
double *Binv,
double *work, int lwork);
/** Compute the mimetic inner products given a grid and cellwise
* permeability tensors.
* *
* @param ncells Number of cells in grid. * Specifically,
* @param d Number of space dimensions. * \f[
* @param max_ncf Maximum number of faces per cell. * \begin{aligned}
* @param pconn Start indices in conn for each cell, plus end * X &= \operatorname{diag}(A) (I - QQ^\mathsf{T})
* marker. The size of pconn is (ncells + 1), and for a * \operatorname{diag}(A), \\
* cell i, [conn[pconn[i]], conn[pconn[i+1]]) is a * Q &= \operatorname{orth}(\operatorname{diag}(A) C)
* half-open interval containing the indices of faces * \end{aligned}
* adjacent to i. * \f]
* @param conn Cell to face mapping. Size shall be equal to the sum of * in which \f$\operatorname{orth}(M)\f$ denotes an orthonormal
* ncf. See pconn for explanation. * basis for the colum space (range) of the matrix \f$M\f$,
* @param fneighbour Face to cell mapping. Its size shall be equal to * represented as a matrix.
* the number of faces times 2. For each face, the *
* two entries are either a cell number or -1 * @param[in] nf Number of faces connected to single grid cell.
* (signifying the outer boundary). The face normal * @param[in] nconn Total number of grid cell connections.
* points out of the first cell and into the second. * Typically equal to @c nf.
* @param fcentroid Face centroids. Size shall be equal to the number * @param[in] d Number of physical dimensions.
* of faces times d. * Assumed less than four.
* @param fnormal Face normale. Size shall be equal to the number * @param[in,out] C Centroid vectors. Specifically,
* of faces times d. * \f$c_{ij} = \Bar{x}_{ij} - \Bar{x}_{cj}\f$.
* @param farea Face areas. * Array of size \f$\mathit{nf}\times d\f$
* @param ccentroid Cell centroids. Size shall be ncells*d. * in column major (Fortran) order.
* @param cvol Cell volumes. * Contents destroyed on output.
* @param perm Permeability. Size shall be ncells*d*d, storing a * @param[in] A Interface areas.
* d-by-d positive definite tensor per cell. * @param[out] X Null space linear operator. Array of size
* @param[out] Binv This is where the inner product will be * \f$\mathit{nconn}\times\mathit{nconn}\f$
* stored. Its size shall be equal to \f$\sum_i * in column major (Fortran) order. On output,
* n_i^2\f$. * the upper left \f$\mathit{nf}\times\mathit{nf}\f$
* sub-matrix contains the required null space
* linear operator.
* @param[out] work Scratch array of size at least @c nconn.
* @param[in] lwork Actual size of scratch array.
*/ */
void mim_ip_simple_all(int ncells, int d, int max_ncf, void
int *pconn, int *conn, mim_ip_span_nullspace(int nf, int nconn, int d,
int *fneighbour, double *fcentroid, double *fnormal, double *C,
double *farea, double *ccentroid, double *cvol, double *A,
double *perm, double *Binv); double *X,
double *work, int lwork);
/**
* Form (inverse) mimetic inner product that reproduces linear
* pressure drops (constant velocity) on general polyhedral cells.
*
* Specifically
* \f[
* B^{-1} = \frac{1}{v} \big(NKN^\mathsf{T} + \frac{6t}{d}\,X\big)
* \f]
* in which \f$t = \operatorname{tr}(K)\f$ is the trace of \f$K\f$
* and \f$X\f$ is the result of function mim_ip_span_nullspace().
*
* @param[in] nf Number of faces connected to single grid cell.
* @param[in] nconn Total number of grid cell connections.
* Typically equal to @c nf.
* @param[in] d Number of physical dimensions.
* Assumed less than four.
* @param[in] vol Cell volume.
* @param[in] K Permeability. A \f$d\times d\f$ matrix in
* column major (Fortran) order.
* @param[in] N Normal vectors. An \f$\mathit{nf}\times d\f$
* matrix in column major (Fortran) order.
* @param[in,out] Binv Inverse inner product result. An
* \f$\mathit{nconn}\times\mathit{nconn}\f$
* matrix in column major format. On input,
* the result of mim_ip_span_nullspace(). On
* output, the upper left
* \f$\mathit{nf}\times\mathit{nf}\f$ sub-matrix
* will be overwritten with \f$B^{-1}\f$.
* @param[in,out] work Scratch array of size at least <CODE>nf * d</CODE>.
* @param[in] lwork Actual size of scratch array.
*/
void
mim_ip_linpress_exact(int nf, int nconn, int d,
double vol, double *K,
double *N,
double *Binv,
double *work, int lwork);
/**
* Convenience wrapper around the function pair mim_ip_span_nullspace()
* and mim_ip_linpress_exact().
*
* @param[in] nf Number of faces connected to single grid cell.
* @param[in] nconn Total number of grid cell connections.
* Typically equal to @c nf.
* @param[in] d Number of physical dimensions.
* Assumed less than four.
* @param[in] v Cell volume.
* @param[in] K Permeability. A \f$d\times d\f$ matrix in
* column major (Fortran) order.
* @param[in,out] C Centroid vectors. Specifically,
* \f$c_{ij} = \Bar{x}_{ij} - \Bar{x}_{cj}\f$.
* Array of size \f$\mathit{nf}\times d\f$
* in column major (Fortran) order.
* Contents destroyed on output.
* @param[in] A Interface areas.
* @param[in] N Outward normal vectors.
* An \f$\mathit{nf}\times d\f$ matrix in
* column major (Fortran) order.
* @param[out] Binv Inverse inner product result. An
* \f$\mathit{nconn}\times\mathit{nconn}\f$
* matrix in column major format. On
* output, the upper left
* \f$\mathit{nf}\times\mathit{nf}\f$ sub-matrix
* will be overwritten with \f$B^{-1}\f$
* defined by function mim_ip_linpress_exact().
* @param[in,out] work Scratch array of size at least <CODE>nf * d</CODE>.
* @param[in] lwork Actual size of scratch array.
*/
void
mim_ip_simple(int nf, int nconn, int d,
double v, double *K, double *C,
double *A, double *N,
double *Binv,
double *work, int lwork);
/**
* Compute the mimetic inner products given a grid and cell-wise
* permeability tensors.
*
* This function applies mim_ip_simple() to all specified cells.
*
* @param[in] ncells Number of cells.
* @param[in] d Number of physical dimensions.
* @param[in] max_ncf Maximum number of connections (faces)
* of any individual cell.
* @param[in] pconn Start pointers of cell-to-face topology
* mapping.
* @param[in] conn Actual cell-to-face topology mapping.
* @param[in] fneighbour Face-to-cell mapping.
* @param[in] fcentroid Face centroids.
* @param[in] fnormal Face normals.
* @param[in] farea Face areas.
* @param[in] ccentroid Cell centroids.
* @param[in] cvol Cell volumes.
* @param[in] perm Cell permeability.
* @param[out] Binv Inverse inner product result. Must point
* to an array of size at least
* \f$\sum_c n_c^2\f$ when \f$n_c\f$ denotes
* the number of connections (faces) of
* cell \f$c\f$.
*/
void
mim_ip_simple_all(int ncells, int d, int max_ncf,
int *pconn, int *conn,
int *fneighbour, double *fcentroid, double *fnormal,
double *farea, double *ccentroid, double *cvol,
double *perm, double *Binv);
/**
* Compute local, static gravity pressure contributions to Darcy
* flow equation discretised using a mimetic finite-difference method.
*
* The pressure contribution of local face \f$i\f$ in cell \f$c\f$ is
* \f[
* \mathit{gpress}_{\mathit{pconn}_c + i} =
* \vec{g}\cdot (\Bar{x}_{\mathit{conn}_{\mathit{pconn}_c + i}}
* - \Bar{x}_c)
* \f]
*
* @param[in] nc Number of cells.
* @param[in] d Number of physcial dimensions.
* @param[in] grav Gravity vector. Array of size @c d.
* @param[in] pconn Start pointers of cell-to-face topology
* mapping.
* @param[in] conn Actual cell-to-face topology mapping.
* @param[in] fcentroid Face centroids.
* @param[in] ccentroid Cell centroids.
* @param[out] gpress Gravity pressure result. Array of size
* at least <CODE>pconn[nc]</CODE>.
*/
void void
mim_ip_compute_gpress(int nc, int d, const double *grav, mim_ip_compute_gpress(int nc, int d, const double *grav,
const int *pconn, const int *conn, const int *pconn, const int *conn,
const double *fcentroid, const double *ccentroid, const double *fcentroid, const double *ccentroid,
double *gpress); double *gpress);
/* inv(B) <- \lambda_t(s)*inv(B)_0 */
/**
* Incorporate effects of multiple phases in mimetic discretisation of
* flow equations.
*
* Specifically, update the (inverse) inner products \f$B^{-1}\f$
* previously computed using function mim_ip_linpress_exact() according
* to the rule
* \f[
* \Tilde{B}_c^{-1} = \frac{1}{\lambda_{T,c}} B_c^{-1},
* \quad i=0,\dots,\mathit{nc}-1
* \f]
* in which \f$B_c^{-1}\f$ denotes the result of mim_ip_linpress_exact()
* for cell \f$c\f$ and \f$\lambda_{T,c}\f$ denotes the total mobility
* of cell \f$c\f$.
*
* @param[in] nc Number of cells.
* @param[in] pconn Start pointers of cell-to-face topology
* mapping.
* @param[in] totmob Total mobility for all cells. Array of size @c nc.
* @param[in] Binv0 Inverse inner product results for all cells.
* @param[out] Binv Inverse inner product results incorporating
* effects of multiple fluid phases.
*/
void void
mim_ip_mobility_update(int nc, const int *pconn, const double *totmob, mim_ip_mobility_update(int nc, const int *pconn, const double *totmob,
const double *Binv0, double *Binv); const double *Binv0, double *Binv);
/* G <- \sum_i \rho_i f_i(s) * G_0 */
/**
* Incorporate effects of multiple fluid phases into existing, local,
* static mimetic discretisations of gravity pressure.
*
* Specifically, update the result of mim_ip_compute_gpress()
* according to the rule
* \f[
* \Tilde{G}_{\mathit{pconn}_c + i} = \omega_c\cdot
* G_{\mathit{pconn}_c + i}, \quad i=\mathit{pconn}_c, \dots,
* \mathit{pconn}_{c+1}-1, \quad c=0,\dots,\mathit{nc}-1
* \f]
* in which \f$\omega_c = (\sum_\alpha \lambda_{\alpha,c}
* \rho_\alpha)/\lambda_{T,c}\f$ and \f$\Tilde{G}\f$ denotes the result
* of function mim_ip_compute_gpress().
*
* @param[in] nc Number of cells.
* @param[in] pconn Start pointers of cell-to-face topology
* mapping.
* @param[in] omega Sum of phase densities weighted by
* fractional flow.
* @param[in] gpress0 Result of mim_ip_compute_gpress().
* @param[out] gpress Gravity pressure incorporating effects
* of multiple fluid phases.
*/
void void
mim_ip_density_update(int nc, const int *pconn, const double *omega, mim_ip_density_update(int nc, const int *pconn, const double *omega,
const double *gpress0, double *gpress); const double *gpress0, double *gpress);