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