Functions
mimetic.h File Reference

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Functions

void mim_ip_span_nullspace (int nf, int nconn, int d, double *C, double *A, 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)
 
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)
 
void mim_ip_compute_gpress (int nc, int d, const double *grav, const int *pconn, const int *conn, const double *fcentroid, const double *ccentroid, double *gpress)
 
void mim_ip_mobility_update (int nc, const int *pconn, const double *totmob, const double *Binv0, double *Binv)
 
void mim_ip_density_update (int nc, const int *pconn, const double *omega, const double *gpress0, double *gpress)
 

Detailed Description

Routines to assist mimetic discretisations of the flow equation.

Function Documentation

◆ mim_ip_compute_gpress()

void mim_ip_compute_gpress ( int  nc,
int  d,
const double *  grav,
const int *  pconn,
const int *  conn,
const double *  fcentroid,
const double *  ccentroid,
double *  gpress 
)

Compute local, static gravity pressure contributions to Darcy flow equation discretised using a mimetic finite-difference method.

The pressure contribution of local face $i$ in cell $c$ is

\[ \mathit{gpress}_{\mathit{pconn}_c + i} = \vec{g}\cdot (\Bar{x}_{\mathit{conn}_{\mathit{pconn}_c + i}} - \Bar{x}_c) \]

Parameters
[in]ncNumber of cells.
[in]dNumber of physcial dimensions.
[in]gravGravity vector. Array of size d.
[in]pconnStart pointers of cell-to-face topology mapping.
[in]connActual cell-to-face topology mapping.
[in]fcentroidFace centroids.
[in]ccentroidCell centroids.
[out]gpressGravity pressure result. Array of size at least pconn[nc].

◆ mim_ip_density_update()

void mim_ip_density_update ( int  nc,
const int *  pconn,
const double *  omega,
const double *  gpress0,
double *  gpress 
)

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

\[ \Tilde{G}_{\mathit{pconn}_c + i} = \omega_c\cdot G_{\mathit{pconn}_c + i}, \quad i=\mathit{pconn}_c, \dots, \mathit{pconn}_{c+1}-1, \quad c=0,\dots,\mathit{nc}-1 \]

in which $\omega_c = (\sum_\alpha \lambda_{\alpha,c} \rho_\alpha)/\lambda_{T,c}$ and $\Tilde{G}$ denotes the result of function mim_ip_compute_gpress().

Parameters
[in]ncNumber of cells.
[in]pconnStart pointers of cell-to-face topology mapping.
[in]omegaSum of phase densities weighted by fractional flow.
[in]gpress0Result of mim_ip_compute_gpress().
[out]gpressGravity pressure incorporating effects of multiple fluid phases.

◆ mim_ip_linpress_exact()

void mim_ip_linpress_exact ( int  nf,
int  nconn,
int  d,
double  vol,
double *  K,
double *  N,
double *  Binv,
double *  work,
int  lwork 
)

Form (inverse) mimetic inner product that reproduces linear pressure drops (constant velocity) on general polyhedral cells.

Specifically

\[ B^{-1} = \frac{1}{v} \big(NKN^\mathsf{T} + \frac{6t}{d}\,X\big) \]

in which $t = \operatorname{tr}(K)$ is the trace of $K$ and $X$ is the result of function mim_ip_span_nullspace().

Parameters
[in]nfNumber of faces connected to single grid cell.
[in]nconnTotal number of grid cell connections. Typically equal to nf.
[in]dNumber of physical dimensions. Assumed less than four.
[in]volCell volume.
[in]KPermeability. A $d\times d$ matrix in column major (Fortran) order.
[in]NNormal vectors. An $\mathit{nf}\times d$ matrix in column major (Fortran) order.
[in,out]BinvInverse inner product result. An $\mathit{nconn}\times\mathit{nconn}$ matrix in column major format. On input, the result of mim_ip_span_nullspace(). On output, the upper left $\mathit{nf}\times\mathit{nf}$ sub-matrix will be overwritten with $B^{-1}$.
[in,out]workScratch array of size at least nf * d.
[in]lworkActual size of scratch array.

◆ mim_ip_mobility_update()

void mim_ip_mobility_update ( int  nc,
const int *  pconn,
const double *  totmob,
const double *  Binv0,
double *  Binv 
)

Incorporate effects of multiple phases in mimetic discretisation of flow equations.

Specifically, update the (inverse) inner products $B^{-1}$ previously computed using function mim_ip_linpress_exact() according to the rule

\[ \Tilde{B}_c^{-1} = \frac{1}{\lambda_{T,c}} B_c^{-1}, \quad i=0,\dots,\mathit{nc}-1 \]

in which $B_c^{-1}$ denotes the result of mim_ip_linpress_exact() for cell $c$ and $\lambda_{T,c}$ denotes the total mobility of cell $c$.

Parameters
[in]ncNumber of cells.
[in]pconnStart pointers of cell-to-face topology mapping.
[in]totmobTotal mobility for all cells. Array of size nc.
[in]Binv0Inverse inner product results for all cells.
[out]BinvInverse inner product results incorporating effects of multiple fluid phases.

◆ mim_ip_simple()

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 
)

Convenience wrapper around the function pair mim_ip_span_nullspace() and mim_ip_linpress_exact().

Parameters
[in]nfNumber of faces connected to single grid cell.
[in]nconnTotal number of grid cell connections. Typically equal to nf.
[in]dNumber of physical dimensions. Assumed less than four.
[in]vCell volume.
[in]KPermeability. A $d\times d$ matrix in column major (Fortran) order.
[in,out]CCentroid vectors. Specifically, $c_{ij} = \Bar{x}_{ij} - \Bar{x}_{cj}$. Array of size $\mathit{nf}\times d$ in column major (Fortran) order. Contents destroyed on output.
[in]AInterface areas.
[in]NOutward normal vectors. An $\mathit{nf}\times d$ matrix in column major (Fortran) order.
[out]BinvInverse inner product result. An $\mathit{nconn}\times\mathit{nconn}$ matrix in column major format. On output, the upper left $\mathit{nf}\times\mathit{nf}$ sub-matrix will be overwritten with $B^{-1}$ defined by function mim_ip_linpress_exact().
[in,out]workScratch array of size at least nf * d.
[in]lworkActual size of scratch array.

◆ mim_ip_simple_all()

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 the mimetic inner products given a grid and cell-wise permeability tensors.

This function applies mim_ip_simple() to all specified cells.

Parameters
[in]ncellsNumber of cells.
[in]dNumber of physical dimensions.
[in]max_ncfMaximum number of connections (faces) of any individual cell.
[in]pconnStart pointers of cell-to-face topology mapping.
[in]connActual cell-to-face topology mapping.
[in]fneighbourFace-to-cell mapping.
[in]fcentroidFace centroids.
[in]fnormalFace normals.
[in]fareaFace areas.
[in]ccentroidCell centroids.
[in]cvolCell volumes.
[in]permCell permeability.
[out]BinvInverse inner product result. Must point to an array of size at least $\sum_c n_c^2$ when $n_c$ denotes the number of connections (faces) of cell $c$.

◆ mim_ip_span_nullspace()

void mim_ip_span_nullspace ( int  nf,
int  nconn,
int  d,
double *  C,
double *  A,
double *  X,
double *  work,
int  lwork 
)

Form linear operator to span the null space of the normal vectors of a grid cell.

Specifically,

\[ \begin{aligned} X &= \operatorname{diag}(A) (I - QQ^\mathsf{T}) \operatorname{diag}(A), \\ Q &= \operatorname{orth}(\operatorname{diag}(A) C) \end{aligned} \]

in which $\operatorname{orth}(M)$ denotes an orthonormal basis for the colum space (range) of the matrix $M$, represented as a matrix.

Parameters
[in]nfNumber of faces connected to single grid cell.
[in]nconnTotal number of grid cell connections. Typically equal to nf.
[in]dNumber of physical dimensions. Assumed less than four.
[in,out]CCentroid vectors. Specifically, $c_{ij} = \Bar{x}_{ij} - \Bar{x}_{cj}$. Array of size $\mathit{nf}\times d$ in column major (Fortran) order. Contents destroyed on output.
[in]AInterface areas.
[out]XNull space linear operator. Array of size $\mathit{nconn}\times\mathit{nconn}$ in column major (Fortran) order. On output, the upper left $\mathit{nf}\times\mathit{nf}$ sub-matrix contains the required null space linear operator.
[out]workScratch array of size at least nconn.
[in]lworkActual size of scratch array.