inline double UpscalerBase<Traits>::computeDelta(const int flow_dir) const
{
double side1_pos = 0.0;
double side2_pos = 0.0;
double side1_area = 0.0;
double side2_area = 0.0;
for (CellIter c = ginterf_.cellbegin(); c != ginterf_.cellend(); ++c) {
for (FaceIter f = c->facebegin(); f != c->faceend(); ++f) {
if (f->boundary()) {
int canon_bid = bcond_.getCanonicalBoundaryId(f->boundaryId());
if ((canon_bid - 1)/2 == flow_dir) {
double area = f->area();
double pos_comp = f->centroid()[flow_dir];
if (canon_bid - 1 == 2*flow_dir) {
side1_pos += area*pos_comp;
side1_area += area;
} else {
side2_pos += area*pos_comp;
side2_area += area;
}
}
}
}
}
// delta is the average length.
return side2_pos/side2_area - side1_pos/side1_area;
}
void getInverseMatrix(const CellIter& c,
FullMatrix<Scalar,SP,FortranOrdering>& Binv) const
{
// Binv = (N*lambda*K*N' + t*diag(A)*(I - Q*Q')*diag(A))/vol
// ^ ^^^^^^^^^^^^^^^^^^^^^^^^^^
// precomputed: n_ precomputed: second_term_
// t = 6/dim * trace(lambda*K)
int ci = c->index();
int nf = Binv.numRows();
ImmutableFortranMatrix n(nf, dim, &n_[ci][0]);
ImmutableFortranMatrix t2(nf, nf, &second_term_[ci][0]);
Binv = t2;
ImmutableFortranMatrix lambdaK(dim, dim, lambdaK_.data());
SharedFortranMatrix T2(nf, dim, &t2_[0]);
// T2 <- N*lambda*K
matMulAdd_NN(Scalar(1.0), n, lambdaK, Scalar(0.0), T2);
// Binv <- (T2*N' + t*Binv) / vol(c)
// == (N*lambda*K*N' + t*(diag(A) * (I - Q*Q') * diag(A))) / vol(c)
//
// where t = 6/d * TRACE(lambda*K) (== 2*TRACE(lambda*K) for 3D).
//
Scalar t = Scalar(6.0) * trace(lambdaK) / dim;
matMulAdd_NT(Scalar(1.0) / c->volume(), T2, n,
t / c->volume(), Binv );
}
double UpscalerBase<Traits>::computeAverageVelocity(const FlowSol& flow_solution,
const int flow_dir,
const int pdrop_dir) const
{
double side1_flux = 0.0;
double side2_flux = 0.0;
double side1_area = 0.0;
double side2_area = 0.0;
int num_faces = 0;
int num_bdyfaces = 0;
int num_side1 = 0;
int num_side2 = 0;
for (CellIter c = ginterf_.cellbegin(); c != ginterf_.cellend(); ++c) {
for (FaceIter f = c->facebegin(); f != c->faceend(); ++f) {
++num_faces;
if (f->boundary()) {
++num_bdyfaces;
int canon_bid = bcond_.getCanonicalBoundaryId(f->boundaryId());
if ((canon_bid - 1)/2 == flow_dir) {
double flux = flow_solution.outflux(f);
double area = f->area();
double norm_comp = f->normal()[flow_dir];
// std::cout << "bid " << f->boundaryId() << " area " << area << " n " << norm_comp << std::endl;
if (canon_bid - 1 == 2*flow_dir) {
++num_side1;
if (flow_dir == pdrop_dir && flux > 0.0) {
#ifdef VERBOSE
std::cerr << "Flow may be in wrong direction at bid: " << f->boundaryId()<<" (canonical: "<<canon_bid
<< ") Magnitude: " << std::fabs(flux) << std::endl;
#endif
// OPM_THROW(std::runtime_error, "Detected outflow at entry face: " << face);
}
side1_flux += flux*norm_comp;
side1_area += area;
} else {
assert(canon_bid - 1 == 2*flow_dir + 1);
++num_side2;
if (flow_dir == pdrop_dir && flux < 0.0) {
#ifdef VERBOSE
std::cerr << "Flow may be in wrong direction at bid: " << f->boundaryId()
<< " Magnitude: " << std::fabs(flux) << std::endl;
#endif
// OPM_THROW(std::runtime_error, "Detected inflow at exit face: " << face);
}
side2_flux += flux*norm_comp;
side2_area += area;
}
}
}
}
}
// std::cout << "Faces: " << num_faces << " Boundary faces: " << num_bdyfaces
// << " Side 1 faces: " << num_side1 << " Side 2 faces: " << num_side2 << std::endl;
// q is the average velocity.
return 0.5*(side1_flux/side1_area + side2_flux/side2_area);
}
double UpscalerBase<Traits>::upscaleNTG() const
{
double total_vol = 0.0;
double total_net_vol = 0.0;
for (CellIter c = ginterf_.cellbegin(); c != ginterf_.cellend(); ++c) {
total_vol += c->volume();
total_net_vol += c->volume()*res_prop_.ntg(c->index());
}
return total_net_vol/total_vol;
}
double UpscalerBase<Traits>::upscaleNetPorosity() const
{
double total_net_vol = 0.0;
double total_pore_vol = 0.0;
for (CellIter c = ginterf_.cellbegin(); c != ginterf_.cellend(); ++c) {
total_net_vol += c->volume()*res_prop_.ntg(c->index());
total_pore_vol += c->volume()*res_prop_.porosity(c->index())*res_prop_.ntg(c->index());
}
if (total_net_vol>0.0) return total_pore_vol/total_net_vol;
else return 0.0;
}
double SteadyStateUpscaler<Traits>::lastSaturationUpscaled() const
{
typedef typename GridInterface::CellIterator CellIter;
double pore_vol = 0.0;
double sat_vol = 0.0;
for (CellIter c = this->ginterf_.cellbegin(); c != this->ginterf_.cellend(); ++c) {
double cell_pore_vol = c->volume()*this->res_prop_.porosity(c->index());
pore_vol += cell_pore_vol;
sat_vol += cell_pore_vol*last_saturation_state_[c->index()];
}
// Dividing by pore volume gives average saturations.
return sat_vol/pore_vol;
}
std::pair<double, double> poreSatVolumes(const GridInterface& grid,
const ReservoirProperties& rp,
const std::vector<double>& sat)
{
typedef typename GridInterface::CellIterator CellIter;
double pore_vol = 0.0;
double sat_vol = 0.0;
for (CellIter c = grid.cellbegin(); c != grid.cellend(); ++c) {
double cell_pore_vol = c->volume()*rp.porosity(c->index());
pore_vol += cell_pore_vol;
sat_vol += cell_pore_vol*sat[c->index()];
}
// Dividing by pore volume gives average saturations.
return std::make_pair(pore_vol, sat_vol);
}
void computeDynamicParams(const CellIter& c,
const FluidInterface& fl,
const std::vector<Sat>& s)
{
const int ci = c->index();
std::array<Scalar, dim * dim> lambda_t;
std::array<Scalar, dim * dim> pmob_data;
SharedFortranMatrix pmob(dim, dim, &pmob_data[0]);
SharedFortranMatrix Kg (dim, 1 , &Kg_[ci][0]);
std::array<Scalar, FluidInterface::NumberOfPhases> rho;
fl.phaseDensities(ci, rho);
std::fill(dyn_Kg_.begin(), dyn_Kg_.end(), Scalar(0.0));
std::fill(lambda_t.begin(), lambda_t.end(), 0.0);
for (int phase = 0; phase < FluidInterface::NumberOfPhases; ++phase) {
fl.phaseMobility(phase, ci, s[ci], pmob);
// dyn_Kg_ += (\rho_phase \lambda_phase) Kg
vecMulAdd_N(rho[phase], pmob, Kg.data(), Scalar(1.0), dyn_Kg_.data());
// \lambda_t += \lambda_phase
std::transform(lambda_t.begin(), lambda_t.end(), pmob_data.begin(),
lambda_t.begin(),
std::plus<Scalar>());
}
// lambdaK_ = (\sum_i \lambda_i) K
SharedFortranMatrix lambdaT(dim, dim, lambda_t.data());
SharedFortranMatrix lambdaK(dim, dim, lambdaK_.data());
prod(lambdaT, prock_->permeability(ci), lambdaK);
}
double UpscalerBase<Traits>::upscaleSOWCR(const bool NTG) const
{
double total_sowcr = 0.0;
double total_pore_vol = 0.0;
if (NTG) {
for (CellIter c = ginterf_.cellbegin(); c != ginterf_.cellend(); ++c) {
total_sowcr += c->volume()*res_prop_.porosity(c->index())*res_prop_.ntg(c->index())*res_prop_.sowcr(c->index());
total_pore_vol += c->volume()*res_prop_.porosity(c->index())*res_prop_.ntg(c->index());
}
}
else {
for (CellIter c = ginterf_.cellbegin(); c != ginterf_.cellend(); ++c) {
total_sowcr += c->volume()*res_prop_.porosity(c->index())*res_prop_.sowcr(c->index());
total_pore_vol += c->volume()*res_prop_.porosity(c->index());
}
}
return total_sowcr/total_pore_vol;
}
void gravityFlux(const CellIter& c,
Vector& gflux) const
{
const int ci = c->index();
const int nf = n_.rowSize(ci) / dim;
ImmutableFortranMatrix N(nf, dim, &n_[ci][0]);
// gflux = N (\sum_i \rho_i \lambda_i) Kg
vecMulAdd_N(Scalar(1.0), N, &dyn_Kg_[0],
Scalar(0.0), &gflux[0]);
}
/// @brief
/// Main evaluation routine. Computes the inverse of the
/// matrix representation of the mimetic inner product in a
/// single cell with kown permeability @f$K@f$. Adds a
/// regularization term in order to guarantee a positive
/// definite matrix.
///
/// @tparam RockInterface
/// Type representing rock properties. Assumed to
/// expose a method @code permeability(i) @endcode which
/// retrieves the static permeability tensor of cell @code
/// i @endcode. The permeability tensor, @$K@$, is in
/// turn, assumed to expose a method @code operator()(int
/// i, int j) @endcode such that the call @code K(i,j)
/// @endcode retrieves the @f$ij@f$'th component of the
/// cell permeability @f$K@f$.
///
/// @param [in] c
/// Cell for which to evaluate the inverse of the mimetic
/// inner product.
///
/// @param [in] r
/// Specific reservoir properties. Only the permeability
/// is used in method @code buildMatrix() @endcode.
///
/// @param [in] nf
/// Number of faces (i.e., number of neighbours) of cell
/// @code *c @endcode.
void buildStaticContrib(const CellIter& c,
const RockInterface& r,
const typename CellIter::Vector& grav,
const int nf)
{
// Binv = (N*lambda*K*N' + t*diag(A)*(I - Q*Q')*diag(A))/vol
// ^ ^^^^^^^^^^^^^^^^^^^^^^^^^^
// precompute: n_ precompute: second_term_
// t = 6/dim * trace(lambda*K)
typedef typename CellIter::FaceIterator FI;
typedef typename CellIter::Vector CV;
typedef typename FI ::Vector FV;
// Now we need to remember the rocks, since we will need
// the permeability for dynamic assembly.
prock_ = &r;
const int ci = c->index();
static_assert (FV::dimension == int(dim), "");
assert (int(t1_.size()) >= nf * dim);
assert (int(t2_.size()) >= nf * dim);
assert (int(fa_.size()) >= nf * nf);
SharedFortranMatrix T2 (nf, dim, &t2_ [0]);
SharedFortranMatrix fa (nf, nf , &fa_ [0]);
SharedFortranMatrix second_term(nf, nf, &second_term_[ci][0]);
SharedFortranMatrix n(nf, dim, &n_[ci][0]);
// Clear matrices of any residual data.
zero(second_term); zero(n); zero(T2); zero(fa);
// Setup: second_term <- I, n <- N, T2 <- C
const CV cc = c->centroid();
int i = 0;
for (FI f = c->facebegin(); f != c->faceend(); ++f, ++i) {
second_term(i,i) = Scalar(1.0);
fa(i,i) = f->area();
FV fc = f->centroid(); fc -= cc; fc *= fa(i,i);
FV fn = f->normal (); fn *= fa(i,i);
for (int j = 0; j < dim; ++j) {
n (i,j) = fn[j];
T2(i,j) = fc[j];
}
}
assert (i == nf);
// T2 <- orth(T2)
if (orthogonalizeColumns(T2) != 0) {
assert (false);
}
// second_term <- second_term - T2*T2' == I - Q*Q'
symmetricUpdate(Scalar(-1.0), T2, Scalar(1.0), second_term);
// second_term <- diag(A) * second_term * diag(A)
symmetricUpdate(fa, second_term);
// Gravity term: Kg_ = K * grav
vecMulAdd_N(Scalar(1.0), r.permeability(ci), &grav[0],
Scalar(0.0), &Kg_[ci][0]);
}
void SteadyStateUpscaler<Traits>::computeInOutFlows(std::pair<double, double>& water_inout,
std::pair<double, double>& oil_inout,
const FlowSol& flow_solution,
const std::vector<double>& saturations) const
{
typedef typename GridInterface::CellIterator CellIter;
typedef typename CellIter::FaceIterator FaceIter;
double side1_flux = 0.0;
double side2_flux = 0.0;
double side1_flux_oil = 0.0;
double side2_flux_oil = 0.0;
std::map<int, double> frac_flow_by_bid;
int num_cells = this->ginterf_.numberOfCells();
std::vector<double> cell_inflows_w(num_cells, 0.0);
std::vector<double> cell_outflows_w(num_cells, 0.0);
// Two passes: First pass, deal with outflow, second pass, deal with inflow.
// This is for the periodic case, so that we are sure all fractional flows have
// been set in frac_flow_by_bid.
for (int pass = 0; pass < 2; ++pass) {
for (CellIter c = this->ginterf_.cellbegin(); c != this->ginterf_.cellend(); ++c) {
for (FaceIter f = c->facebegin(); f != c->faceend(); ++f) {
if (f->boundary()) {
double flux = flow_solution.outflux(f);
const SatBC& sc = this->bcond_.satCond(f);
if (flux < 0.0 && pass == 1) {
// This is an inflow face.
double frac_flow = 0.0;
if (sc.isPeriodic()) {
assert(sc.saturationDifference() == 0.0);
int partner_bid = this->bcond_.getPeriodicPartner(f->boundaryId());
std::map<int, double>::const_iterator it = frac_flow_by_bid.find(partner_bid);
if (it == frac_flow_by_bid.end()) {
OPM_THROW(std::runtime_error, "Could not find periodic partner fractional flow. Face bid = " << f->boundaryId()
<< " and partner bid = " << partner_bid);
}
frac_flow = it->second;
} else {
assert(sc.isDirichlet());
frac_flow = this->res_prop_.fractionalFlow(c->index(), sc.saturation());
}
cell_inflows_w[c->index()] += flux*frac_flow;
side1_flux += flux*frac_flow;
side1_flux_oil += flux*(1.0 - frac_flow);
} else if (flux >= 0.0 && pass == 0) {
// This is an outflow face.
double frac_flow = this->res_prop_.fractionalFlow(c->index(), saturations[c->index()]);
if (sc.isPeriodic()) {
frac_flow_by_bid[f->boundaryId()] = frac_flow;
// std::cout << "Inserted bid " << f->boundaryId() << std::endl;
}
cell_outflows_w[c->index()] += flux*frac_flow;
side2_flux += flux*frac_flow;
side2_flux_oil += flux*(1.0 - frac_flow);
}
}
}
}
}
water_inout = std::make_pair(side1_flux, side2_flux);
oil_inout = std::make_pair(side1_flux_oil, side2_flux_oil);
}