/// Solve the linear system Ax = b, with A being the
/// combined derivative matrix of the residual and b
/// being the residual itself.
/// \param[in] residual residual object containing A and b.
/// \return the solution x
NewtonIterationBlackoilSimple::SolutionVector
NewtonIterationBlackoilSimple::computeNewtonIncrement(const LinearisedBlackoilResidual& residual) const
{
typedef LinearisedBlackoilResidual::ADB ADB;
const int np = residual.material_balance_eq.size();
ADB mass_res = residual.material_balance_eq[0];
for (int phase = 1; phase < np; ++phase) {
mass_res = vertcat(mass_res, residual.material_balance_eq[phase]);
}
const ADB well_res = vertcat(residual.well_flux_eq, residual.well_eq);
const ADB total_residual = collapseJacs(vertcat(mass_res, well_res));
Eigen::SparseMatrix<double, Eigen::RowMajor> matr;
total_residual.derivative()[0].toSparse(matr);
SolutionVector dx(SolutionVector::Zero(total_residual.size()));
Opm::LinearSolverInterface::LinearSolverReport rep
= linsolver_->solve(matr.rows(), matr.nonZeros(),
matr.outerIndexPtr(), matr.innerIndexPtr(), matr.valuePtr(),
total_residual.value().data(), dx.data(), parallelInformation_);
// store iterations
iterations_ = rep.iterations;
if (!rep.converged) {
OPM_THROW(LinearSolverProblem,
"FullyImplicitBlackoilSolver::solveJacobianSystem(): "
"Linear solver convergence failure.");
}
return dx;
}
ADB SolventPropsAdFromDeck::muSolvent(const ADB& pg,
const Cells& cells) const
{
const int n = cells.size();
assert(pg.value().size() == n);
V mu(n);
V dmudp(n);
for (int i = 0; i < n; ++i) {
const double& pg_i = pg.value()[i];
int regionIdx = cellPvtRegionIdx_[cells[i]];
double tempInvB = b_[regionIdx](pg_i);
double tempInvBmu = inverseBmu_[regionIdx](pg_i);
mu[i] = tempInvB / tempInvBmu;
dmudp[i] = (tempInvBmu * b_[regionIdx].derivative(pg_i)
- tempInvB * inverseBmu_[regionIdx].derivative(pg_i)) / (tempInvBmu * tempInvBmu);
}
ADB::M dmudp_diag(dmudp.matrix().asDiagonal());
const int num_blocks = pg.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = dmudp_diag * pg.derivative()[block];
}
return ADB::function(std::move(mu), std::move(jacs));
}
/// Water viscosity.
/// \param[in] pw Array of n water pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n viscosity values.
ADB BlackoilPropsAd::muWat(const ADB& pw,
const Cells& cells) const
{
#if 1
return ADB::constant(muWat(pw.value(), cells), pw.blockPattern());
#else
if (!pu_.phase_used[Water]) {
OPM_THROW(std::runtime_error, "Cannot call muWat(): water phase not present.");
}
const int n = cells.size();
assert(pw.value().size() == n);
const int np = props_.numPhases();
Block z = Block::Zero(n, np);
Block mu(n, np);
Block dmu(n, np);
props_.viscosity(n, pw.value().data(), z.data(), cells.data(), mu.data(), dmu.data());
ADB::M dmu_diag = spdiag(dmu.col(pu_.phase_pos[Water]));
const int num_blocks = pw.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = dmu_diag * pw.derivative()[block];
}
return ADB::function(mu.col(pu_.phase_pos[Water]), jacs);
#endif
}
/// Gas viscosity.
/// \param[in] pg Array of n gas pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n viscosity values.
ADB BlackoilPropsAd::muGas(const ADB& pg,
const Cells& cells) const
{
#if 1
return ADB::constant(muGas(pg.value(), cells), pg.blockPattern());
#else
if (!pu_.phase_used[Gas]) {
THROW("Cannot call muGas(): gas phase not present.");
}
const int n = cells.size();
ASSERT(pg.value().size() == n);
const int np = props_.numPhases();
Block z = Block::Zero(n, np);
Block mu(n, np);
Block dmu(n, np);
props_.viscosity(n, pg.value().data(), z.data(), cells.data(), mu.data(), dmu.data());
ADB::M dmu_diag = spdiag(dmu.col(pu_.phase_pos[Gas]));
const int num_blocks = pg.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = dmu_diag * pg.derivative()[block];
}
return ADB::function(mu.col(pu_.phase_pos[Gas]), jacs);
#endif
}
/// Oil viscosity.
/// \param[in] po Array of n oil pressure values.
/// \param[in] rs Array of n gas solution factor values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n viscosity values.
ADB BlackoilPropsAd::muOil(const ADB& po,
const ADB& rs,
const Cells& cells) const
{
#if 1
return ADB::constant(muOil(po.value(), rs.value(), cells), po.blockPattern());
#else
if (!pu_.phase_used[Oil]) {
THROW("Cannot call muOil(): oil phase not present.");
}
const int n = cells.size();
ASSERT(po.value().size() == n);
const int np = props_.numPhases();
Block z = Block::Zero(n, np);
if (pu_.phase_used[Gas]) {
// Faking a z with the right ratio:
// rs = zg/zo
z.col(pu_.phase_pos[Oil]) = V::Ones(n, 1);
z.col(pu_.phase_pos[Gas]) = rs.value();
}
Block mu(n, np);
Block dmu(n, np);
props_.viscosity(n, po.value().data(), z.data(), cells.data(), mu.data(), dmu.data());
ADB::M dmu_diag = spdiag(dmu.col(pu_.phase_pos[Oil]));
const int num_blocks = po.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
// For now, we deliberately ignore the derivative with respect to rs,
// since the BlackoilPropertiesInterface class does not evaluate it.
// We would add to the next line: + dmu_drs_diag * rs.derivative()[block]
jacs[block] = dmu_diag * po.derivative()[block];
}
return ADB::function(mu.col(pu_.phase_pos[Oil]), jacs);
#endif
}
/// Gas viscosity.
/// \param[in] pg Array of n gas pressure values.
/// \param[in] rv Array of n vapor oil/gas ratio
/// \param[in] cond Array of n objects, each specifying which phases are present with non-zero saturation in a cell.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n viscosity values.
ADB BlackoilPropsAd::muGas(const ADB& pg,
const ADB& rv,
const std::vector<PhasePresence>& cond,
const Cells& cells) const
{
#if 1
return ADB::constant(muGas(pg.value(), rv.value(),cond,cells), pg.blockPattern());
#else
if (!pu_.phase_used[Gas]) {
OPM_THROW(std::runtime_error, "Cannot call muGas(): gas phase not present.");
}
const int n = cells.size();
assert(pg.value().size() == n);
const int np = props_.numPhases();
Block z = Block::Zero(n, np);
if (pu_.phase_used[Oil]) {
// Faking a z with the right ratio:
// rv = zo/zg
z.col(pu_.phase_pos[Oil]) = rv;
z.col(pu_.phase_pos[Gas]) = V::Ones(n, 1);
}
Block mu(n, np);
Block dmu(n, np);
props_.viscosity(n, pg.value().data(), z.data(), cells.data(), mu.data(), dmu.data());
ADB::M dmu_diag = spdiag(dmu.col(pu_.phase_pos[Gas]));
const int num_blocks = pg.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = dmu_diag * pg.derivative()[block];
}
return ADB::function(mu.col(pu_.phase_pos[Gas]), jacs);
#endif
}
/// Oil formation volume factor.
/// \param[in] po Array of n oil pressure values.
/// \param[in] rs Array of n gas solution factor values.
/// \param[in] cond Array of n taxonomies classifying fluid condition.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n formation volume factor values.
ADB BlackoilPropsAd::bOil(const ADB& po,
const ADB& rs,
const std::vector<PhasePresence>& /*cond*/,
const Cells& cells) const
{
if (!pu_.phase_used[Oil]) {
OPM_THROW(std::runtime_error, "Cannot call muOil(): oil phase not present.");
}
const int n = cells.size();
assert(po.value().size() == n);
const int np = props_.numPhases();
Block z = Block::Zero(n, np);
if (pu_.phase_used[Gas]) {
// Faking a z with the right ratio:
// rs = zg/zo
z.col(pu_.phase_pos[Oil]) = V::Ones(n, 1);
z.col(pu_.phase_pos[Gas]) = rs.value();
}
Block matrix(n, np*np);
Block dmatrix(n, np*np);
props_.matrix(n, po.value().data(), z.data(), cells.data(), matrix.data(), dmatrix.data());
const int phase_ind = pu_.phase_pos[Oil];
const int column = phase_ind*np + phase_ind; // Index of our sought diagonal column.
ADB::M db_diag = spdiag(dmatrix.col(column));
const int num_blocks = po.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
// For now, we deliberately ignore the derivative with respect to rs,
// since the BlackoilPropertiesInterface class does not evaluate it.
// We would add to the next line: + db_drs_diag * rs.derivative()[block]
jacs[block] = db_diag * po.derivative()[block];
}
return ADB::function(matrix.col(column), jacs);
}
/// Oil formation volume factor.
/// \param[in] po Array of n oil pressure values.
/// \param[in] rs Array of n gas solution factor values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n formation volume factor values.
ADB BlackoilPropsAdFromDeck::bOil(const ADB& po,
const ADB& rs,
const Cells& cells) const
{
if (!phase_usage_.phase_used[Oil]) {
OPM_THROW(std::runtime_error, "Cannot call muOil(): oil phase not present.");
}
const int n = cells.size();
assert(po.size() == n);
V b(n);
V dbdp(n);
V dbdr(n);
props_[phase_usage_.phase_pos[Oil]]->b(n, po.value().data(), rs.value().data(),
b.data(), dbdp.data(), dbdr.data());
ADB::M dbdp_diag = spdiag(dbdp);
ADB::M dbdr_diag = spdiag(dbdr);
const int num_blocks = po.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = dbdp_diag * po.derivative()[block] + dbdr_diag * rs.derivative()[block];
}
return ADB::function(b, jacs);
}
/// Gas formation volume factor.
/// \param[in] pg Array of n gas pressure values.
/// \param[in] rv Array of n vapor oil/gas ratio
/// \param[in] cond Array of n objects, each specifying which phases are present with non-zero saturation in a cell.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n formation volume factor values.
ADB BlackoilPropsAd::bGas(const ADB& pg,
const ADB& rv,
const std::vector<PhasePresence>& /*cond*/,
const Cells& cells) const
{
if (!pu_.phase_used[Gas]) {
OPM_THROW(std::runtime_error, "Cannot call muGas(): gas phase not present.");
}
const int n = cells.size();
assert(pg.value().size() == n);
const int np = props_.numPhases();
Block z = Block::Zero(n, np);
if (pu_.phase_used[Oil]) {
// Faking a z with the right ratio:
// rv = zo/zg
z.col(pu_.phase_pos[Oil]) = rv.value();
z.col(pu_.phase_pos[Gas]) = V::Ones(n, 1);
}
Block matrix(n, np*np);
Block dmatrix(n, np*np);
props_.matrix(n, pg.value().data(), z.data(), cells.data(), matrix.data(), dmatrix.data());
const int phase_ind = pu_.phase_pos[Gas];
const int column = phase_ind*np + phase_ind; // Index of our sought diagonal column.
ADB::M db_diag = spdiag(dmatrix.col(column));
const int num_blocks = pg.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = db_diag * pg.derivative()[block];
}
return ADB::function(matrix.col(column), jacs);
}
ADB PolymerPropsAd::polymerWaterVelocityRatio(const ADB& c) const
{
const int nc = c.size();
V mc(nc);
V dmc(nc);
for (int i = 0; i < nc; ++i) {
double m = 0;
double dm = 0;
polymer_props_.computeMcWithDer(c.value()(i), m, dm);
mc(i) = m;
dmc(i) = dm;
}
ADB::M dmc_diag(dmc.matrix().asDiagonal());
const int num_blocks = c.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = dmc_diag * c.derivative()[block];
}
return ADB::function(std::move(mc), std::move(jacs));
}
/// Gas formation volume factor.
/// \param[in] pg Array of n gas pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n formation volume factor values.
ADB BlackoilPropsAdFromDeck::bGas(const ADB& pg,
const Cells& cells) const
{
if (!phase_usage_.phase_used[Gas]) {
OPM_THROW(std::runtime_error, "Cannot call muGas(): gas phase not present.");
}
const int n = cells.size();
assert(pg.size() == n);
V b(n);
V dbdp(n);
V dbdr(n);
const double* rs = 0;
props_[phase_usage_.phase_pos[Gas]]->b(n, pg.value().data(), rs,
b.data(), dbdp.data(), dbdr.data());
ADB::M dbdp_diag = spdiag(dbdp);
const int num_blocks = pg.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = dbdp_diag * pg.derivative()[block];
}
return ADB::function(b, jacs);
}
BOOST_FIXTURE_TEST_CASE(ViscosityAD, TestFixture<SetupSimple>)
{
const Opm::BlackoilPropsAdFromDeck::Cells cells(5, 0);
typedef Opm::BlackoilPropsAdFromDeck::V V;
typedef Opm::BlackoilPropsAdFromDeck::ADB ADB;
V Vpw;
Vpw.resize(cells.size());
Vpw[0] = 1*Opm::unit::barsa;
Vpw[1] = 2*Opm::unit::barsa;
Vpw[2] = 4*Opm::unit::barsa;
Vpw[3] = 8*Opm::unit::barsa;
Vpw[4] = 16*Opm::unit::barsa;
// standard temperature
V T = V::Constant(cells.size(), 273.15+20);
typedef Opm::BlackoilPropsAdFromDeck::ADB ADB;
const V VmuWat = boprops_ad.muWat(ADB::constant(Vpw), ADB::constant(T), cells).value();
for (V::Index i = 0, n = Vpw.size(); i < n; ++i) {
const std::vector<int> bp(1, grid.c_grid()->number_of_cells);
const Opm::BlackoilPropsAdFromDeck::Cells c(1, 0);
const V pw = V(1, 1) * Vpw[i];
const ADB Apw = ADB::variable(0, pw, bp);
const ADB AT = ADB::constant(T);
const ADB AmuWat = boprops_ad.muWat(Apw, AT, c);
BOOST_CHECK_EQUAL(AmuWat.value()[0], VmuWat[i]);
}
}
ADB
PolymerPropsAd::effectiveRelPerm(const ADB& c,
const ADB& cmax_cells,
const ADB& krw) const
{
const int nc = c.value().size();
V one = V::Ones(nc);
ADB ads = adsorption(c, cmax_cells);
V krw_eff = effectiveRelPerm(c.value(), cmax_cells.value(), krw.value());
double max_ads = polymer_props_.cMaxAds();
double res_factor = polymer_props_.resFactor();
double factor = (res_factor - 1.) / max_ads;
ADB rk = one + ads * factor;
return krw / rk;
}
inline
double infinityNormWell( const ADB& a, const boost::any& pinfo )
{
static_cast<void>(pinfo); // Suppress warning in non-MPI case.
double result=0;
if( a.value().size() > 0 ) {
result = a.value().matrix().template lpNorm<Eigen::Infinity> ();
}
#if HAVE_MPI
if ( pinfo.type() == typeid(ParallelISTLInformation) )
{
const ParallelISTLInformation& real_info =
boost::any_cast<const ParallelISTLInformation&>(pinfo);
result = real_info.communicator().max(result);
}
#endif
return result;
}
ADB SolventPropsAdFromDeck::makeADBfromTables(const ADB& X_AD,
const Cells& cells,
const std::vector<int>& regionIdx,
const std::vector<NonuniformTableLinear<double>>& tables) const {
const int n = cells.size();
assert(X_AD.value().size() == n);
V x(n);
V dx(n);
for (int i = 0; i < n; ++i) {
const double& X_i = X_AD.value()[i];
x[i] = tables[regionIdx[cells[i]]](X_i);
dx[i] = tables[regionIdx[cells[i]]].derivative(X_i);
}
ADB::M dx_diag(dx.matrix().asDiagonal());
const int num_blocks = X_AD.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
fastSparseProduct(dx_diag, X_AD.derivative()[block], jacs[block]);
}
return ADB::function(std::move(x), std::move(jacs));
}
std::vector<ADB> BlackoilPropsAd::capPress(const ADB& sw,
const ADB& so,
const ADB& sg,
const Cells& cells) const
{
const int numCells = cells.size();
const int numActivePhases = numPhases();
const int numBlocks = so.numBlocks();
Block activeSat(numCells, numActivePhases);
if (pu_.phase_used[Water]) {
assert(sw.value().size() == numCells);
activeSat.col(pu_.phase_pos[Water]) = sw.value();
}
if (pu_.phase_used[Oil]) {
assert(so.value().size() == numCells);
activeSat.col(pu_.phase_pos[Oil]) = so.value();
} else {
OPM_THROW(std::runtime_error, "BlackoilPropsAdFromDeck::relperm() assumes oil phase is active.");
}
if (pu_.phase_used[Gas]) {
assert(sg.value().size() == numCells);
activeSat.col(pu_.phase_pos[Gas]) = sg.value();
}
Block pc(numCells, numActivePhases);
Block dpc(numCells, numActivePhases*numActivePhases);
props_.capPress(numCells, activeSat.data(), cells.data(), pc.data(), dpc.data());
std::vector<ADB> adbCapPressures;
adbCapPressures.reserve(3);
const ADB* s[3] = { &sw, &so, &sg };
for (int phase1 = 0; phase1 < 3; ++phase1) {
if (pu_.phase_used[phase1]) {
const int phase1_pos = pu_.phase_pos[phase1];
std::vector<ADB::M> jacs(numBlocks);
for (int block = 0; block < numBlocks; ++block) {
jacs[block] = ADB::M(numCells, s[phase1]->derivative()[block].cols());
}
for (int phase2 = 0; phase2 < 3; ++phase2) {
if (!pu_.phase_used[phase2])
continue;
const int phase2_pos = pu_.phase_pos[phase2];
// Assemble dpc1/ds2.
const int column = phase1_pos + numActivePhases*phase2_pos; // Recall: Fortran ordering from props_.relperm()
ADB::M dpc1_ds2_diag = spdiag(dpc.col(column));
for (int block = 0; block < numBlocks; ++block) {
jacs[block] += dpc1_ds2_diag * s[phase2]->derivative()[block];
}
}
adbCapPressures.emplace_back(ADB::function(pc.col(phase1_pos), jacs));
} else {
adbCapPressures.emplace_back(ADB::null());
}
}
return adbCapPressures;
}
/// Water formation volume factor.
/// \param[in] pw Array of n water pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n formation volume factor values.
ADB BlackoilPropsAd::bWat(const ADB& pw,
const Cells& cells) const
{
if (!pu_.phase_used[Water]) {
OPM_THROW(std::runtime_error, "Cannot call muWat(): water phase not present.");
}
const int n = cells.size();
assert(pw.value().size() == n);
const int np = props_.numPhases();
Block z = Block::Zero(n, np);
Block matrix(n, np*np);
Block dmatrix(n, np*np);
props_.matrix(n, pw.value().data(), z.data(), cells.data(), matrix.data(), dmatrix.data());
const int phase_ind = pu_.phase_pos[Water];
const int column = phase_ind*np + phase_ind; // Index of our sought diagonal column.
ADB::M db_diag = spdiag(dmatrix.col(column));
const int num_blocks = pw.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = db_diag * pw.derivative()[block];
}
return ADB::function(matrix.col(column), jacs);
}
/// Gas formation volume factor.
/// \param[in] pg Array of n gas pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n formation volume factor values.
ADB BlackoilPropsAd::bGas(const ADB& pg,
const Cells& cells) const
{
if (!pu_.phase_used[Gas]) {
THROW("Cannot call muGas(): gas phase not present.");
}
const int n = cells.size();
ASSERT(pg.value().size() == n);
const int np = props_.numPhases();
Block z = Block::Zero(n, np);
Block matrix(n, np*np);
Block dmatrix(n, np*np);
props_.matrix(n, pg.value().data(), z.data(), cells.data(), matrix.data(), dmatrix.data());
const int phase_ind = pu_.phase_pos[Gas];
const int column = phase_ind*np + phase_ind; // Index of our sought diagonal column.
ADB::M db_diag = spdiag(dmatrix.col(column));
const int num_blocks = pg.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = db_diag * pg.derivative()[block];
}
return ADB::function(matrix.col(column), jacs);
}
/// Relative permeabilities for all phases.
/// \param[in] sw Array of n water saturation values.
/// \param[in] so Array of n oil saturation values.
/// \param[in] sg Array of n gas saturation values.
/// \param[in] cells Array of n cell indices to be associated with the saturation values.
/// \return An std::vector with 3 elements, each an array of n relperm values,
/// containing krw, kro, krg. Use PhaseIndex for indexing into the result.
std::vector<ADB> BlackoilPropsAd::relperm(const ADB& sw,
const ADB& so,
const ADB& sg,
const Cells& cells) const
{
const int n = cells.size();
const int np = props_.numPhases();
Block s_all(n, np);
if (pu_.phase_used[Water]) {
assert(sw.value().size() == n);
s_all.col(pu_.phase_pos[Water]) = sw.value();
}
if (pu_.phase_used[Oil]) {
assert(so.value().size() == n);
s_all.col(pu_.phase_pos[Oil]) = so.value();
} else {
OPM_THROW(std::runtime_error, "BlackoilPropsAd::relperm() assumes oil phase is active.");
}
if (pu_.phase_used[Gas]) {
assert(sg.value().size() == n);
s_all.col(pu_.phase_pos[Gas]) = sg.value();
}
Block kr(n, np);
Block dkr(n, np*np);
props_.relperm(n, s_all.data(), cells.data(), kr.data(), dkr.data());
const int num_blocks = so.numBlocks();
std::vector<ADB> relperms;
relperms.reserve(3);
typedef const ADB* ADBPtr;
ADBPtr s[3] = { &sw, &so, &sg };
for (int phase1 = 0; phase1 < 3; ++phase1) {
if (pu_.phase_used[phase1]) {
const int phase1_pos = pu_.phase_pos[phase1];
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = ADB::M(n, s[phase1]->derivative()[block].cols());
}
for (int phase2 = 0; phase2 < 3; ++phase2) {
if (!pu_.phase_used[phase2]) {
continue;
}
const int phase2_pos = pu_.phase_pos[phase2];
// Assemble dkr1/ds2.
const int column = phase1_pos + np*phase2_pos; // Recall: Fortran ordering from props_.relperm()
ADB::M dkr1_ds2_diag = spdiag(dkr.col(column));
for (int block = 0; block < num_blocks; ++block) {
jacs[block] += dkr1_ds2_diag * s[phase2]->derivative()[block];
}
}
relperms.emplace_back(ADB::function(kr.col(phase1_pos), jacs));
} else {
relperms.emplace_back(ADB::null());
}
}
return relperms;
}
ADB PolymerPropsAd::adsorption(const ADB& c, const ADB& cmax_cells) const
{
const int nc = c.value().size();
V ads(nc);
V dads(nc);
for (int i = 0; i < nc; ++i) {
double c_ads = 0;
double dc_ads = 0;
polymer_props_.adsorptionWithDer(c.value()(i), cmax_cells.value()(i), c_ads, dc_ads);
ads(i) = c_ads;
dads(i) = dc_ads;
}
ADB::M dads_diag(dads.matrix().asDiagonal());
int num_blocks = c.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = dads_diag * c.derivative()[block];
}
return ADB::function(std::move(ads), std::move(jacs));
}
inline
double infinityNorm( const ADB& a, const boost::any& pinfo = boost::any() )
{
static_cast<void>(pinfo); // Suppress warning in non-MPI case.
#if HAVE_MPI
if ( pinfo.type() == typeid(ParallelISTLInformation) )
{
const ParallelISTLInformation& real_info =
boost::any_cast<const ParallelISTLInformation&>(pinfo);
double result=0;
real_info.computeReduction(a.value(), Reduction::makeLInfinityNormFunctor<double>(), result);
return result;
}
else
#endif
{
if( a.value().size() > 0 ) {
return a.value().matrix().template lpNorm<Eigen::Infinity> ();
}
else { // this situation can occur when no wells are present
return 0.0;
}
}
}
/// Bubble point curve for Rs as function of oil pressure.
/// \param[in] po Array of n oil pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
ADB BlackoilPropsAdFromDeck::rsMax(const ADB& po,
const Cells& cells) const
{
if (!phase_usage_.phase_used[Oil]) {
OPM_THROW(std::runtime_error, "Cannot call rsMax(): oil phase not present.");
}
const int n = cells.size();
assert(po.size() == n);
V rbub(n);
V drbubdp(n);
props_[Oil]->rbub(n, po.value().data(), rbub.data(), drbubdp.data());
ADB::M drbubdp_diag = spdiag(drbubdp);
const int num_blocks = po.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = drbubdp_diag * po.derivative()[block];
}
return ADB::function(rbub, jacs);
}
ADB PolymerPropsAd::effectiveInvWaterVisc(const ADB& c,
const double* visc) const
{
const int nc = c.size();
V inv_mu_w_eff(nc);
V dinv_mu_w_eff(nc);
for (int i = 0; i < nc; ++i) {
double im = 0, dim = 0;
polymer_props_.effectiveInvViscWithDer(c.value()(i), visc, im, dim);
inv_mu_w_eff(i) = im;
dinv_mu_w_eff(i) = dim;
}
ADB::M dim_diag = spdiag(dinv_mu_w_eff);
const int num_blocks = c.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = dim_diag * c.derivative()[block];
}
return ADB::function(std::move(inv_mu_w_eff), std::move(jacs));
}
ADB
PolymerPropsAd::viscMult(const ADB& c) const
{
const int nc = c.size();
V visc_mult(nc);
V dvisc_mult(nc);
for (int i = 0; i < nc; ++i) {
double im = 0, dim = 0;
im = polymer_props_.viscMultWithDer(c.value()(i), &dim);
visc_mult(i) = im;
dvisc_mult(i) = dim;
}
ADB::M dim_diag(dvisc_mult.matrix().asDiagonal());
const int num_blocks = c.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = dim_diag * c.derivative()[block];
}
return ADB::function(std::move(visc_mult), std::move(jacs));
}
/// Water viscosity.
/// \param[in] pw Array of n water pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n viscosity values.
ADB BlackoilPropsAdFromDeck::muWat(const ADB& pw,
const Cells& cells) const
{
if (!phase_usage_.phase_used[Water]) {
OPM_THROW(std::runtime_error, "Cannot call muWat(): water phase not present.");
}
const int n = cells.size();
assert(pw.size() == n);
V mu(n);
V dmudp(n);
V dmudr(n);
const double* rs = 0;
props_[phase_usage_.phase_pos[Water]]->mu(n, pw.value().data(), rs,
mu.data(), dmudp.data(), dmudr.data());
ADB::M dmudp_diag = spdiag(dmudp);
const int num_blocks = pw.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = dmudp_diag * pw.derivative()[block];
}
return ADB::function(mu, jacs);
}
ADB PolymerPropsAd::effectiveInvPolymerVisc(const ADB& c, const V& mu_w) const
{
assert(c.size() == mu_w.size());
const int nc = c.size();
V inv_mu_p_eff(nc);
V dinv_mu_p_eff(nc);
for (int i = 0; i < nc; ++i) {
double im = 0;
double dim = 0;
polymer_props_.effectiveInvPolyViscWithDer(c.value()(i), mu_w(i), im, dim);
inv_mu_p_eff(i) = im;
dinv_mu_p_eff(i) = dim;
}
ADB::M dim_diag(dinv_mu_p_eff.matrix().asDiagonal());
const int num_blocks = c.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = dim_diag * c.derivative()[block];
}
return ADB::function(std::move(inv_mu_p_eff), std::move(jacs));
}
VFPProdProperties::ADB VFPProdProperties::bhp(const std::vector<int>& table_id,
const ADB& aqua,
const ADB& liquid,
const ADB& vapour,
const ADB& thp_arg,
const ADB& alq) const {
const int nw = thp_arg.size();
std::vector<int> block_pattern = detail::commonBlockPattern(aqua, liquid, vapour, thp_arg, alq);
assert(static_cast<int>(table_id.size()) == nw);
assert(aqua.size() == nw);
assert(liquid.size() == nw);
assert(vapour.size() == nw);
assert(thp_arg.size() == nw);
assert(alq.size() == nw);
//Allocate data for bhp's and partial derivatives
ADB::V value = ADB::V::Zero(nw);
ADB::V dthp = ADB::V::Zero(nw);
ADB::V dwfr = ADB::V::Zero(nw);
ADB::V dgfr = ADB::V::Zero(nw);
ADB::V dalq = ADB::V::Zero(nw);
ADB::V dflo = ADB::V::Zero(nw);
//Get the table for each well
std::vector<const VFPProdTable*> well_tables(nw, nullptr);
for (int i=0; i<nw; ++i) {
if (table_id[i] >= 0) {
well_tables[i] = detail::getTable(m_tables, table_id[i]);
}
}
//Get the right FLO/GFR/WFR variable for each well as a single ADB
const ADB flo = detail::combineADBVars<VFPProdTable::FLO_TYPE>(well_tables, aqua, liquid, vapour);
const ADB wfr = detail::combineADBVars<VFPProdTable::WFR_TYPE>(well_tables, aqua, liquid, vapour);
const ADB gfr = detail::combineADBVars<VFPProdTable::GFR_TYPE>(well_tables, aqua, liquid, vapour);
//Compute the BHP for each well independently
for (int i=0; i<nw; ++i) {
const VFPProdTable* table = well_tables[i];
if (table != nullptr) {
//First, find the values to interpolate between
//Value of FLO is negative in OPM for producers, but positive in VFP table
auto flo_i = detail::findInterpData(-flo.value()[i], table->getFloAxis());
auto thp_i = detail::findInterpData( thp_arg.value()[i], table->getTHPAxis());
auto wfr_i = detail::findInterpData( wfr.value()[i], table->getWFRAxis());
auto gfr_i = detail::findInterpData( gfr.value()[i], table->getGFRAxis());
auto alq_i = detail::findInterpData( alq.value()[i], table->getALQAxis());
detail::VFPEvaluation bhp_val = detail::interpolate(table->getTable(), flo_i, thp_i, wfr_i, gfr_i, alq_i);
value[i] = bhp_val.value;
dthp[i] = bhp_val.dthp;
dwfr[i] = bhp_val.dwfr;
dgfr[i] = bhp_val.dgfr;
dalq[i] = bhp_val.dalq;
dflo[i] = bhp_val.dflo;
}
else {
value[i] = -1e100; //Signal that this value has not been calculated properly, due to "missing" table
}
}
//Create diagonal matrices from ADB::Vs
ADB::M dthp_diag(dthp.matrix().asDiagonal());
ADB::M dwfr_diag(dwfr.matrix().asDiagonal());
ADB::M dgfr_diag(dgfr.matrix().asDiagonal());
ADB::M dalq_diag(dalq.matrix().asDiagonal());
ADB::M dflo_diag(dflo.matrix().asDiagonal());
//Calculate the Jacobians
const int num_blocks = block_pattern.size();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
//Could have used fastSparseProduct and temporary variables
//but may not save too much on that.
jacs[block] = ADB::M(nw, block_pattern[block]);
if (!thp_arg.derivative().empty()) {
jacs[block] += dthp_diag * thp_arg.derivative()[block];
}
if (!wfr.derivative().empty()) {
jacs[block] += dwfr_diag * wfr.derivative()[block];
}
if (!gfr.derivative().empty()) {
jacs[block] += dgfr_diag * gfr.derivative()[block];
}
if (!alq.derivative().empty()) {
jacs[block] += dalq_diag * alq.derivative()[block];
}
if (!flo.derivative().empty()) {
jacs[block] -= dflo_diag * flo.derivative()[block];
}
}
ADB retval = ADB::function(std::move(value), std::move(jacs));
return retval;
}
int main()
try
{
typedef Opm::AutoDiffBlock<double> ADB;
typedef ADB::V V;
typedef Eigen::SparseMatrix<double> S;
Opm::time::StopWatch clock;
clock.start();
const Opm::GridManager gm(3,3);//(50, 50, 10);
const UnstructuredGrid& grid = *gm.c_grid();
using namespace Opm::unit;
using namespace Opm::prefix;
// const Opm::IncompPropertiesBasic props(2, Opm::SaturationPropsBasic::Linear,
// { 1000.0, 800.0 },
// { 1.0*centi*Poise, 5.0*centi*Poise },
// 0.2, 100*milli*darcy,
// grid.dimensions, grid.number_of_cells);
// const Opm::IncompPropertiesBasic props(2, Opm::SaturationPropsBasic::Linear,
// { 1000.0, 1000.0 },
// { 1.0, 1.0 },
// 1.0, 1.0,
// grid.dimensions, grid.number_of_cells);
const Opm::IncompPropertiesBasic props(2, Opm::SaturationPropsBasic::Linear,
{ 1000.0, 1000.0 },
{ 1.0, 30.0 },
1.0, 1.0,
grid.dimensions, grid.number_of_cells);
V htrans(grid.cell_facepos[grid.number_of_cells]);
tpfa_htrans_compute(const_cast<UnstructuredGrid*>(&grid), props.permeability(), htrans.data());
V trans_all(grid.number_of_faces);
// tpfa_trans_compute(const_cast<UnstructuredGrid*>(&grid), htrans.data(), trans_all.data());
const int nc = grid.number_of_cells;
std::vector<int> allcells(nc);
for (int i = 0; i < nc; ++i) {
allcells[i] = i;
}
std::cerr << "Opm core " << clock.secsSinceLast() << std::endl;
// Define neighbourhood-derived operator matrices.
const Opm::HelperOps ops(grid);
const int num_internal = ops.internal_faces.size();
std::cerr << "Topology matrices " << clock.secsSinceLast() << std::endl;
typedef Opm::AutoDiffBlock<double> ADB;
typedef ADB::V V;
// q
V q(nc);
q.setZero();
q[0] = 1.0;
q[nc-1] = -1.0;
// s0 - this is explicit now
typedef Eigen::Array<double, Eigen::Dynamic, 2, Eigen::RowMajor> TwoCol;
TwoCol s0(nc, 2);
s0.leftCols<1>().setZero();
s0.rightCols<1>().setOnes();
// totmob - explicit as well
TwoCol kr(nc, 2);
props.relperm(nc, s0.data(), allcells.data(), kr.data(), 0);
const V krw = kr.leftCols<1>();
const V kro = kr.rightCols<1>();
const double* mu = props.viscosity();
const V totmob = krw/mu[0] + kro/mu[1];
// Moved down here because we need total mobility.
tpfa_eff_trans_compute(const_cast<UnstructuredGrid*>(&grid), totmob.data(),
htrans.data(), trans_all.data());
// Still explicit, and no upwinding!
V mobtransf(num_internal);
for (int fi = 0; fi < num_internal; ++fi) {
mobtransf[fi] = trans_all[ops.internal_faces[fi]];
}
std::cerr << "Property arrays " << clock.secsSinceLast() << std::endl;
// Initial pressure.
V p0(nc,1);
p0.fill(200*Opm::unit::barsa);
// First actual AD usage: defining pressure variable.
const std::vector<int> bpat = { nc };
// Could actually write { nc } instead of bpat below,
// but we prefer a named variable since we will repeat it.
const ADB p = ADB::variable(0, p0, bpat);
const ADB ngradp = ops.ngrad*p;
// We want flux = totmob*trans*(p_i - p_j) for the ij-face.
const ADB flux = mobtransf*ngradp;
const ADB residual = ops.div*flux - q;
std::cerr << "Construct AD residual " << clock.secsSinceLast() << std::endl;
// It's the residual we want to be zero. We know it's linear in p,
// so we just need a single linear solve. Since we have formulated
// ourselves with a residual and jacobian we do this with a single
// Newton step (hopefully easy to extend later):
// p = p0 - J(p0) \ R(p0)
// Where R(p0) and J(p0) are contained in residual.value() and
// residual.derived()[0].
#if HAVE_SUITESPARSE_UMFPACK_H
typedef Eigen::UmfPackLU<S> LinSolver;
#else
typedef Eigen::BiCGSTAB<S> LinSolver;
#endif // HAVE_SUITESPARSE_UMFPACK_H
LinSolver solver;
S pmatr;
residual.derivative()[0].toSparse(pmatr);
pmatr.coeffRef(0,0) *= 2.0;
pmatr.makeCompressed();
solver.compute(pmatr);
if (solver.info() != Eigen::Success) {
std::cerr << "Pressure/flow Jacobian decomposition error\n";
return EXIT_FAILURE;
}
// const Eigen::VectorXd dp = solver.solve(residual.value().matrix());
ADB::V residual_v = residual.value();
const V dp = solver.solve(residual_v.matrix()).array();
if (solver.info() != Eigen::Success) {
std::cerr << "Pressure/flow solve failure\n";
return EXIT_FAILURE;
}
const V p1 = p0 - dp;
std::cerr << "Solve " << clock.secsSinceLast() << std::endl;
// std::cout << p1 << std::endl;
// ------ Transport solve ------
// Now we'll try to do a transport step as well.
// Residual formula is
// R_w = s_w - s_w^0 + dt/pv * (div v_w)
// where
// v_w = f_w v
// and f_w is (for now) based on averaged mobilities, not upwind.
double res_norm = 1e100;
const V sw0 = s0.leftCols<1>();
// V sw1 = sw0;
V sw1 = 0.5*V::Ones(nc,1);
const V ndp = (ops.ngrad * p1.matrix()).array();
const V dflux = mobtransf * ndp;
const Opm::UpwindSelector<double> upwind(grid, ops, dflux);
const V pv = Eigen::Map<const V>(props.porosity(), nc, 1)
* Eigen::Map<const V>(grid.cell_volumes, nc, 1);
const double dt = 0.0005;
const V dtpv = dt/pv;
const V qneg = q.min(V::Zero(nc,1));
const V qpos = q.max(V::Zero(nc,1));
std::cout.setf(std::ios::scientific);
std::cout.precision(16);
int it = 0;
do {
const ADB sw = ADB::variable(0, sw1, bpat);
const std::vector<ADB> pmobc = phaseMobility<ADB>(props, allcells, sw.value());
const std::vector<ADB> pmobf = upwind.select(pmobc);
const ADB fw_cell = fluxFunc(pmobc);
const ADB fw_face = fluxFunc(pmobf);
const ADB flux1 = fw_face * dflux;
const ADB qtr_ad = qpos + fw_cell*qneg;
const ADB transport_residual = sw - sw0 + dtpv*(ops.div*flux1 - qtr_ad);
res_norm = transport_residual.value().matrix().norm();
std::cout << "res_norm[" << it << "] = "
<< res_norm << std::endl;
S smatr;
transport_residual.derivative()[0].toSparse(smatr);
smatr.makeCompressed();
solver.compute(smatr);
if (solver.info() != Eigen::Success) {
std::cerr << "Transport Jacobian decomposition error\n";
return EXIT_FAILURE;
}
ADB::V transport_residual_v = transport_residual.value();
const V ds = solver.solve(transport_residual_v.matrix()).array();
if (solver.info() != Eigen::Success) {
std::cerr << "Transport solve failure\n";
return EXIT_FAILURE;
}
sw1 = sw.value() - ds;
std::cerr << "Solve for s[" << it << "]: "
<< clock.secsSinceLast() << '\n';
sw1 = sw1.min(V::Ones(nc,1)).max(V::Zero(nc,1));
it += 1;
} while (res_norm > 1e-7);
std::cout << "Saturation solution:\n"
<< "function s1 = solution\n"
<< "s1 = [\n" << sw1 << "\n];\n";
}
catch (const std::exception &e) {
std::cerr << "Program threw an exception: " << e.what() << "\n";
throw;
}
