opm-simulators/opm/autodiff/ImpesTPFAAD.hpp

/*
  Copyright 2013 SINTEF ICT, Applied Mathematics.
  Copyright 2013 Statoil ASA.

  This file is part of the Open Porous Media Project (OPM).

  OPM is free software: you can redistribute it and/or modify
  it under the terms of the GNU General Public License as published by
  the Free Software Foundation, either version 3 of the License, or
  (at your option) any later version.

  OPM is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU General Public License for more details.

  You should have received a copy of the GNU General Public License
  along with OPM.  If not, see <http://www.gnu.org/licenses/>.
*/

#ifndef OPM_IMPESTPFAAD_HEADER_INCLUDED
#define OPM_IMPESTPFAAD_HEADER_INCLUDED

#include <opm/autodiff/AutoDiffBlock.hpp>
#include <opm/autodiff/AutoDiffHelpers.hpp>

#include <opm/core/simulator/BlackoilState.hpp>
#include <opm/core/simulator/WellState.hpp>
#include <opm/core/utility/ErrorMacros.hpp>
#include <opm/core/linalg/LinearSolverInterface.hpp>
#include <opm/core/wells.h>

#include <algorithm>
#include <cassert>
#include <vector>
#include <iterator>

#include <boost/shared_ptr.hpp>

struct UnstructuredGrid;

namespace {
    std::vector<int>
    buildAllCells(const int nc)
    {
        std::vector<int> all_cells(nc);

        for (int c = 0; c < nc; ++c) { all_cells[c] = c; }

        return all_cells;
    }

    template <class GeoProps>
    AutoDiff::ForwardBlock<double>::M
    gravityOperator(const UnstructuredGrid& grid,
                    const HelperOps&        ops ,
                    const GeoProps&         geo )
    {
        const int nc = grid.number_of_cells;

        std::vector<int> f2hf(2 * grid.number_of_faces, -1);
        for (int c = 0, i = 0; c < nc; ++c) {
            for (; i < grid.cell_facepos[c + 1]; ++i) {
                const int f = grid.cell_faces[ i ];
                const int p = 0 + (grid.face_cells[2*f + 0] != c);

                f2hf[2*f + p] = i;
            }
        }

        typedef AutoDiff::ForwardBlock<double>::V V;
        typedef AutoDiff::ForwardBlock<double>::M M;

        const V& gpot  = geo.gravityPotential();
        const V& trans = geo.transmissibility();

        const HelperOps::IFaces::Index ni = ops.internal_faces.size();

        typedef Eigen::Triplet<double> Tri;
        std::vector<Tri> grav;  grav.reserve(2 * ni);
        for (HelperOps::IFaces::Index i = 0; i < ni; ++i) {
            const int f  = ops.internal_faces[ i ];
            const int c1 = grid.face_cells[2*f + 0];
            const int c2 = grid.face_cells[2*f + 1];

            assert ((c1 >= 0) && (c2 >= 0));

            const double dG1 = gpot[ f2hf[2*f + 0] ];
            const double dG2 = gpot[ f2hf[2*f + 1] ];
            const double t   = trans[ f ];

            grav.push_back(Tri(i, c1,   t * dG1));
            grav.push_back(Tri(i, c2, - t * dG2));
        }

        M G(ni, nc);  G.setFromTriplets(grav.begin(), grav.end());

        return G;
    }
}

namespace Opm {


    template <class BOFluid, class GeoProps>
    class ImpesTPFAAD {
    public:
        ImpesTPFAAD(const UnstructuredGrid& grid ,
                    const BOFluid&          fluid,
                    const GeoProps&         geo  ,
                    const Wells&            wells,
                    const LinearSolverInterface& linsolver)
            : grid_     (grid)
            , fluid_    (fluid)
            , geo_      (geo)
            , wells_    (wells)
            , linsolver_(linsolver)
            // , pdepfdata_(grid.number_of_cells, fluid)
            , ops_      (grid)
            , grav_     (gravityOperator(grid_, ops_, geo_))
            , cell_residual_ (ADB::null())
            , well_flow_residual_ ()
            , well_residual_ (ADB::null())
        {
        }

        void
        solve(const double   dt,
              BlackoilState& state,
              WellState& well_state)
        {
            const int nc = grid_.number_of_cells;
            const int np = state.numPhases();

            well_flow_residual_.resize(np, ADB::null());

            // Compute relperms once and for all (since saturations are explicit).
            DataBlock s = Eigen::Map<const DataBlock>(state.saturation().data(), nc, np);
            ASSERT(np == 2);
            kr_ = fluid_.relperm(s.col(0), s.col(1), V::Zero(nc,1), buildAllCells(nc));
            // Compute relperms for wells. This must be revisited for crossflow.
            const int nw = wells_.number_of_wells;
            const int nperf = wells_.well_connpos[nw];
            DataBlock well_s(nperf, np);
            for (int w = 0; w < nw; ++w) {
                const double* comp_frac = &wells_.comp_frac[np*w];
                for (int j = wells_.well_connpos[w]; j < wells_.well_connpos[w+1]; ++j) {
                    well_s.row(j) = Eigen::Map<const DataBlock>(comp_frac, 1, np);
                }
            }
            const std::vector<int> well_cells(wells_.well_cells,
                                              wells_.well_cells + nperf);
            well_kr_ = fluid_.relperm(well_s.col(0), well_s.col(1), V::Zero(nperf,1), well_cells);

            const double atol  = 1.0e-15;
            const double rtol  = 5.0e-10;
            const int    maxit = 15;

            assemble(dt, state, well_state);

            const double r0  = residualNorm();
            int          it  = 0;
            bool resTooLarge = r0 > atol;
            while (resTooLarge && (it < maxit)) {
                solveJacobianSystem(state, well_state);

                assemble(dt, state, well_state);

                const double r = residualNorm();

                resTooLarge = (r > atol) && (r > rtol*r0);

                it += 1;
            }

            if (resTooLarge) {
                THROW("Failed to compute converged pressure solution");
            }
            else {
                computeFluxes(state);
            }
        }

    private:
        // Disallow copying and assignment
        ImpesTPFAAD(const ImpesTPFAAD& rhs);
        ImpesTPFAAD& operator=(const ImpesTPFAAD& rhs);

        // typedef PressureDependentFluidData<double, BOFluid> PDepFData;
        // typedef typename PDepFData::ADB ADB;
        typedef AutoDiff::ForwardBlock<double> ADB;
        typedef ADB::V V;
        typedef ADB::M M;
        typedef Eigen::Array<double,
                             Eigen::Dynamic,
                             Eigen::Dynamic,
                             Eigen::RowMajor> DataBlock;

        const UnstructuredGrid&      grid_;
        const BOFluid&               fluid_;
        const GeoProps&              geo_ ;
        const Wells&                 wells_;
        const LinearSolverInterface& linsolver_;
        HelperOps                    ops_;
        const M                      grav_;
        ADB                          cell_residual_;
        std::vector<ADB>             well_flow_residual_;
        ADB                          well_residual_;
        std::vector<V>               kr_;
        std::vector<V>               well_kr_;

        enum { Water = BOFluid::Water,
               Oil = BOFluid::Oil,
               Gas = BOFluid::Gas };





        void
        assemble(const double         dt,
                 const BlackoilState& state,
                 const WellState& well_state)
        {

            const V& pv = geo_.poreVolume();
            const int nc = grid_.number_of_cells;
            const int np = state.numPhases();
            const int nw = wells_.number_of_wells;
            const int nperf = wells_.well_connpos[nw];

            const std::vector<int> cells = buildAllCells(nc);

            const Eigen::Map<const DataBlock> z0all(&state.surfacevol()[0], nc, np);
            const DataBlock qall = DataBlock::Zero(nc, np);
            const V delta_t = dt * V::Ones(nc, 1);
            const V transi = subset(geo_.transmissibility(),
                                    ops_.internal_faces);
            const std::vector<int> well_cells(wells_.well_cells,
                                              wells_.well_cells + nperf);
            const V transw = Eigen::Map<const V>(wells_.WI, nperf, 1);

            // Initialize AD variables: p (cell pressures), qs (well rates) and bhp (well bhp).
            const V p0 = Eigen::Map<const V>(&state.pressure()[0], nc, 1);
            const V qs0 = V::Zero(np*nw, 1); // WellState has no member for this!
            const V bhp0 = Eigen::Map<const V>(&well_state.bhp()[0], nw, 1);
            std::vector<V> vars0 = { p0, qs0, bhp0 };
            std::vector<ADB> vars= ADB::variables(vars0);
            const ADB& p = vars[0];
            const ADB& qs = vars[1];
            const ADB& bhp = vars[2];
            std::vector<int> bpat = p.blockPattern();

            // Compute T_ij * (p_i - p_j) and use for upwinding.
            const ADB nkgradp = transi * (ops_.ngrad * p);
            const UpwindSelector<double> upwind(grid_, ops_, nkgradp.value());

            // Extract variables for perforation cell pressures
            // and corresponding perforation well pressures.
            const ADB p_perfcell = subset(p, well_cells);
            // Construct matrix to map wells->perforations.
            M well_to_perf(well_cells.size(), nw);
            typedef Eigen::Triplet<double> Tri;
            std::vector<Tri> w2p;
            for (int w = 0; w < nw; ++w) {
                for (int perf = wells_.well_connpos[w]; perf < wells_.well_connpos[w+1]; ++perf) {
                    w2p.emplace_back(perf, w, 1.0);
                }
            }
            well_to_perf.setFromTriplets(w2p.begin(), w2p.end());
            const M perf_to_well = well_to_perf.transpose();
            // Construct pressure difference vector for wells.
            const V well_perf_dp = V::Zero(well_cells.size()); // No gravity yet!
            // Finally construct well perforation pressures and well flows.
            const ADB p_perfwell = well_to_perf*bhp + well_perf_dp;
            const ADB nkgradp_well = transw * (p_perfcell - p_perfwell);
            const Selector<double> cell_to_well_selector(nkgradp_well.value());

            cell_residual_ = ADB::constant(pv, bpat);
            well_residual_ = ADB::constant(V::Zero(nw,1), bpat);
            ADB divcontrib_sum = ADB::constant(V::Zero(nc,1), bpat);
            for (int phase = 0; phase < np; ++phase) {
                const ADB cell_b = fluidFvf(phase, p, cells);
                const ADB cell_rho = fluidRho(phase, p, cells);
                const ADB well_b = fluidFvf(phase, p_perfwell, well_cells);
                const V kr = fluidKr(phase);
                // Explicitly not asking for derivatives of viscosity,
                // since they are not available yet.
                const V mu = fluidMu(phase, p.value(), cells);
                const V cell_mob = kr / mu;
                const V face_mob = upwind.select(cell_mob);
                const V well_kr = fluidKrWell(phase);
                const V well_mu = fluidMu(phase, p_perfwell.value(), well_cells);
                const V well_mob = well_kr / well_mu;
                const V perf_mob = cell_to_well_selector.select(subset(cell_mob, well_cells), well_mob);
                const ADB flux = face_mob * (nkgradp + (grav_ * cell_rho));
                const ADB perf_flux = perf_mob * (nkgradp_well); // No gravity term for perforations.
                const ADB face_b = upwind.select(cell_b);
                const ADB perf_b = cell_to_well_selector.select(subset(cell_b, well_cells), well_b);
                const V z0 = z0all.block(0, phase, nc, 1);
                const V q  = qall .block(0, phase, nc, 1);
                const ADB well_contrib = superset(perf_flux*perf_b, well_cells, nc);
                const ADB divcontrib = delta_t * (ops_.div * (flux * face_b)
                                                  + well_contrib);
                const V qcontrib = delta_t * q;
                const ADB pvcontrib = ADB::constant(pv*z0, bpat);
                const ADB component_contrib = pvcontrib + qcontrib;
                divcontrib_sum = divcontrib_sum - divcontrib/cell_b;
                cell_residual_ = cell_residual_ - (component_contrib/cell_b);
                const ADB well_rates = perf_to_well * (perf_flux*perf_b);
                std::vector<int> well_flow_res_phase_idx(nw);
                for (int w = 0; w < nw; ++w) {
                    well_flow_res_phase_idx[w] = w + phase*nw;
                }
                well_flow_residual_[phase] = well_rates - subset(qs, well_flow_res_phase_idx);
            }
            cell_residual_ = cell_residual_ + divcontrib_sum;
            // Assuming bhp wells.
            V bhp_targets(nw,1);
            for (int w = 0; w < nw; ++w) {
                const WellControls* wc = wells_.ctrls[w];
                if (wc->type[wc->current] != BHP) {
                    THROW("Only BHP wells for now, please!");
                }
                bhp_targets[w] = wc->target[wc->current];
            }
            well_residual_ = bhp - bhp_targets;
        }





        void
        solveJacobianSystem(BlackoilState& state,
                            WellState& well_state) const
        {
            const int nc = grid_.number_of_cells;
            const int nw = wells_.number_of_wells;
            const int np = state.numPhases();

            ASSERT(np == 2);
            const ADB well_flow_res = vertcat(well_flow_residual_[0], well_flow_residual_[1]);
            const ADB well_res = vertcat(well_flow_res, well_residual_);
            const ADB total_res = collapseJacs(vertcat(cell_residual_, well_res));
            Eigen::SparseMatrix<double, Eigen::RowMajor> matr = total_res.derivative()[0];

            std::cout << total_res;

#if HACK_INCOMPRESSIBLE_GRAVITY
            matr.coeffRef(0, 0) *= 2;
#endif

            V dx(total_res.size());
            Opm::LinearSolverInterface::LinearSolverReport rep
                = linsolver_.solve(matr.rows(), matr.nonZeros(),
                                   matr.outerIndexPtr(), matr.innerIndexPtr(), matr.valuePtr(),
                                   total_res.value().data(), dx.data());
            if (!rep.converged) {
                THROW("ImpesTPFAAD::solve(): Linear solver convergence failure.");
            }
            const V p0 = Eigen::Map<const V>(&state.pressure()[0], nc, 1);
            const V dp = subset(dx, buildAllCells(nc));
            const V p = p0 - dp;
            std::copy(&p[0], &p[0] + nc, state.pressure().begin());
            const V bhp0 = Eigen::Map<const V>(&well_state.bhp()[0], nw, 1);
            std::vector<int> bhp_dofs(nw);
            for (int w = 0; w < nw; ++w) {
                bhp_dofs[w] = nc + np*nw + w;
            }
            ASSERT(bhp_dofs.back() + 1 == total_res.size());
            const V dbhp = subset(dx, bhp_dofs);
            const V bhp = bhp0 - dbhp;
            std::copy(&bhp[0], &bhp[0] + nw, well_state.bhp().begin());
        }





        double
        residualNorm() const
        {
            return cell_residual_.value().matrix().norm();
        }





        void
        computeFluxes(BlackoilState& state) const
        {
            const int nc = grid_.number_of_cells;
            const int np = state.numPhases();

            const std::vector<int> cells = buildAllCells(nc);

            const V   p0 = Eigen::Map<const V>(&state.pressure()[0], nc, 1);
            const ADB p  = ADB::constant(p0, cell_residual_.blockPattern());

            const V transi  = subset(geo_.transmissibility(),
                                     ops_.internal_faces);
            const V nkgradp = transi * (ops_.ngrad * p0.matrix()).array();

            V flux = V::Zero(ops_.internal_faces.size(), 1);

            for (int phase = 0; phase < np; ++phase) {
                const ADB cell_rho = fluidRho(phase, p, cells);
                const V head = nkgradp + (grav_ * cell_rho.value().matrix()).array();
                const UpwindSelector<double> upwind(grid_, ops_, head);
                const V kr = fluidKr(phase);
                const V mu = fluidMu(phase, p.value(), cells);
                const V mf = upwind.select(kr / mu);

                flux += mf * head;
            }
            V all_flux = superset(flux, ops_.internal_faces, grid_.number_of_faces);
            std::copy(all_flux.data(), all_flux.data() + grid_.number_of_faces, state.faceflux().data());
        }





        V fluidMu(const int phase, const V& p, const std::vector<int>& cells) const
        {
            switch (phase) {
            case Water:
                return fluid_.muWat(p, cells);
            case Oil: {
                V dummy_rs = V::Zero(p.size(), 1) * p;
                return fluid_.muOil(p, dummy_rs, cells);
            }
            case Gas:
                return fluid_.muGas(p, cells);
            default:
                THROW("Unknown phase index " << phase);
            }
        }





        ADB fluidMu(const int phase, const ADB& p, const std::vector<int>& cells) const
        {
            switch (phase) {
            case Water:
                return fluid_.muWat(p, cells);
            case Oil: {
                ADB dummy_rs = V::Zero(p.size(), 1) * p;
                return fluid_.muOil(p, dummy_rs, cells);
            }
            case Gas:
                return fluid_.muGas(p, cells);
            default:
                THROW("Unknown phase index " << phase);
            }
        }





        ADB fluidFvf(const int phase, const ADB& p, const std::vector<int>& cells) const
        {
            switch (phase) {
            case Water:
                return fluid_.bWat(p, cells);
            case Oil: {
                ADB dummy_rs = V::Zero(p.size(), 1) * p;
                return fluid_.bOil(p, dummy_rs, cells);
            }
            case Gas:
                return fluid_.bGas(p, cells);
            default:
                THROW("Unknown phase index " << phase);
            }
        }





        ADB fluidRho(const int phase, const ADB& p, const std::vector<int>& cells) const
        {
            const double* rhos = fluid_.surfaceDensity();
            ADB b = fluidFvf(phase, p, cells);
            ADB rho = V::Constant(p.size(), 1, rhos[phase]) * b;
            return rho;
        }





        V fluidKr(const int phase) const
        {
            return kr_[phase];
        }





        V fluidKrWell(const int phase) const
        {
            return well_kr_[phase];
        }

    };
} // namespace Opm

#endif  /* OPM_IMPESTPFAAD_HEADER_INCLUDED */