opm-simulators/sim_simple.cpp

/*
  Copyright 2013 SINTEF ICT, Applied Mathematics.

  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/>.
*/

#include "AutoDiffBlock.hpp"
#include <opm/core/grid.h>
#include <opm/core/grid/GridManager.hpp>
#include <opm/core/props/IncompPropertiesBasic.hpp>
#include <opm/core/utility/Units.hpp>
#include <opm/core/utility/StopWatch.hpp>
#include <opm/core/pressure/tpfa/trans_tpfa.h>
#include <Eigen/UmfPackSupport>

#include <iostream>
#include <cstdlib>

/*
  Equations for incompressible two-phase flow.

  Using s and p as variables:

  PV (s_i - s0_i) / dt + sum_{j \in U(i)} f(s_j) v_{ij} + sum_{j in D(i) f(s_i) v_{ij} = qw_i

  where

  v_{ij} = totmob_ij T_ij (p_i - p_j)


  Pressure equation:

  sum_{j \in N(i)} totmob_ij T_ij (p_i - p_j) = q_i

*/

/// Contains vectors and sparse matrices that represent subsets or
/// operations on (AD or regular) vectors of data.
struct HelperOps
{
    typedef AutoDiff::ForwardBlock<double>::M M;
    typedef AutoDiff::ForwardBlock<double>::V V;

    /// A list of internal faces.
    typedef Eigen::Array<int, Eigen::Dynamic, 1> iFaces;
    iFaces internal_faces;

    /// Extract for each face the difference of its adjacent cells'values.
    M ngrad;
    /// Extract for each face the average of its adjacent cells' values.
    M caver;
    /// Extract for each cell the sum of its adjacent faces' (signed) values.
    M div;

    /// Constructs all helper vectors and matrices.
    HelperOps(const UnstructuredGrid& grid)
    {
        const int nc = grid.number_of_cells;
        const int nf = grid.number_of_faces;
        // Define some neighbourhood-derived helper arrays.
        typedef Eigen::Array<int, Eigen::Dynamic, 1> OneColInt;
        typedef Eigen::Array<bool, Eigen::Dynamic, 1> OneColBool;
        typedef Eigen::Array<int, Eigen::Dynamic, 2, Eigen::RowMajor> TwoColInt;
        typedef Eigen::Array<bool, Eigen::Dynamic, 2, Eigen::RowMajor> TwoColBool;
        TwoColInt nb = Eigen::Map<TwoColInt>(grid.face_cells, nf, 2);
        // std::cout << "nb = \n" << nb << std::endl;
        TwoColBool nbib = nb >= 0;
        OneColBool ifaces = nbib.rowwise().all();
        const int num_internal = ifaces.cast<int>().sum();
        // std::cout << num_internal << " internal faces." << std::endl;
        TwoColInt nbi(num_internal, 2);
        internal_faces.resize(num_internal);
        int fi = 0;
        for (int f = 0; f < nf; ++f) {
            if (ifaces[f]) {
                internal_faces[fi] = f;
                nbi.row(fi) = nb.row(f);
                ++fi;
            }
        }
        // std::cout << "nbi = \n" << nbi << std::endl;
        // Create matrices.
        ngrad.resize(num_internal, nc);
        caver.resize(num_internal, nc);
        typedef Eigen::Triplet<double> Tri;
        std::vector<Tri> ngrad_tri;
        std::vector<Tri> caver_tri;
        ngrad_tri.reserve(2*num_internal);
        caver_tri.reserve(2*num_internal);
        for (int i = 0; i < num_internal; ++i) {
            ngrad_tri.emplace_back(i, nbi(i,0), 1.0);
            ngrad_tri.emplace_back(i, nbi(i,1), -1.0);
            caver_tri.emplace_back(i, nbi(i,0), 0.5);
            caver_tri.emplace_back(i, nbi(i,1), 0.5);
        }
        ngrad.setFromTriplets(ngrad_tri.begin(), ngrad_tri.end());
        caver.setFromTriplets(caver_tri.begin(), caver_tri.end());
        div = ngrad.transpose();
    }
};

#if !defined(NDEBUG)
#include <cstdio>
#endif  // !defined(NDEBUG)

namespace {
#if !defined(NDEBUG)
    void
    printSparseMatrix(const Eigen::SparseMatrix<double>& A,
                      std::FILE*                         fp)
    {
        typedef Eigen::SparseMatrix<double>::Index Index;

        const Index*  const p = A.outerIndexPtr();
        const Index*  const i = A.innerIndexPtr();
        const double* const x = A.valuePtr();

        const Index cols = A.outerSize();
        assert (A.innerSize() == cols);

        for (Index j = 0; j < cols; j++) {
            for (Index k = p[j]; k < p[j + 1]; k++) {
                std::fprintf(fp, "%lu %lu %26.18e\n",
                             static_cast<unsigned long>(i[k] + 1),
                             static_cast<unsigned long>(j    + 1), x[k]);
            }
        }
    }

    void
    printSparseMatrix(const Eigen::SparseMatrix<double>& A ,
                      const char* const                  fn)
    {
        std::FILE* fp;

        fp = std::fopen(fn, "w");
        if (fp != 0) {
            printSparseMatrix(A, fp);
        }

        std::fclose(fp);
    }
#endif  // !defined(NDEBUG)

    template <typename Scalar>
    class UpwindSelector {
    public:
        typedef AutoDiff::ForwardBlock<Scalar> ADB;

        UpwindSelector(const UnstructuredGrid& g,
                       const HelperOps&        h)
            : g_(g), h_(h)
        {
        }

        // Upwind selection in absence of counter-current flow (i.e.,
        // without effects of gravity and/or capillary pressure).
        std::vector<ADB>
        select(const typename ADB::V&  press,
               const std::vector<ADB>& xc   ) const
        {
            typedef HelperOps::iFaces::Index ifIndex;
            const ifIndex nif = h_.internal_faces.size();

            // Define selector structure.
            typedef typename Eigen::Triplet<Scalar> Triplet;
            std::vector<Triplet> s;  s.reserve(nif);
            for (ifIndex i = 0; i < nif; ++i) {
                const int f  = h_.internal_faces[i];
                const int c1 = g_.face_cells[2*f + 0];
                const int c2 = g_.face_cells[2*f + 1];

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

                const Scalar dp = press[c1] - press[c2];
                const int c = (! (dp < Scalar(0))) ? c1 : c2;

                s.push_back(Triplet(i, c, Scalar(1)));
            }

            // Assemble explicit selector operator.
            typename ADB::M S(nif, g_.number_of_cells);
            S.setFromTriplets(s.begin(), s.end());

            // Apply selector.
            //
            // Absence of counter-current flow means that the same
            // selector applies to all quantities, 'x', defined per
            // cell.
            std::vector<ADB> xf;  xf.reserve(xc.size());
            for (typename std::vector<ADB>::const_iterator
                     b = xc.begin(), e = xc.end(); b != e; ++b)
            {
                xf.push_back(S * (*b));
            }

            return xf;
        }

    private:
        const UnstructuredGrid& g_;
        const HelperOps&        h_;
    };
}

template <class ADB>
std::vector<ADB>
phaseMobility(const Opm::IncompPropertiesInterface& props,
              const std::vector<int>& cells,
              const typename ADB::V& sw)
{
    typedef Eigen::Array<double, Eigen::Dynamic, 2, Eigen::RowMajor> TwoCol;
    typedef Eigen::Array<double, Eigen::Dynamic, 4, Eigen::RowMajor> FourCol;
    typedef typename ADB::V V;
    typedef typename ADB::M M;
    const int nc = props.numCells();
    TwoCol s(nc, 2);
    s.leftCols<1>() = sw;
    s.rightCols<1>() = 1.0 - s.leftCols<1>();
    TwoCol kr(nc, 2);
    FourCol dkr(nc, 4);
    props.relperm(nc, s.data(), cells.data(), kr.data(), dkr.data());
    V krw = kr.leftCols<1>();
    V kro = kr.rightCols<1>();
    V dkrw = dkr.leftCols<1>();  // Left column is top-left of dkr/ds 2x2 matrix.
    V dkro = -dkr.rightCols<1>(); // Right column is bottom-right of dkr/ds 2x2 matrix.
    M krwjac(nc,nc);
    M krojac(nc,nc);
    auto sizes = Eigen::ArrayXi::Ones(nc);
    krwjac.reserve(sizes);
    krojac.reserve(sizes);
    for (int c = 0; c < nc; ++c) {
        krwjac.insert(c,c) = dkrw(c);
        krojac.insert(c,c) = dkro(c);
    }
    const double* mu = props.viscosity();
    std::vector<M> dmw = { krwjac/mu[0] };
    std::vector<M> dmo = { krojac/mu[1] };

    std::vector<ADB> pmobc = { ADB::function(krw / mu[0], dmw) ,
                               ADB::function(kro / mu[1], dmo) };
    return pmobc;
}

/// Returns fw(sw).
template <class ADB>
ADB
fluxFunc(const std::vector<ADB>& m)
{
    assert (m.size() == 2);

    ADB f = m[0] / (m[0] + m[1]);

    return f;
}


int main()
{
    typedef AutoDiff::ForwardBlock<double> ADB;
    typedef ADB::V V;
    typedef ADB::M M;

    Opm::time::StopWatch clock;
    clock.start();
    Opm::GridManager gm(3,3);//(50, 50, 10);
    const UnstructuredGrid& grid = *gm.c_grid();
    using namespace Opm::unit;
    using namespace Opm::prefix;
    // 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);
    // 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);
    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);
    std::vector<double> htrans(grid.cell_facepos[grid.number_of_cells]);
    tpfa_htrans_compute((UnstructuredGrid*)&grid, props.permeability(), htrans.data());
    // std::vector<double> trans(grid.number_of_faces);
    V trans_all(grid.number_of_faces);
    tpfa_trans_compute((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.
    HelperOps ops(grid);
    const int num_internal = ops.internal_faces.size();
    V transi(num_internal);
    for (int fi = 0; fi < num_internal; ++fi) {
        transi[fi] = trans_all[ops.internal_faces[fi]];
    }
    std::cerr << "Topology matrices " << clock.secsSinceLast() << std::endl;

    typedef AutoDiff::ForwardBlock<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);
    V krw = kr.leftCols<1>();
    V kro = kr.rightCols<1>();
    const double* mu = props.viscosity();
    V totmob = krw/mu[0] + kro/mu[1];
    V totmobf = (ops.caver*totmob.matrix()).array();

    // Mobility-weighted transmissibilities per internal face.
    // Still explicit, and no upwinding!
    V mobtransf = totmobf*transi;

    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.
    std::vector<int> block_pattern = { nc };
    // Could actually write { nc } instead of block_pattern below,
    // but we prefer a named variable since we will repeat it.
    ADB p = ADB::variable(0, p0, block_pattern);
    ADB ngradp = ops.ngrad*p;
    // We want flux = totmob*trans*(p_i - p_j) for the ij-face.
    // We only need to multiply mobtransf and pdiff_face,
    // but currently multiplication with constants is not in,
    // so we define an AD constant to multiply with.
    ADB mobtransf_ad = ADB::constant(mobtransf, block_pattern);
    ADB flux = mobtransf_ad*ngradp;
    ADB residual = ops.div*flux - ADB::constant(q, block_pattern);
    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].

    Eigen::UmfPackLU<M> solver;
    M matr = residual.derivative()[0];
    matr.coeffRef(0,0) *= 2.0;
    matr.makeCompressed();
    solver.compute(matr);
    if (solver.info() != Eigen::Success) {
        std::cerr << "Pressure/flow Jacobian decomposition error\n";
        return EXIT_FAILURE;
    }
    Eigen::VectorXd x = solver.solve(residual.value().matrix());
    if (solver.info() != Eigen::Success) {
        std::cerr << "Pressure/flow solve failure\n";
        return EXIT_FAILURE;
    }
    V p1 = p0 - x.array();
    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;
    V s1 =  /*s0.leftCols<1>()*/0.5*V::Ones(nc,1); // Initial guess.
    UpwindSelector<double> upws(grid, ops);
    const ADB nkdp = (ADB::constant(transi                 , block_pattern) *
                      ADB::constant(ops.ngrad * p1.matrix(), block_pattern));
    const ADB s00 = ADB::constant(s0.leftCols<1>(), block_pattern);
    const std::vector<ADB> pmobc0 = phaseMobility<ADB>(props, allcells, s00.value());
    const std::vector<ADB> pmobf0 = upws.select(p1, pmobc0);
    const std::vector<ADB::M> null = { ADB::M(transi.size(), nc) };
    const ADB dflux = (ADB::function((pmobf0[0] + pmobf0[1]).value(), null) *
                       ADB::function(nkdp.value()                   , null));

    std::cout.setf(std::ios::scientific);
    std::cout.precision(16);

    int it = 0;
    do {
        const std::vector<int>& bp = block_pattern;
        ADB s = ADB::variable(0, s1, bp);
        const double dt = 0.0005;
        V pv = Eigen::Map<const V>(props.porosity(), nc, 1)
            * Eigen::Map<const V>(grid.cell_volumes, nc, 1);
        V dtpv = dt/pv;
        // std::cout << dtpv;
        std::vector<ADB> pmobc = phaseMobility<ADB>(props, allcells, s.value());
        std::vector<ADB> pmobf = upws.select(p1, pmobc);

        ADB fw_cell = fluxFunc(pmobc);
        const ADB fw_face = fluxFunc(pmobf);
        ADB flux1 = fw_face * dflux;
        // std::cout << flux1;
        V qneg = dtpv*q;
        V qpos = dtpv*q;
        // Cheating a bit...
        qneg[0] = 0.0;
        qpos[nc-1] = 0.0;
        ADB qtr_ad = ADB::constant(qpos, bp) + fw_cell*ADB::constant(qneg, bp);
        ADB transport_residual = s - ADB::constant(s0.leftCols<1>(), bp)
            + ADB::constant(dtpv, bp)*(ops.div*flux1)
            - qtr_ad;
        res_norm = transport_residual.value().matrix().norm();
        std::cout << "res_norm[" << it << "] = "
                  << res_norm << std::endl;

        matr = transport_residual.derivative()[0];
        matr.makeCompressed();
        // std::cout << transport_residual;
        solver.compute(matr);
        if (solver.info() != Eigen::Success) {
            std::cerr << "Transport Jacobian decomposition error\n";
            return EXIT_FAILURE;
        }
        x = solver.solve(transport_residual.value().matrix());
        if (solver.info() != Eigen::Success) {
            std::cerr << "Transport solve failure\n";
            return EXIT_FAILURE;
        }
        // std::cout << x << std::endl;
        s1 = s.value() - x.array();
        std::cerr << "Solve for s[" << it << "]: "
                  << clock.secsSinceLast() << '\n';
        for (int c = 0; c < nc; ++c) {
            s1[c] = std::min(1.0, std::max(0.0, s1[c]));
        }

        it += 1;
    } while (res_norm > 1e-7);

    std::cout << "Saturation solution:\n"
              << "function s1 = solution\n"
              << "s1 = [\n" << s1 << "\n]\n";
}