/*  Lattice Boltzmann sample, written in C++, using the OpenLB
 *  library
 *
 *  Copyright (C) 2007, 2012 Jonas Latt, Mathias J. Krause
 *  Vojtech Cvrcek, Peter Weisbrod
 *  E-mail contact: info@openlb.net
 *  The most recent release of OpenLB can be downloaded at
 *  <http://www.openlb.net/>
 *
 *  This program 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 2
 *  of the License, or (at your option) any later version.
 *
 *  This program 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 this program; if not, write to the Free
 *  Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
 *  Boston, MA  02110-1301, USA.
 */

#include "olb2D.h"
#include "olb2D.hh"

#include <vector>
#include <cmath>
#include <iostream>
#include <iomanip>
#include <fstream>

using namespace olb;
using namespace olb::descriptors;
using namespace olb::graphics;
using namespace std;

typedef double T;

#define DESCRIPTOR D2Q9Descriptor

const T lx  = 2.;             // length of the channel
const T ly  = 1.;             // height of the channel
const int N = 16;             // resolution of the model
const T Re = 10.;             // Reynolds number
const T maxPhysT = 40.;       // max. simulation time in s, SI unit
const T physInterval = 0.25;  // interval for the convergence check in s
const T residuum = 1e-5;      // residuum for the convergence check


void prepareGeometry(UnitConverter<T,DESCRIPTOR> const& converter,
                     SuperGeometry2D<T>& superGeometry)
{

  OstreamManager clout(std::cout,"prepareGeometry");
  clout << "Prepare Geometry ..." << std::endl;

  superGeometry.rename(0,2);
  // Set material number for bounce back boundaries
  superGeometry.rename(2,1,0,1);

  Vector<T,2> extend;
  Vector<T,2> origin;
  T physSpacing = converter.getPhysDeltaX();

  // Set material number for inflow
  extend[1] = ly;
  extend[0] = physSpacing / 2;
  origin[0] -= physSpacing / 4;
  IndicatorCuboid2D<T> inflow(extend, origin);
  superGeometry.rename(1,3,1,inflow);

  // Set material number for outflow
  origin[0] = lx - physSpacing / 4;
  IndicatorCuboid2D<T> outflow(extend, origin);
  superGeometry.rename(1,4,1,outflow);

  // Removes all not needed boundary voxels outside the surface
  superGeometry.clean();
  // Removes all not needed boundary voxels inside the surface
  superGeometry.innerClean();
  superGeometry.checkForErrors();

  superGeometry.print();

  clout << "Prepare Geometry ... OK" << std::endl;
}

void prepareCoarseLattice(UnitConverter<T,DESCRIPTOR> const& converter,
                          SuperLattice2D<T, DESCRIPTOR>& sLattice,
                          Dynamics<T, DESCRIPTOR>& bulkDynamics,
                          sOnLatticeBoundaryCondition2D<T,DESCRIPTOR>& sBoundaryCondition,
                          SuperGeometry2D<T>& superGeometry)
{
  OstreamManager clout(std::cout,"prepareLattice");
  clout << "Prepare coarse lattice ..." << std::endl;

  const T omega = converter.getLatticeRelaxationFrequency();

  sLattice.defineDynamics(superGeometry, 0, &instances::getNoDynamics<T, DESCRIPTOR>());
  sLattice.defineDynamics(superGeometry, 1, &bulkDynamics); // bulk
  sLattice.defineDynamics(superGeometry, 2, &instances::getBounceBack<T, DESCRIPTOR>());
  sLattice.defineDynamics(superGeometry, 3, &bulkDynamics); // inflow

  sBoundaryCondition.addVelocityBoundary(superGeometry, 3, omega);

  T Lx = converter.getLatticeLength(lx);
  T Ly = converter.getLatticeLength(ly);

  T p0 =8.*converter.getLatticeViscosity()*converter.getCharLatticeVelocity()*Lx/(Ly*Ly);
  AnalyticalLinear2D<T,T> rho(-p0/lx*DESCRIPTOR<T>::invCs2, 0, p0*DESCRIPTOR<T>::invCs2+1);

  AnalyticalConst2D<T,T> iniRho(1);
  AnalyticalConst2D<T,T> iniU(std::vector<T> {0.,0.});

  sLattice.defineRhoU(superGeometry, 1, iniRho, iniU);
  sLattice.iniEquilibrium(superGeometry, 1, iniRho, iniU);
  sLattice.defineRhoU(superGeometry, 2, iniRho, iniU);
  sLattice.iniEquilibrium(superGeometry, 2, iniRho, iniU);

  T maxVelocity = converter.getCharLatticeVelocity();
  T distance2Wall = converter.getConversionFactorLength();
  Poiseuille2D<T> u(superGeometry, 3, maxVelocity, distance2Wall);

  sLattice.defineRhoU(superGeometry, 3, rho, u);
  sLattice.iniEquilibrium(superGeometry, 3, rho, u);

  sLattice.initialize();

  clout << "Prepare Lattice ... OK" << std::endl;
}

void prepareFineLattice(UnitConverter<T,DESCRIPTOR> const& converter,
                        SuperLattice2D<T, DESCRIPTOR>& sLattice,
                        Dynamics<T, DESCRIPTOR>& bulkDynamics,
                        sOnLatticeBoundaryCondition2D<T,DESCRIPTOR>& sBoundaryCondition,
                        SuperGeometry2D<T>& superGeometry)
{
  OstreamManager clout(std::cout,"prepareLattice");
  clout << "Prepare Lattice ..." << std::endl;

  const T omega = converter.getLatticeRelaxationFrequency();

  sLattice.defineDynamics(superGeometry, 0, &instances::getNoDynamics<T, DESCRIPTOR>());
  sLattice.defineDynamics(superGeometry, 1, &bulkDynamics); // bulk
  sLattice.defineDynamics(superGeometry, 2, &instances::getBounceBack<T, DESCRIPTOR>());
  sLattice.defineDynamics(superGeometry, 4, &bulkDynamics); // outflow

  sBoundaryCondition.addPressureBoundary(superGeometry, 4, omega);

  T Lx = converter.getLatticeLength(lx);
  T Ly = converter.getLatticeLength(ly);

  T p0 =8.*converter.getLatticeViscosity()*converter.getCharLatticeVelocity()*Lx/(Ly*Ly);
  AnalyticalLinear2D<T,T> rho(-p0/lx*DESCRIPTOR<T>::invCs2, 0, p0*DESCRIPTOR<T>::invCs2+1);

  AnalyticalConst2D<T,T> iniRho(1);
  AnalyticalConst2D<T,T> iniU(std::vector<T> {0.,0.});

  sLattice.defineRhoU(superGeometry, 1, iniRho, iniU);
  sLattice.iniEquilibrium(superGeometry, 1, iniRho, iniU);
  sLattice.defineRhoU(superGeometry, 2, iniRho, iniU);
  sLattice.iniEquilibrium(superGeometry, 2, iniRho, iniU);
  sLattice.defineRhoU(superGeometry, 4, iniRho, iniU);
  sLattice.iniEquilibrium(superGeometry, 4, iniRho, iniU);

  sLattice.initialize();

  clout << "Prepare Lattice ... OK" << std::endl;
}

void getResults(const std::string& prefix,
                SuperLattice2D<T,DESCRIPTOR>& sLattice,
                UnitConverter<T,DESCRIPTOR> const& converter, int iT,
                SuperGeometry2D<T>& superGeometry, Timer<T>& timer, bool hasConverged)
{
  OstreamManager clout(std::cout,"getResults");

  SuperVTMwriter2D<T> vtmWriter(prefix + "poiseuille2d");
  SuperLatticePhysVelocity2D<T, DESCRIPTOR> velocity(sLattice, converter);
  SuperLatticePhysPressure2D<T, DESCRIPTOR> pressure(sLattice, converter);
  SuperLatticeGeometry2D<T, DESCRIPTOR> geometry( sLattice, superGeometry );
  vtmWriter.addFunctor(geometry);
  vtmWriter.addFunctor(velocity);
  vtmWriter.addFunctor(pressure);

  const int statIter = converter.getLatticeTime(maxPhysT/10.);

  if (iT==0) {
    vtmWriter.createMasterFile();
  }

  if (iT%100==0) {
    vtmWriter.write(iT);
  }

  if (iT%statIter==0 || hasConverged) {
    timer.update(iT);
    timer.printStep();

    sLattice.getStatistics().print(iT,converter.getPhysTime(iT));
  }
}

template <typename T, template<typename> class DESCRIPTOR>
class Grid {
private:
  std::unique_ptr<UnitConverter<T,DESCRIPTOR>>  _converter;
  std::unique_ptr<CuboidGeometry2D<T>>          _cuboids;
  std::unique_ptr<LoadBalancer<T>>              _balancer;
  std::unique_ptr<SuperGeometry2D<T>>           _geometry;
  std::unique_ptr<SuperLattice2D<T,DESCRIPTOR>> _lattice;

public:
  Grid(IndicatorF2D<T>& domainF, int resolution, T tau, int re):
    _converter(new UnitConverterFromResolutionAndRelaxationTime<T,DESCRIPTOR>(
                 resolution, // resolution: number of voxels per charPhysL
                 tau,        // latticeRelaxationTime: relaxation time, has to be greater than 0.5!
                 T{1},       // charPhysLength: reference length of simulation geometry
                 T{1},       // charPhysVelocity: maximal/highest expected velocity during simulation in __m / s__
                 T{1./re},   // physViscosity: physical kinematic viscosity in __m^2 / s__
                 T{1})),     // physDensity: physical density in __kg / m^3__
    _cuboids(new CuboidGeometry2D<T>(
               domainF,
               _converter->getConversionFactorLength(),
               1)),
    _balancer(new HeuristicLoadBalancer<T>(
                *_cuboids)),
    _geometry(new SuperGeometry2D<T>(
                *_cuboids,
                *_balancer,
                2)),
    _lattice(new SuperLattice2D<T,DESCRIPTOR>(
               *_geometry))
  {
    _converter->print();
  }

  UnitConverter<T,DESCRIPTOR>& getConverter()
  {
    return *_converter;
  }

  CuboidGeometry2D<T>& getCuboidGeometry()
  {
    return *_cuboids;
  }

  LoadBalancer<T>& getLoadBalancer()
  {
    return *_balancer;
  }

  SuperGeometry2D<T>& getSuperGeometry()
  {
    return *_geometry;
  }

  SuperLattice2D<T,DESCRIPTOR>& getSuperLattice()
  {
    return *_lattice;
  }

  T getScalingFactor()
  {
    return 4. - _converter->getLatticeRelaxationFrequency();
  }

  T getInvScalingFactor()
  {
    return 1./getScalingFactor();
  }
};

T order4interpolation(T fm3, T fm1, T f1, T f3)
{
  return 9./16. * (fm1 + f1) - 1./16. * (fm3 + f3);
}

T order3interpolation(T fm1, T f1, T f3)
{
  return 3./8. * fm1 + 3./4. * f1 - 1./8. * f3;
}

template <typename T, template<typename> class DESCRIPTOR>
void coupleC2F(Grid<T,DESCRIPTOR>& coarse, Grid<T,DESCRIPTOR>& fine)
{
  auto& coarseLattice = coarse.getSuperLattice().getBlockLattice(0);
  auto& fineLattice   = fine.getSuperLattice().getBlockLattice(0);

  const int x = coarseLattice.getNx()-2;

  for (int y=0; y < coarseLattice.getNy(); ++y) {
    for (int i=0; i < DESCRIPTOR<T>::q; ++i) {
      fineLattice.get(0, 2*y)[i] = coarseLattice.get(x,y)[i];
    }
  }

  for (int y=2; y < coarseLattice.getNy()-2; ++y) {
    for (int i=0; i < DESCRIPTOR<T>::q; ++i) {
      fineLattice.get(0,1+2*y)[i] = order4interpolation(
                                      coarseLattice.get(x,y-1)[i],
                                      coarseLattice.get(x,y)[i],
                                      coarseLattice.get(x,y+1)[i],
                                      coarseLattice.get(x,y+2)[i]
                                    );
    }
  }

  for (int i=0; i < DESCRIPTOR<T>::q; ++i) {
    fineLattice.get(0,1)[i] = order3interpolation(
                                coarseLattice.get(x,0)[i],
                                coarseLattice.get(x,1)[i],
                                coarseLattice.get(x,2)[i]
                              );
    fineLattice.get(0,fineLattice.getNy()-2)[i] = order3interpolation(
          coarseLattice.get(x,coarseLattice.getNy()-1)[i],
          coarseLattice.get(x,coarseLattice.getNy()-2)[i],
          coarseLattice.get(x,coarseLattice.getNy()-3)[i]
        );
  }
}

template <typename T, template<typename> class DESCRIPTOR>
void computeFneq(const Cell<T,DESCRIPTOR>& cell, T fNeq[DESCRIPTOR<T>::q])
{
  T rho{};
  T u[2]{};
  cell.computeRhoU(rho, u);
  lbHelpers<T,DESCRIPTOR>::computeFneq(cell, fNeq, rho, u);
}

template <typename T, template<typename> class DESCRIPTOR>
void computeFeq(const Cell<T,DESCRIPTOR>& cell, T fEq[DESCRIPTOR<T>::q])
{
  T rho{};
  T u[2]{};
  cell.computeRhoU(rho, u);
  const T uSqr = u[0]*u[0] + u[1]*u[1];
  for (int i=0; i < DESCRIPTOR<T>::q; ++i) {
    fEq[i] = lbHelpers<T,DESCRIPTOR>::equilibrium(i, rho, u, uSqr);
  }
}

template <typename T, template<typename> class DESCRIPTOR>
T computeRestrictedFneq(const BlockLatticeView2D<T,DESCRIPTOR>& lattice, int x, int y)
{
  T sum = T{0};
  for (int i=0; i < DESCRIPTOR<T>::q; ++i) {
    T fNeq[DESCRIPTOR<T>::q]{};
    computeFneq(lattice.get(x + DESCRIPTOR<T>::c[i][0], y + DESCRIPTOR<T>::c[i][1]), fNeq);
    sum += fNeq[i];
  }
  return sum / DESCRIPTOR<T>::q;
}

template <typename T, template<typename> class DESCRIPTOR>
void coupleF2C(Grid<T,DESCRIPTOR>& coarse, Grid<T,DESCRIPTOR>& fine)
{
  auto& coarseLattice = coarse.getSuperLattice().getBlockLattice(0);
  auto& fineLattice   = fine.getSuperLattice().getBlockLattice(0);

  const int x = coarseLattice.getNx()-1;
  for (int y=0; y < coarseLattice.getNy(); ++y) {
    T fEq[DESCRIPTOR<T>::q]{};
    computeFeq(fineLattice.get(2,2*y), fEq);

    const T restrictedFneq = computeRestrictedFneq(fineLattice, 2, 2*y);

    for (int i=0; i < DESCRIPTOR<T>::q; ++i) {
      coarseLattice.get(x,y)[i] = fEq[i] + coarse.getInvScalingFactor() * restrictedFneq;
    }
  }
}

int main(int argc, char* argv[])
{
  olbInit(&argc, &argv);
  singleton::directories().setOutputDir("./tmp/");
  OstreamManager clout(std::cout,"main");

  const T coarseDeltaX = 1./N;

  Vector<T,2> coarseOrigin { 0.0, 0.0 };
  Vector<T,2> coarseExtend { 0.5 * lx, ly  };
  IndicatorCuboid2D<T> coarseCuboid(coarseExtend, coarseOrigin);
  Vector<T,2> fineOrigin   { 0.5 * lx - coarseDeltaX, 0.0 };
  Vector<T,2> fineExtend   { 0.5 * lx + coarseDeltaX, ly  };
  IndicatorCuboid2D<T> fineCuboid(fineExtend, fineOrigin);

  Grid<T,DESCRIPTOR> coarseGrid(
    coarseCuboid,
    N,
    0.8,
    Re);
  Grid<T,DESCRIPTOR> fineGrid(
    fineCuboid,
    2*coarseGrid.getConverter().getResolution(),
    2.0*coarseGrid.getConverter().getLatticeRelaxationTime() - 0.5,
    Re);

  prepareGeometry(coarseGrid.getConverter(), coarseGrid.getSuperGeometry());
  prepareGeometry(fineGrid.getConverter(), fineGrid.getSuperGeometry());

  Dynamics<T, DESCRIPTOR>* coarseBulkDynamics;
  coarseBulkDynamics = new BGKdynamics<T, DESCRIPTOR>(
    coarseGrid.getConverter().getLatticeRelaxationFrequency(),
    instances::getBulkMomenta<T, DESCRIPTOR>());

  sOnLatticeBoundaryCondition2D<T, DESCRIPTOR> coarseSBoundaryCondition(coarseGrid.getSuperLattice());
  createLocalBoundaryCondition2D<T, DESCRIPTOR>(coarseSBoundaryCondition);

  prepareCoarseLattice(
    coarseGrid.getConverter(),
    coarseGrid.getSuperLattice(),
    *coarseBulkDynamics,
    coarseSBoundaryCondition,
    coarseGrid.getSuperGeometry());

  Dynamics<T, DESCRIPTOR>* fineBulkDynamics;
  fineBulkDynamics = new BGKdynamics<T, DESCRIPTOR>(
    fineGrid.getConverter().getLatticeRelaxationFrequency(),
    instances::getBulkMomenta<T, DESCRIPTOR>());

  sOnLatticeBoundaryCondition2D<T, DESCRIPTOR> fineSBoundaryCondition(fineGrid.getSuperLattice());
  createLocalBoundaryCondition2D<T, DESCRIPTOR>(fineSBoundaryCondition);

  prepareFineLattice(
    fineGrid.getConverter(),
    fineGrid.getSuperLattice(),
    *fineBulkDynamics,
    fineSBoundaryCondition,
    fineGrid.getSuperGeometry());

  clout << "starting simulation..." << endl;
  Timer<T> timer(
    coarseGrid.getConverter().getLatticeTime(maxPhysT),
    coarseGrid.getSuperGeometry().getStatistics().getNvoxel());
  util::ValueTracer<T> converge(
    fineGrid.getConverter().getLatticeTime(physInterval),
    residuum);
  timer.start();

  for (int iT = 0; iT < coarseGrid.getConverter().getLatticeTime(maxPhysT); ++iT) {
    if (converge.hasConverged()) {
      clout << "Simulation converged." << endl;
      break;
    }

    coarseGrid.getSuperLattice().collideAndStream();
    fineGrid.getSuperLattice().collideAndStream();
    coupleC2F(coarseGrid, fineGrid);
    fineGrid.getSuperLattice().collideAndStream();
    coupleC2F(coarseGrid, fineGrid);
    coupleF2C(coarseGrid, fineGrid);

    getResults(
      "coarse_",
      coarseGrid.getSuperLattice(),
      coarseGrid.getConverter(),
      iT,
      coarseGrid.getSuperGeometry(),
      timer,
      converge.hasConverged());
    getResults(
      "fine_",
      fineGrid.getSuperLattice(),
      fineGrid.getConverter(),
      iT,
      fineGrid.getSuperGeometry(),
      timer,
      converge.hasConverged());

    converge.takeValue(fineGrid.getSuperLattice().getStatistics().getAverageEnergy(), true);
  }

  timer.stop();
  timer.printSummary();
}