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diff --git a/src/boundary/inamuroNewtonRaphsonDynamics.hh b/src/boundary/inamuroNewtonRaphsonDynamics.hh new file mode 100644 index 0000000..8e28ed7 --- /dev/null +++ b/src/boundary/inamuroNewtonRaphsonDynamics.hh @@ -0,0 +1,456 @@ +/* This file is part of the OpenLB library + * + * Copyright (C) 2006, Orestis Malaspinas and Jonas Latt + * 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. +*/ + +#ifndef INAMURO_NEWTON_RAPHSON_DYNAMICS_HH +#define INAMURO_NEWTON_RAPHSON_DYNAMICS_HH + +#include "inamuroNewtonRaphsonDynamics.h" +#include "dynamics/latticeDescriptors.h" +#include "core/util.h" +#include "dynamics/lbHelpers.h" +#include <cmath> + + +namespace olb { + + + +template<typename T, typename DESCRIPTOR, typename Dynamics, int direction, int orientation> +InamuroNewtonRaphsonDynamics<T,DESCRIPTOR,Dynamics,direction,orientation>::InamuroNewtonRaphsonDynamics ( + T omega, Momenta<T,DESCRIPTOR>& momenta ) + : BasicDynamics<T,DESCRIPTOR>(momenta), + _boundaryDynamics(omega, momenta), + clout(std::cout,"InamuroNewtonRaphsonDynamics") +{ + _xi[0] = (T)1; + for (int iDim = 1; iDim < DESCRIPTOR::d; ++iDim) { + _xi[iDim] = T(); + } +} + +template<typename T, typename DESCRIPTOR, typename Dynamics, int direction, int orientation> +T InamuroNewtonRaphsonDynamics<T,DESCRIPTOR, Dynamics, direction, orientation>:: +computeEquilibrium(int iPop, T rho, const T u[DESCRIPTOR::d], T uSqr) const +{ + return _boundaryDynamics.computeEquilibrium(iPop, rho, u, uSqr); +} + +template<typename T, typename DESCRIPTOR, typename Dynamics, int direction, int orientation> +void InamuroNewtonRaphsonDynamics<T,DESCRIPTOR,Dynamics,direction,orientation>::collide ( + Cell<T,DESCRIPTOR>& cell, + LatticeStatistics<T>& statistics ) +{ + typedef DESCRIPTOR L; + + T rho, u[L::d]; + this->_momenta.computeRhoU(cell,rho,u); + + std::vector<int> missingIndexes = util::subIndexOutgoing<L,direction,orientation>(); + std::vector<int> knownIndexes; + bool test[L::q]; + for (int iPop = 0; iPop < L::q; ++iPop) { + test[iPop] = true; + } + + for (unsigned iPop = 0; iPop < missingIndexes.size(); ++iPop) { + test[missingIndexes[iPop]] = false; + } + for (int iPop = 0; iPop < L::q; ++iPop) { + if (test[iPop]) { + knownIndexes.push_back(iPop); + } + } + + T approxMomentum[L::d]; + + computeApproxMomentum(approxMomentum,cell,rho,u,_xi,knownIndexes,missingIndexes); + + T error = computeError(rho, u,approxMomentum); + int counter = 0; + + while (error > 1.0e-15) { + ++counter; + + T gradError[L::d], gradGradError[L::d][L::d]; + computeGradGradError(gradGradError,gradError,rho,u,_xi,approxMomentum,missingIndexes); + + bool everythingWentFine = newtonRaphson(_xi,gradError,gradGradError); + if ((counter > 100000) || everythingWentFine == false) { + // if we need more that 100000 iterations or + // if we have a problem with the inversion of the + // jacobian matrix, we stop the program and + // print this error message on the screen. + clout << "Failed to converge...." << std::endl; + clout << "Error = " << error << std::endl; + clout << "u = (" << rho*u[0]; + for (int iD=1; iD<DESCRIPTOR::d; ++iD) { + clout << ", " << rho*u[iD]; + } + clout << ")" << std::endl; + clout << "uApprox = (" << approxMomentum[0]; + for (int iD=1; iD<DESCRIPTOR::d; ++iD) { + clout << ", " << approxMomentum[iD]; + } + clout << ")" << std::endl; + clout << "xi = (" << _xi[0]; + for (int iD=1; iD<DESCRIPTOR::d; ++iD) { + clout << ", " << _xi[iD]; + } + clout << ")" << std::endl; + + exit(1); + } + + computeApproxMomentum(approxMomentum,cell,rho,u,_xi,knownIndexes,missingIndexes); + error = computeError(rho, u,approxMomentum); + + } + + T uCs[L::d]; + int counterDim = 0; + for (int iDim = 0; iDim < L::d; ++iDim) { + if (direction == iDim) { + ++counterDim; + uCs[iDim] = u[iDim]; + } else { + uCs[iDim] = u[iDim] + _xi[iDim+1-counterDim]; + } + } + + T uCsSqr = util::normSqr<T,L::d>(uCs); + + for (unsigned iPop = 0; iPop < missingIndexes.size(); ++iPop) { + cell[missingIndexes[iPop]] = computeEquilibrium(missingIndexes[iPop],_xi[0],uCs,uCsSqr); + } + + _boundaryDynamics.collide(cell, statistics); +} + +template<typename T, typename DESCRIPTOR, typename Dynamics, int direction, int orientation> +T InamuroNewtonRaphsonDynamics<T,DESCRIPTOR,Dynamics,direction,orientation>::getOmega() const +{ + return _boundaryDynamics.getOmega(); +} + +template<typename T, typename DESCRIPTOR, typename Dynamics, int direction, int orientation> +void InamuroNewtonRaphsonDynamics<T,DESCRIPTOR,Dynamics,direction,orientation>::setOmega(T omega) +{ + _boundaryDynamics.setOmega(omega); +} + +template<typename T, typename DESCRIPTOR, typename Dynamics, int direction, int orientation> +void InamuroNewtonRaphsonDynamics<T,DESCRIPTOR,Dynamics,direction,orientation>:: +computeApproxMomentum(T approxMomentum[DESCRIPTOR::d],const Cell<T,DESCRIPTOR> &cell, + const T &rho, const T u[DESCRIPTOR::d], const T xi[DESCRIPTOR::d], + const std::vector<int> knownIndexes,const std::vector<int> missingIndexes) +{ + typedef DESCRIPTOR L; + + T csVel[L::d]; + int counter = 0; + for (int iDim = 0; iDim < L::d; ++iDim) { + if (direction == iDim) { + ++counter; + csVel[iDim] = u[iDim]; + } else { + csVel[iDim] = u[iDim] + xi[iDim+1-counter]; + } + } + + T csVelSqr = util::normSqr<T,L::d>(csVel); + + for (int iDim = 0; iDim < L::d; ++iDim) { + approxMomentum[iDim] = T(); + for (unsigned iPop = 0; iPop < knownIndexes.size(); ++iPop) { + approxMomentum[iDim] += descriptors::c<L>(knownIndexes[iPop],iDim) * + cell[knownIndexes[iPop]]; + } + for (unsigned iPop = 0; iPop < missingIndexes.size(); ++iPop) { + approxMomentum[iDim] += descriptors::c<L>(missingIndexes[iPop],iDim) * + computeEquilibrium(missingIndexes[iPop],xi[0],csVel,csVelSqr); + } + } +} + +template<typename T, typename DESCRIPTOR, typename Dynamics, int direction, int orientation> +T InamuroNewtonRaphsonDynamics<T,DESCRIPTOR,Dynamics,direction,orientation>:: +computeError(const T &rho, const T u[DESCRIPTOR::d], const T approxMomentum[DESCRIPTOR::d]) +{ + typedef DESCRIPTOR L; + + T err = T(); + for (int iDim = 0; iDim < L::d; ++iDim) { + err += (rho * u[iDim]-approxMomentum[iDim]) * (rho * u[iDim]-approxMomentum[iDim]); + } + return sqrt(err); +} + +template<typename T, typename DESCRIPTOR, typename Dynamics, int direction, int orientation> +void InamuroNewtonRaphsonDynamics<T,DESCRIPTOR,Dynamics,direction,orientation>::computeGradGradError( + T gradGradError[DESCRIPTOR::d][DESCRIPTOR::d],T gradError[DESCRIPTOR::d], + const T &rho, const T u[DESCRIPTOR::d],const T xi[DESCRIPTOR::d], + const T approxMomentum[DESCRIPTOR::d], + const std::vector<int> missingIndexes) +{ + typedef DESCRIPTOR L; + + T csVel[L::d]; + int counter = 0; + for (int iDim = 0; iDim < L::d; ++iDim) { + if (direction == iDim) { + ++counter; + csVel[iDim] = u[iDim]; + } else { + csVel[iDim] = u[iDim] + xi[iDim+1-counter]; + } + } + T csVelSqr = util::normSqr<T,L::d>(csVel); + + std::vector<T> df[L::d]; + + for (int iXi = 0; iXi < L::d; ++iXi) { + for (unsigned iPop = 0; iPop < missingIndexes.size(); ++iPop) { + df[iXi].push_back(T()); + } + } + + // all the null terms are allready contained in df (no need for else in the ifs) + + for (unsigned iPop = 0; iPop < missingIndexes.size(); ++iPop) { + T cu = T(); + for (int iDim = 0; iDim < L::d; ++iDim) { + cu += descriptors::c<L>(missingIndexes[iPop],iDim) * csVel[iDim]; + } + df[0][iPop] = descriptors::t<T,L>(missingIndexes[iPop]) + * ((T)1+descriptors::invCs2<T,L>()*cu + + 0.5 * descriptors::invCs2<T,L>() * descriptors::invCs2<T,L>() * cu * cu + - 0.5 * descriptors::invCs2<T,L>() * csVelSqr); + } + + counter = 0; + for (int iDim = 0; iDim < L::d; ++iDim) { + if (direction == iDim) { + ++counter; + } else { + for (unsigned iPop = 0; iPop < missingIndexes.size(); ++iPop) { + T temp = T(); + for (int jDim = 0; jDim < L::d; ++jDim) { + temp += descriptors::c<L>(missingIndexes[iPop],jDim) * csVel[jDim]; + } + + df[iDim+1-counter][iPop] = xi[0]*descriptors::t<T,L>(missingIndexes[iPop]) * + (descriptors::invCs2<T,L>()*descriptors::c<L>(missingIndexes[iPop],iDim) + + descriptors::invCs2<T,L>()*descriptors::invCs2<T,L>()*descriptors::c<L>(missingIndexes[iPop],iDim)*temp + - descriptors::invCs2<T,L>()*csVel[iDim]); + } + } + } + + std::vector<T> ddf[L::d][L::d]; + + for (int iAlpha = 0; iAlpha < L::d; ++iAlpha) { + for (int iBeta = 0; iBeta < L::d; ++iBeta) { + for (unsigned iPop = 0; iPop < missingIndexes.size(); ++iPop) { + ddf[iAlpha][iBeta].push_back(T()); + } + } + } + + // ddf contains allready all the zero terms + + counter = 0; + for (int iDim = 0; iDim < L::d; ++iDim) { + if (direction == iDim) { + ++counter; + } else { + for (unsigned iPop = 0; iPop < missingIndexes.size(); ++iPop) { + T temp = T(); + for (int jDim = 0; jDim < L::d; ++jDim) { + temp += descriptors::c<L>(missingIndexes[iPop],jDim) * csVel[jDim]; + } + + T d_rho_sa = descriptors::t<T,L>(missingIndexes[iPop]) * + (descriptors::invCs2<T,L>()*descriptors::c<L>(missingIndexes[iPop],iDim) + + descriptors::invCs2<T,L>()*descriptors::invCs2<T,L>()*descriptors::c<L>(missingIndexes[iPop],iDim)*temp + - descriptors::invCs2<T,L>()*csVel[iDim]); + + ddf[iDim+1-counter][0][iPop] = d_rho_sa; + ddf[0][iDim+1-counter][iPop] = d_rho_sa; + } + } + } + + for (int iAlpha = 1; iAlpha < L::d; ++iAlpha) { + for (int iBeta = 1; iBeta < L::d; ++iBeta) { + for (unsigned iPop = 0; iPop < missingIndexes.size(); ++iPop) { + ddf[iAlpha][iBeta][iPop] = descriptors::t<T,L>(missingIndexes[iPop])*xi[0] * + descriptors::invCs2<T,L>()*descriptors::invCs2<T,L>()*descriptors::c<L>(missingIndexes[iPop],iAlpha)*descriptors::c<L>(missingIndexes[iPop],iBeta); + if (iAlpha == iBeta) { + ddf[iAlpha][iBeta][iPop] -= descriptors::t<T,L>(missingIndexes[iPop])*xi[0] * descriptors::invCs2<T,L>(); + } + } + } + } + + // computation of the vector gradError + counter = 0; + for (int iDim = 0; iDim < L::d; ++iDim) { + T du[L::d]; + gradError[iDim] = T(); + for (int jDim = 0; jDim < L::d; ++jDim) { + du[jDim] = T(); + for (unsigned iPop = 0; iPop < missingIndexes.size(); ++iPop) { + du[jDim] += descriptors::c<L>(missingIndexes[iPop],jDim) * df[iDim][iPop]; + } + gradError[iDim] += (approxMomentum[jDim]- rho * u[jDim]) * du[jDim]; + } + gradError[iDim] *= (T)2; + } + + // computation of the matrix gradGradError + + for (int iAlpha = 0; iAlpha < L::d; ++iAlpha) { + for (int iBeta = 0; iBeta < L::d; ++iBeta) { + gradGradError[iAlpha][iBeta] = T(); + + T duAlpha[L::d], duBeta[L::d], ddu[L::d]; + for (int iDim = 0; iDim < L::d; ++iDim) { + duAlpha[iDim] = T(); + duBeta[iDim] = T(); + ddu[iDim] = T(); + for (unsigned iPop = 0; iPop < missingIndexes.size(); ++iPop) { + duAlpha[iDim] += descriptors::c<L>(missingIndexes[iPop],iDim) + * df[iAlpha][iPop]; + + duBeta[iDim] += descriptors::c<L>(missingIndexes[iPop],iDim) + * df[iBeta][iPop]; + + ddu[iDim] += descriptors::c<L>(missingIndexes[iPop],iDim) + * ddf[iAlpha][iBeta][iPop]; + } + gradGradError[iAlpha][iBeta] += duAlpha[iDim] * duBeta[iDim] + + (approxMomentum[iDim]-rho * u[iDim]) * ddu[iDim]; + } + gradGradError[iAlpha][iBeta] *= (T)2; + // gradGradError = 2*sum_alpha(du_alpha/dxi_beta*du_alpha/dxi_gamma + + // approxMomentum_alpha-u_alpha*d^2u_alpha/(dxi_gamma*dxi_beta)) + } + } +} + +template<typename T, typename DESCRIPTOR, typename Dynamics, int direction, int orientation> +bool InamuroNewtonRaphsonDynamics<T,DESCRIPTOR,Dynamics,direction,orientation>:: +newtonRaphson(T xi[DESCRIPTOR::d], + const T gradError[DESCRIPTOR::d], + const T gradGradError[DESCRIPTOR::d][DESCRIPTOR::d]) +{ + typedef DESCRIPTOR L; + + T invGradGradError[L::d][L::d]; + bool inversion = invert(gradGradError,invGradGradError); + + for (int iXi = 0; iXi < L::d; ++iXi) { + T correction = T(); + for (int iAlpha = 0; iAlpha < L::d; ++iAlpha) { + correction += invGradGradError[iXi][iAlpha] * gradError[iAlpha]; + } + + xi[iXi] -= correction; + } + + return inversion; +} + +template<typename T, typename DESCRIPTOR, typename Dynamics, int direction, int orientation> +bool InamuroNewtonRaphsonDynamics<T,DESCRIPTOR,Dynamics,direction,orientation>:: +invert(const T a[2][2],T invA[2][2]) +{ + T detA = a[0][0]*a[1][1] - a[0][1]*a[1][0]; + + if (fabs(detA) < 1.0e-13) { + clout << "error detA too small! = " << detA << std::endl; + for (int iAlpha = 0; iAlpha < 2; ++iAlpha) { + for (int iBeta = 0; iBeta < 2; ++iBeta) { + clout << a[iAlpha][iBeta] << "\t"; + } + clout << std::endl; + } + return false; + } else { + invA[0][0] = a[1][1]; + invA[1][1] = a[0][0]; + + invA[0][1] = -a[1][0]; + invA[1][0] = -a[0][1]; + + for (int iPop = 0; iPop < 2; ++iPop) { + for (int jPop = 0; jPop < 2; ++jPop) { + invA[iPop][jPop] /= detA; + } + } + return true; + } +} + +template<typename T, typename DESCRIPTOR, typename Dynamics, int direction, int orientation> +bool InamuroNewtonRaphsonDynamics<T,DESCRIPTOR,Dynamics,direction,orientation>::invert(const T a[3][3],T invA[3][3]) +{ + T detA = a[0][0]*a[1][1]*a[2][2] + a[1][0]*a[2][1]*a[0][2] + a[2][0]*a[0][1]*a[1][2] + - a[0][0]*a[2][1]*a[1][2] - a[2][0]*a[1][1]*a[0][2] - a[1][0]*a[0][1]*a[2][2]; + + + if (fabs(detA) < 1.0e-13) { + clout << "Error: detA too small! = " << detA << std::endl; + for (int iAlpha = 0; iAlpha < 3; ++iAlpha) { + for (int iBeta = 0; iBeta < 3; ++iBeta) { + clout << a[iAlpha][iBeta] << "\t"; + } + clout << std::endl; + } + return false; + } else { + invA[0][0] = a[1][1]*a[2][2]-a[1][2]*a[2][1]; + invA[0][1] = a[0][2]*a[2][1]-a[0][1]*a[2][2]; + invA[0][2] = a[0][1]*a[1][2]-a[0][2]*a[1][1]; + + invA[1][0] = a[1][2]*a[2][0]-a[1][0]*a[2][2]; + invA[1][1] = a[0][0]*a[2][2]-a[0][2]*a[2][0]; + invA[1][2] = a[0][2]*a[1][0]-a[0][0]*a[1][2]; + + invA[2][0] = a[1][0]*a[2][1]-a[1][1]*a[2][0]; + invA[2][1] = a[0][1]*a[2][0]-a[0][0]*a[2][1]; + invA[2][2] = a[0][0]*a[1][1]-a[0][1]*a[1][0]; + + for (int iPop = 0; iPop < 3; ++iPop) { + for (int jPop = 0; jPop < 3; ++jPop) { + invA[iPop][jPop] /= detA; + } + } + return true; + } +} + +} // namespace olb + + +#endif |