SolidCRKSPHHydroBaseRZ.cc

//---------------------------------Spheral++----------------------------------//
// SolidCRKSPHHydroBase -- The CRKSPH/ACRKSPH solid material hydrodynamic
// package for Spheral++.
//
// This is the area-weighted RZ specialization.
//
// Created by JMO, Fri May 13 10:50:36 PDT 2016
//----------------------------------------------------------------------------//
#include "FileIO/FileIO.hh"
#include "RK/ReproducingKernel.hh"
#include "RK/RKFieldNames.hh"
#include "CRKSPH/CRKSPHHydroBase.hh"
#include "CRKSPH/computeCRKSPHSumMassDensity.hh"
#include "Physics/GenericHydro.hh"
#include "Hydro/HydroFieldNames.hh"
#include "Hydro/RZNonSymmetricSpecificThermalEnergyPolicy.hh"
#include "Strength/SolidFieldNames.hh"
#include "NodeList/SolidNodeList.hh"
#include "Strength/BulkModulusPolicy.hh"
#include "Strength/ShearModulusPolicy.hh"
#include "Strength/YieldStrengthPolicy.hh"
#include "DataBase/State.hh"
#include "DataBase/StateDerivatives.hh"
#include "DataBase/IncrementState.hh"
#include "DataBase/IncrementBoundedState.hh"
#include "DataBase/ReplaceState.hh"
#include "DataBase/ReplaceBoundedState.hh"
#include "RK/ContinuityVolumePolicyRZ.hh"
#include "ArtificialViscosity/ArtificialViscosity.hh"
#include "DataBase/DataBase.hh"
#include "Field/FieldList.hh"
#include "Field/NodeIterators.hh"
#include "Boundary/Boundary.hh"
#include "Neighbor/ConnectivityMap.hh"
#include "Utilities/safeInv.hh"
#include "Utilities/range.hh"
#include "Utilities/NodeCoupling.hh"
#include "SolidMaterial/SolidEquationOfState.hh"
#include "Geometry/GeometryRegistrar.hh"

#include "CRKSPH/SolidCRKSPHHydroBaseRZ.hh"

#include <limits.h>
#include <float.h>
#include <algorithm>
#include <fstream>
#include <map>
#include <vector>
using std::vector;
using std::string;
using std::pair;
using std::make_pair;
using std::cout;
using std::cerr;
using std::endl;
using std::min;
using std::max;
using std::abs;

namespace Spheral {

//------------------------------------------------------------------------------
// Compute the artificial tensile stress correction tensor for the given 
// stress tensor
//------------------------------------------------------------------------------
inline
Dim<1>::SymTensor
tensileStressCorrection(const Dim<1>::SymTensor& sigma) {
  if (sigma.xx() > 0.0) {
    return -sigma;
  } else {
    return Dim<1>::SymTensor();
  }
}

inline
Dim<2>::SymTensor
tensileStressCorrection(const Dim<2>::SymTensor& sigma) {
  const EigenStruct<2> eigen = sigma.eigenVectors();
  const double lambdax = eigen.eigenValues.x();
  const double lambday = eigen.eigenValues.y();
  Dim<2>::SymTensor result((lambdax > 0.0 ? -lambdax : 0.0), 0.0,
                           0.0, (lambday > 0.0 ? -lambday : 0.0));
  result.rotationalTransform(eigen.eigenVectors);
  return result;
}

inline
Dim<3>::SymTensor
tensileStressCorrection(const Dim<3>::SymTensor& sigma) {
  const EigenStruct<3> eigen = sigma.eigenVectors();
  const double lambdax = eigen.eigenValues.x();
  const double lambday = eigen.eigenValues.y();
  const double lambdaz = eigen.eigenValues.z();
  Dim<3>::SymTensor result((lambdax > 0.0 ? -lambdax : 0.0), 0.0, 0.0,
                           0.0, (lambday > 0.0 ? -lambday : 0.0), 0.0,
                           0.0, 0.0, (lambdaz > 0.0 ? -lambdaz : 0.0));
  result.rotationalTransform(eigen.eigenVectors);
  return result;
}

//------------------------------------------------------------------------------
// Construct with the given artificial viscosity and kernels.
//------------------------------------------------------------------------------
SolidCRKSPHHydroBaseRZ::
SolidCRKSPHHydroBaseRZ(DataBase<Dimension>& dataBase,
                       ArtificialViscosity<Dimension>& Q,
                       const RKOrder order,
                       const double filter,
                       const double cfl,
                       const bool useVelocityMagnitudeForDt,
                       const bool compatibleEnergyEvolution,
                       const bool evolveTotalEnergy,
                       const bool XSPH,
                       const MassDensityType densityUpdate,
                       const double epsTensile,
                       const double nTensile,
                       const bool damageRelieveRubble):
  SolidCRKSPHHydroBase<Dimension>(dataBase,
                                  Q,
                                  order,
                                  filter,
                                  cfl,
                                  useVelocityMagnitudeForDt,
                                  compatibleEnergyEvolution,
                                  evolveTotalEnergy,
                                  XSPH,
                                  densityUpdate,
                                  epsTensile,
                                  nTensile,
                                  damageRelieveRubble) {
}

//------------------------------------------------------------------------------
// Destructor
//------------------------------------------------------------------------------
SolidCRKSPHHydroBaseRZ::
~SolidCRKSPHHydroBaseRZ() {
}

//------------------------------------------------------------------------------
// On problem start up, we need to initialize our internal data.
//------------------------------------------------------------------------------
void
SolidCRKSPHHydroBaseRZ::
initializeProblemStartup(DataBase<Dim<2>>& dataBase) {
  GeometryRegistrar::coords(CoordinateType::RZ);
}

//------------------------------------------------------------------------------
// On problem start up, we need to initialize our internal data.
//------------------------------------------------------------------------------
void
SolidCRKSPHHydroBaseRZ::
initializeProblemStartupDependencies(DataBase<Dim<2>>& dataBase,
                                     State<Dim<2>>& state,
                                     StateDerivatives<Dim<2>>& derivs) {

  // Correct the mass to mass/r.
  auto mass = dataBase.fluidMass();
  const auto pos = dataBase.fluidPosition();
  const unsigned numNodeLists = mass.numFields();
  for (unsigned nodeListi = 0; nodeListi != numNodeLists; ++nodeListi) {
    const unsigned n = mass[nodeListi]->numElements();
    for (unsigned i = 0; i != n; ++i) {
      const Scalar circi = 2.0*M_PI*abs(pos(nodeListi, i).y());
      mass(nodeListi, i) /= circi;
    }
  }

  // Call the ancestor.
  SolidCRKSPHHydroBase<Dimension>::initializeProblemStartupDependencies(dataBase, state, derivs);

  // Convert back to mass.
  for (unsigned nodeListi = 0; nodeListi != numNodeLists; ++nodeListi) {
    const unsigned n = mass[nodeListi]->numElements();
    for (unsigned i = 0; i != n; ++i) {
      const Scalar circi = 2.0*M_PI*abs(pos(nodeListi, i).y());
      mass(nodeListi, i) *= circi;
    }
  }
}

//------------------------------------------------------------------------------
// Register the state we need/are going to evolve.
//------------------------------------------------------------------------------
void
SolidCRKSPHHydroBaseRZ::
registerState(DataBase<Dim<2>>& dataBase,
              State<Dim<2>>& state) {

  // Call the ancestor.
  SolidCRKSPHHydroBase<Dimension>::registerState(dataBase, state);

  // // Reregister the deviatoric stress and plastic strain policies to the RZ specialized versions
  // // that account for the theta-theta component of the stress.
  // auto ps = state.fields(SolidFieldNames::plasticStrain, 0.0);
  // PolicyPointer plasticStrainPolicy(new RZPlasticStrainPolicy());
  // state.enroll(ps, plasticStrainPolicy);

  // Reregister the volume update
  auto vol = state.fields(HydroFieldNames::volume, 0.0);
  state.enroll(vol, make_policy<ContinuityVolumePolicyRZ>());

  // Are we using the compatible energy evolution scheme?
  // If so we need to override the ordinary energy registration with a specialized version.
  if (mCompatibleEnergyEvolution) {
    auto specificThermalEnergy = dataBase.fluidSpecificThermalEnergy();
    state.enroll(specificThermalEnergy, make_policy<RZNonSymmetricSpecificThermalEnergyPolicy>(dataBase));

    // Get the policy for the position, and add the specific energy as a dependency.
    auto positionPolicies = state.policies(HydroFieldNames::position);
    for (auto& keyval: positionPolicies) {
      keyval.second->addDependency(HydroFieldNames::specificThermalEnergy);
    }
  }
}

//------------------------------------------------------------------------------
// This method is called once at the beginning of a timestep, after all state registration.
//------------------------------------------------------------------------------
void
SolidCRKSPHHydroBaseRZ::
preStepInitialize(const DataBase<Dim<2>>& dataBase, 
                  State<Dim<2>>& state,
                  StateDerivatives<Dim<2>>& derivs) {

  // Convert the mass to mass per unit length first.
  auto mass = state.fields(HydroFieldNames::mass, 0.0);
  const auto pos = state.fields(HydroFieldNames::position, Vector::zero);
  const unsigned numNodeLists = mass.numFields();
  for (unsigned nodeListi = 0; nodeListi != numNodeLists; ++nodeListi) {
    const unsigned n = mass[nodeListi]->numElements();
    for (unsigned i = 0; i != n; ++i) {
      const auto circi = 2.0*M_PI*abs(pos(nodeListi, i).y());
#ifdef WIN32
      if (circi > 0.0) mass(nodeListi, i) /= circi;
#else
      mass(nodeListi, i) /= circi;
#endif
    }
  }

  // Base class finalization does most of the work.
  CRKSPHHydroBase<Dimension>::preStepInitialize(dataBase, state, derivs);

  // Now convert back to true masses.
  for (unsigned nodeListi = 0; nodeListi != numNodeLists; ++nodeListi) {
    const unsigned n = mass[nodeListi]->numElements();
    for (unsigned i = 0; i != n; ++i) {
      const auto& xi = pos(nodeListi, i);
      const auto circi = 2.0*M_PI*abs(xi.y());
#ifdef WIN32
      if (circi > 0.0) mass(nodeListi, i) *= circi;
#else
      mass(nodeListi, i) *= circi;
#endif
    }
  }
}

//------------------------------------------------------------------------------
// Determine the principle derivatives.
//------------------------------------------------------------------------------
void
SolidCRKSPHHydroBaseRZ::
evaluateDerivatives(const Dim<2>::Scalar /*time*/,
                    const Dim<2>::Scalar dt,
                    const DataBase<Dim<2>>& dataBase,
                    const State<Dim<2>>& state,
                    StateDerivatives<Dim<2>>& derivatives) const {

  // Get the ArtificialViscosity.
  auto& Q = this->artificialViscosity();

  // The kernels and such.
  const auto  order = this->correctionOrder();
  const auto& WR = state.template get<ReproducingKernel<Dimension>>(RKFieldNames::reproducingKernel(order));

  // A few useful constants we'll use in the following loop.
  //const double tiny = 1.0e-30;
  const auto  compatibleEnergy = this->compatibleEnergyEvolution();
  const auto  XSPH = this->XSPH();
  const auto  damageRelieveRubble = this->damageRelieveRubble();

  // The connectivity.
  const auto& connectivityMap = dataBase.connectivityMap();
  const auto& nodeLists = connectivityMap.nodeLists();
  const auto  numNodeLists = nodeLists.size();
  const auto& pairs = connectivityMap.nodePairList();
  const auto  npairs = pairs.size();

  // Get the state and derivative FieldLists.
  // State FieldLists.
  const auto mass = state.fields(HydroFieldNames::mass, 0.0);
  const auto volume = state.fields(HydroFieldNames::volume, 0.0);
  const auto position = state.fields(HydroFieldNames::position, Vector::zero);
  const auto velocity = state.fields(HydroFieldNames::velocity, Vector::zero);
  const auto massDensity = state.fields(HydroFieldNames::massDensity, 0.0);
  const auto specificThermalEnergy = state.fields(HydroFieldNames::specificThermalEnergy, 0.0);
  const auto H = state.fields(HydroFieldNames::H, SymTensor::zero);
  const auto pressure = state.fields(HydroFieldNames::pressure, 0.0);
  const auto soundSpeed = state.fields(HydroFieldNames::soundSpeed, 0.0);
  const auto S = state.fields(SolidFieldNames::deviatoricStress, SymTensor::zero);
  const auto mu = state.fields(SolidFieldNames::shearModulus, 0.0);
  const auto damage = state.fields(SolidFieldNames::tensorDamage, SymTensor::zero);
  const auto fragIDs = state.fields(SolidFieldNames::fragmentIDs, int(1));
  const auto pTypes = state.fields(SolidFieldNames::particleTypes, int(0));
  const auto corrections = state.fields(RKFieldNames::rkCorrections(order), RKCoefficients<Dimension>());
  const auto surfacePoint = state.fields(HydroFieldNames::surfacePoint, 0);
  CHECK(mass.size() == numNodeLists);
  CHECK(position.size() == numNodeLists);
  CHECK(velocity.size() == numNodeLists);
  CHECK(massDensity.size() == numNodeLists);
  CHECK(specificThermalEnergy.size() == numNodeLists);
  CHECK(H.size() == numNodeLists);
  CHECK(pressure.size() == numNodeLists);
  CHECK(soundSpeed.size() == numNodeLists);
  CHECK(S.size() == numNodeLists);
  CHECK(mu.size() == numNodeLists);
  CHECK(damage.size() == numNodeLists);
  CHECK(fragIDs.size() == numNodeLists);
  CHECK(pTypes.size() == numNodeLists);
  CHECK(corrections.size() == numNodeLists);
  CHECK(surfacePoint.size() == numNodeLists);

  // Derivative FieldLists.
  auto  DxDt = derivatives.fields(IncrementState<Dimension, Vector>::prefix() + HydroFieldNames::position, Vector::zero);
  auto  DrhoDt = derivatives.fields(IncrementState<Dimension, Scalar>::prefix() + HydroFieldNames::massDensity, 0.0);
  auto  DvDt = derivatives.fields(HydroFieldNames::hydroAcceleration, Vector::zero);
  auto  DepsDt = derivatives.fields(IncrementState<Dimension, Scalar>::prefix() + HydroFieldNames::specificThermalEnergy, 0.0);
  auto  DvDx = derivatives.fields(HydroFieldNames::velocityGradient, Tensor::zero);
  auto  localDvDx = derivatives.fields(HydroFieldNames::internalVelocityGradient, Tensor::zero);
  auto  maxViscousPressure = derivatives.fields(HydroFieldNames::maxViscousPressure, 0.0);
  auto  effViscousPressure = derivatives.fields(HydroFieldNames::effectiveViscousPressure, 0.0);
  auto  viscousWork = derivatives.fields(HydroFieldNames::viscousWork, 0.0);
  auto& pairAccelerations = derivatives.get(HydroFieldNames::pairAccelerations, vector<Vector>());
  auto  XSPHDeltaV = derivatives.fields(HydroFieldNames::XSPHDeltaV, Vector::zero);
  auto  DSDt = derivatives.fields(IncrementState<Dimension, SymTensor>::prefix() + SolidFieldNames::deviatoricStress, SymTensor::zero);
  CHECK(DxDt.size() == numNodeLists);
  CHECK(DrhoDt.size() == numNodeLists);
  CHECK(DvDt.size() == numNodeLists);
  CHECK(DepsDt.size() == numNodeLists);
  CHECK(DvDx.size() == numNodeLists);
  CHECK(localDvDx.size() == numNodeLists);
  CHECK(maxViscousPressure.size() == numNodeLists);
  CHECK(effViscousPressure.size() == numNodeLists);
  CHECK(viscousWork.size() == numNodeLists);
  CHECK(XSPHDeltaV.size() == numNodeLists);
  CHECK(DSDt.size() == numNodeLists);

  // Size up the pair-wise accelerations before we start.
  if (compatibleEnergy) pairAccelerations.resize(2*npairs + dataBase.numInternalNodes());

  // Build the functor we use to compute the effective coupling between nodes.
  const NodeCoupling coupling;

  // Walk all the interacting pairs.
#pragma omp parallel
  {
    // Thread private scratch variables
    int i, j, nodeListi, nodeListj;
    Scalar Wi, Wj;
    Tensor QPiij, QPiji;
    Vector gradWi, gradWj;
    Vector deltagrad, forceij, forceji;
    Vector xij, vij, etai, etaj;
    SymTensor sigmai, sigmaj, xijdyad;

    typename SpheralThreads<Dimension>::FieldListStack threadStack;
    auto DvDt_thread = DvDt.threadCopy(threadStack);
    auto DepsDt_thread = DepsDt.threadCopy(threadStack);
    auto DvDx_thread = DvDx.threadCopy(threadStack);
    auto localDvDx_thread = localDvDx.threadCopy(threadStack);
    auto maxViscousPressure_thread = maxViscousPressure.threadCopy(threadStack, ThreadReduction::MAX);
    auto effViscousPressure_thread = effViscousPressure.threadCopy(threadStack);
    auto viscousWork_thread = viscousWork.threadCopy(threadStack);
    auto XSPHDeltaV_thread = XSPHDeltaV.threadCopy(threadStack);

#pragma omp for
    for (auto kk = 0u; kk < npairs; ++kk) {
      i = pairs[kk].i_node;
      j = pairs[kk].j_node;
      nodeListi = pairs[kk].i_list;
      nodeListj = pairs[kk].j_list;

      // Get the state for node i.
      const auto& posi = position(nodeListi, i);
      const auto  ri = abs(posi.y());
      const auto  circi = 2.0*M_PI*ri;
      const auto  mi = mass(nodeListi, i);
      const auto  mRZi = mi/circi;
      const auto& vi = velocity(nodeListi, i);
      const auto  rhoi = massDensity(nodeListi, i);
      //const auto  epsi = specificThermalEnergy(nodeListi, i);
      const auto  Pi = pressure(nodeListi, i);
      const auto& Hi = H(nodeListi, i);
      const auto  ci = soundSpeed(nodeListi, i);
      const auto  Si = S(nodeListi, i);
      const auto  pTypei = pTypes(nodeListi, i);
      const auto& correctionsi = corrections(nodeListi, i);
      const auto  weighti = volume(nodeListi, i);  // Change CRKSPH weights here if need be!
      CHECK(mi > 0.0);
      CHECK(rhoi > 0.0);
      CHECK(weighti > 0.0);

      //auto& DrhoDti = DrhoDt(nodeListi, i);
      auto& DvDti = DvDt(nodeListi, i);
      auto& DepsDti = DepsDt(nodeListi, i);
      auto& DvDxi = DvDx(nodeListi, i);
      auto& localDvDxi = localDvDx(nodeListi, i);
      auto& maxViscousPressurei = maxViscousPressure(nodeListi, i);
      auto& effViscousPressurei = effViscousPressure(nodeListi, i);
      auto& viscousWorki = viscousWork(nodeListi, i);
      auto& XSPHDeltaVi = XSPHDeltaV(nodeListi, i);

      // Get the state for node j
      const auto& posj = position(nodeListj, j);
      const auto  rj = abs(posj.y());
      const auto  circj = 2.0*M_PI*rj;
      const auto  mj = mass(nodeListj, j);
      const auto  mRZj = mj/circj;
      const auto& vj = velocity(nodeListj, j);
      const auto  rhoj = massDensity(nodeListj, j);
      //const auto  epsj = specificThermalEnergy(nodeListj, j);
      const auto  Pj = pressure(nodeListj, j);
      const auto& Hj = H(nodeListj, j);
      const auto  cj = soundSpeed(nodeListj, j);
      const auto  pTypej = pTypes(nodeListj, j);
      const auto& correctionsj = corrections(nodeListj, j);
      const auto& Sj = S(nodeListj, j);
      const auto  weightj = volume(nodeListj, j);     // Change CRKSPH weights here if need be!
      CHECK(mj > 0.0);
      CHECK(rhoj > 0.0);
      CHECK(weightj > 0.0);

      auto& DvDtj = DvDt(nodeListj, j);
      auto& DepsDtj = DepsDt(nodeListj, j);
      auto& DvDxj = DvDx(nodeListj, j);
      auto& localDvDxj = localDvDx(nodeListj, j);
      auto& maxViscousPressurej = maxViscousPressure(nodeListj, j);
      auto& effViscousPressurej = effViscousPressure(nodeListj, j);
      auto& viscousWorkj = viscousWork(nodeListj, j);
      auto& XSPHDeltaVj = XSPHDeltaV(nodeListj, j);

      // Node displacement.
      xij = posi - posj;
      vij = vi - vj;
      etai = Hi*xij;
      etaj = Hj*xij;

      // Flag if this is a contiguous material pair or not.
      const auto sameMatij = true; // nodeListi == nodeListj; // (nodeListi == nodeListj and fragIDi == fragIDj);

      // Flag if at least one particle is free (0).
      const auto freeParticle = (pTypei == 0 or pTypej == 0);

      // Symmetrized kernel weight and gradient.
      std::tie(Wj, gradWj) = WR.evaluateKernelAndGradient( xij, Hj, correctionsi);  // Hj because we compute RK using scatter formalism
      std::tie(Wi, gradWi) = WR.evaluateKernelAndGradient(-xij, Hi, correctionsj);
      deltagrad = gradWj - gradWi;

      // Find the damaged pair weighting scaling.
      const auto fDij = coupling(pairs[kk]);
      CHECK(fDij >= 0.0 and fDij <= 1.0);

      // Compute the artificial viscous pressure (Pi = P/rho^2 actually).
      std::tie(QPiij, QPiji) = Q.Piij(nodeListi, i, nodeListj, j,
                                      posi, etai, vi, rhoi, ci, Hi,
                                      posj, etaj, vj, rhoj, cj, Hj);
      const auto Qaccij = (rhoi*rhoi*QPiij + rhoj*rhoj*QPiji).dot(deltagrad);
      const auto workQi = rhoj*rhoj*QPiji.dot(vij).dot(deltagrad);          // CRK
      const auto workQj = rhoi*rhoi*QPiij.dot(vij).dot(deltagrad);          // CRK
      const auto Qi = rhoi*rhoi*(QPiij.diagonalElements().maxAbsElement());
      const auto Qj = rhoj*rhoj*(QPiji.diagonalElements().maxAbsElement());
      maxViscousPressurei = max(maxViscousPressurei, 4.0*Qi);               // We need tighter timestep controls on the Q with CRK
      maxViscousPressurej = max(maxViscousPressurej, 4.0*Qj);
      effViscousPressurei += weightj * Qi * Wj;
      effViscousPressurej += weighti * Qj * Wi;
      viscousWorki += 0.5*weighti*weightj/mRZi*workQi;
      viscousWorkj += 0.5*weighti*weightj/mRZj*workQj;

      // Velocity gradient.
      DvDxi -= fDij * weightj*vij.dyad(gradWj);
      DvDxj += fDij * weighti*vij.dyad(gradWi);
      if (sameMatij) {
        localDvDxi -= fDij * weightj*vij.dyad(gradWj);
        localDvDxj += fDij * weighti*vij.dyad(gradWi);
      }

      // Compute the stress tensors.
      if (sameMatij) {
        sigmai = fDij*Si - Pi * SymTensor::one;
        sigmaj = fDij*Sj - Pj * SymTensor::one;
      } else {
        sigmai = -Pi * SymTensor::one;
        sigmaj = -Pj * SymTensor::one;
      }

      // We decide between RK and CRK for the momentum and energy equations based on the surface condition.
      // Momentum
      forceij = (true ? // surfacePoint(nodeListi, i) <= 1 ? 
                 0.5*weighti*weightj*(-(sigmai + sigmaj)*deltagrad + Qaccij) :                                               // Type III CRK interpoint force.
                 mi*weightj*((-(sigmaj - sigmai)*gradWj)/rhoi + rhoi*QPiij.dot(gradWj)));                                    // RK
      forceji = (true ? // surfacePoint(nodeListj, j) <= 1 ?
                 0.5*weighti*weightj*(-(sigmai + sigmaj)*deltagrad + Qaccij) :                                               // Type III CRK interpoint force.
                 mj*weighti*((-(sigmaj - sigmai)*gradWi)/rhoj - rhoj*QPiji.dot(gradWi)));                                    // RK
      if (freeParticle) {
        DvDti -= forceij/mRZi;
        DvDtj += forceji/mRZj;
      }
      if (compatibleEnergy) {
        pairAccelerations[kk]   = -forceij/mRZi;
        pairAccelerations[2*kk] =  forceji/mRZj;
      }

      // Energy
      DepsDti += (true ? // surfacePoint(nodeListi, i) <= 1 ?
                  0.5*weighti*weightj*(-sigmaj.dot(vij).dot(deltagrad) + workQi)/mRZi :                                      // CRK
                  weightj*rhoi*QPiij.dot(vij).dot(gradWj));                                                                  // RK, Q term only -- adiabatic portion added later
      DepsDtj += (true ? // surfacePoint(nodeListj, j) <= 1 ?
                  0.5*weighti*weightj*(-sigmai.dot(vij).dot(deltagrad) + workQj)/mRZj :                                      // CRK
                 -weighti*rhoj*QPiji.dot(vij).dot(gradWi));                                                                  // RK, Q term only -- adiabatic portion added later

      // Estimate of delta v (for XSPH).
      XSPHDeltaVi -= fDij*weightj*Wj*vij;
      XSPHDeltaVj += fDij*weighti*Wi*vij;
    }

    // Reduce the thread values to the master.
    threadReduceFieldLists<Dimension>(threadStack);

  }   // OMP parallel

  // Finish up the derivatives for each point.
  auto offset = 2*npairs;
  for (auto nodeListi = 0u; nodeListi < numNodeLists; ++nodeListi) {
    const auto& nodeList = mass[nodeListi]->nodeList();
    const auto ni = nodeList.numInternalNodes();

    // Check if we can identify a reference density.
    auto rho0 = 0.0;
    try {
      rho0 = dynamic_cast<const SolidEquationOfState<Dimension>&>(dynamic_cast<const SolidNodeList<Dimension>&>(nodeList).equationOfState()).referenceDensity();
      // cerr << "Setting reference density to " << rho0 << endl;
    } catch(...) {
      // cerr << "BLAGO!" << endl;
    }

#pragma omp parallel for
    for (auto i = 0u; i < ni; ++i) {

      // Get the state for node i.
      const auto& posi = position(nodeListi, i);
      const auto  ri = abs(posi.y());
      //const auto  circi = 2.0*M_PI*ri;
      const auto  mi = mass(nodeListi, i);
      //const auto  mRZi = mi/circi;
      const auto& vi = velocity(nodeListi, i);
      const auto  rhoi = massDensity(nodeListi, i);
      //const auto  epsi = specificThermalEnergy(nodeListi, i);
      const auto  Pi = pressure(nodeListi, i);
      const auto& Hi = H(nodeListi, i);
      //const auto  ci = soundSpeed(nodeListi, i);
      const auto  Si = S(nodeListi, i);
      const auto  STTi = -Si.Trace();
      const auto  mui = mu(nodeListi, i);
      const auto  zetai = abs((Hi*posi).y());
      const auto  hri = ri*safeInv(zetai);
      const auto  riInv = safeInv(ri, 0.25*hri);

      auto& DxDti = DxDt(nodeListi, i);
      auto& DrhoDti = DrhoDt(nodeListi, i);
      auto& DvDti = DvDt(nodeListi, i);
      auto& DepsDti = DepsDt(nodeListi, i);
      // auto& DvDxi = DvDx(nodeListi, i);
      auto& localDvDxi = localDvDx(nodeListi, i);
      auto& XSPHDeltaVi = XSPHDeltaV(nodeListi, i);
      auto& DSDti = DSDt(nodeListi, i);

      // Determine the position evolution, based on whether we're doing XSPH or not.
      if (XSPH) {
        DxDti = vi + XSPHDeltaVi;
      } else {
        DxDti = vi;
      }

      // Finish the acceleration.
      const Vector deltaDvDti(Si(1,0)/rhoi*riInv,
                              (Si(1,1) - STTi)/rhoi*riInv);
      DvDti += deltaDvDti;
      if (compatibleEnergy) pairAccelerations[offset + i] = deltaDvDti;

      // Time evolution of the mass density.
      const auto vri = vi.y(); // + XSPHDeltaVi.y();
      DrhoDti = -rhoi*(localDvDxi.Trace() + vri*riInv);

      // For a surface point, add the RK thermal energy evolution.
      // if (surfacePoint(nodeListi, i) > 1) DepsDti += (Si - Pi*SymTensor::one).doubledot(DvDxi)/rhoi;

      // Finish the specific thermal energy evolution.
      DepsDti += (STTi - Pi)/rhoi*vri*riInv;

      // If needed finish the total energy derivative.
      if (this->evolveTotalEnergy()) DepsDti = mi*(vi.dot(DvDti) + DepsDti);

      // Optionally use damage to ramp down stress on damaged material.
      const auto Di = (damageRelieveRubble ? 
                       max(0.0, min(1.0, damage(nodeListi, i).Trace() - 1.0)) :
                       0.0);
      // Hideali = (1.0 - Di)*Hideali + Di*Hfield0(nodeListi, i);
      // DHDti = (1.0 - Di)*DHDti + Di*(Hfield0(nodeListi, i) - Hi)*0.25/dt;

      // We also adjust the density evolution in the presence of damage.
      if (rho0 > 0.0) DrhoDti = (1.0 - Di)*DrhoDti - 0.25/dt*Di*(rhoi - rho0);

      // Determine the deviatoric stress evolution.
      const auto deformation = localDvDxi.Symmetric();
      const auto deformationTT = vi.y()*riInv;
      const auto spin = localDvDxi.SkewSymmetric();
      const auto deviatoricDeformation = deformation - ((deformation.Trace() + deformationTT)/3.0)*SymTensor::one;
      const auto spinCorrection = (spin*Si + Si*spin).Symmetric();
      DSDti = spinCorrection + (2.0*mui)*deviatoricDeformation;

      // In the presence of damage, add a term to reduce the stress on this point.
      DSDti = (1.0 - Di)*DSDti - Di*Si*0.25/dt;
    }
    offset += ni;
  }
}

//------------------------------------------------------------------------------
// Apply the ghost boundary conditions for hydro state fields.
//------------------------------------------------------------------------------
void
SolidCRKSPHHydroBaseRZ::
applyGhostBoundaries(State<Dim<2>>& state,
                     StateDerivatives<Dim<2>>& derivs) {

  // Convert the mass to mass/length before BCs are applied.
  FieldList<Dimension, Scalar> mass = state.fields(HydroFieldNames::mass, 0.0);
  const FieldList<Dimension, Vector> pos = state.fields(HydroFieldNames::position, Vector::zero);
  const unsigned numNodeLists = mass.numFields();
  for (unsigned nodeListi = 0; nodeListi != numNodeLists; ++nodeListi) {
    const unsigned n = mass[nodeListi]->numElements();
    for (unsigned i = 0; i != n; ++i) {
      const Scalar circi = 2.0*M_PI*abs(pos(nodeListi, i).y());
      CHECK(circi > 0.0);
#ifdef WIN32
      if (circi > 0.0) mass(nodeListi, i) /= circi;
#else
      mass(nodeListi, i) /= circi;
#endif
    }
  }

  // Apply ordinary BCs.
  SolidCRKSPHHydroBase<Dim<2>>::applyGhostBoundaries(state, derivs);
  for (auto boundaryPtr: range(this->boundaryBegin(), this->boundaryEnd())) boundaryPtr->finalizeGhostBoundary();

  // Scale back to mass.
  for (unsigned nodeListi = 0; nodeListi != numNodeLists; ++nodeListi) {
    const unsigned n = mass[nodeListi]->numElements();
    for (unsigned i = 0; i != n; ++i) {
      const Scalar circi = 2.0*M_PI*abs(pos(nodeListi, i).y());
      CHECK(circi > 0.0);
#ifdef WIN32
      if (circi > 0.0) mass(nodeListi, i) *= circi;
#else
      mass(nodeListi, i) *= circi;
#endif
    }
  }
}

//------------------------------------------------------------------------------
// Enforce the boundary conditions for hydro state fields.
//------------------------------------------------------------------------------
void
SolidCRKSPHHydroBaseRZ::
enforceBoundaries(State<Dim<2>>& state,
                  StateDerivatives<Dim<2>>& derivs) {

  // Convert the mass to mass/length before BCs are applied.
  FieldList<Dimension, Scalar> mass = state.fields(HydroFieldNames::mass, 0.0);
  FieldList<Dimension, Vector> pos = state.fields(HydroFieldNames::position, Vector::zero);
  const unsigned numNodeLists = mass.numFields();
  for (unsigned nodeListi = 0; nodeListi != numNodeLists; ++nodeListi) {
    const unsigned n = mass[nodeListi]->numInternalElements();
    for (unsigned i = 0; i != n; ++i) {
      const Scalar circi = 2.0*M_PI*abs(pos(nodeListi, i).y());
      CHECK(circi > 0.0);
#ifdef WIN32
      if (circi > 0.0) mass(nodeListi, i) /= circi;
#else
      mass(nodeListi, i) /= circi;
#endif
    }
  }

  // Apply ordinary BCs.
  SolidCRKSPHHydroBase<Dim<2>>::enforceBoundaries(state, derivs);

  // Scale back to mass.
  // We also ensure no point approaches the z-axis too closely.
  FieldList<Dimension, SymTensor> H = state.fields(HydroFieldNames::H, SymTensor::zero);
  for (unsigned nodeListi = 0; nodeListi != numNodeLists; ++nodeListi) {
    const unsigned n = mass[nodeListi]->numInternalElements();
    //const Scalar nPerh = mass[nodeListi]->nodeList().nodesPerSmoothingScale();
    for (unsigned i = 0; i != n; ++i) {
      Vector& posi = pos(nodeListi, i);
      const Scalar circi = 2.0*M_PI*abs(posi.y());
#ifdef WIN32
      if (circi > 0.0) mass(nodeListi, i) *= circi;
#else
      mass(nodeListi, i) *= circi;
#endif
    }
  }
}

}