merged current master

Former-commit-id: a54b06bb

code/src/solvers/pnsolver.cpp

 #include "solvers/pnsolver.h"
 #include "common/config.h"
 #include "common/io.h"
+#include "common/mesh.h"
 #include "fluxes/numericalflux.h"
 #include "toolboxes/errormessages.h"
 #include "toolboxes/textprocessingtoolbox.h"
@@ -31,6 +32,10 @@ PNSolver::PNSolver( Config* settings ) : Solver( settings ) {
     // Initialize Scatter Matrix
     _scatterMatDiag = Vector( _nTotalEntries, 0 );
 
+    // Initialize temporary storages of solution derivatives
+    _solDx = VectorVector( _nCells, Vector( _nTotalEntries, 0.0 ) );
+    _solDy = VectorVector( _nCells, Vector( _nTotalEntries, 0.0 ) );
+
     // Fill System Matrices
     ComputeSystemMatrices();
 
@@ -71,6 +76,15 @@ void PNSolver::ComputeRadFlux() {
 }
 
 void PNSolver::FluxUpdate() {
+    if( _reconsOrder > 1 ) {
+        _mesh->ReconstructSlopesU( _nTotalEntries, _solDx, _solDy, _sol );    // unstructured reconstruction
+        //_mesh->ComputeSlopes( _nTotalEntries, _solDx, _solDy, _sol );    // unstructured reconstruction
+    }
+    //Vector solL( _nTotalEntries );
+    //Vector solR( _nTotalEntries );
+    auto solL = _sol[2];
+    auto solR = _sol[2];
+
     // Loop over all spatial cells
     for( unsigned idx_cell = 0; idx_cell < _nCells; idx_cell++ ) {
 
@@ -89,16 +103,60 @@ void PNSolver::FluxUpdate() {
             if( _boundaryCells[idx_cell] == BOUNDARY_TYPE::NEUMANN && _neighbors[idx_cell][idx_neighbor] == _nCells )
                 _solNew[idx_cell] += _g->Flux(
                     _AxPlus, _AxMinus, _AyPlus, _AyMinus, _AzPlus, _AzMinus, _sol[idx_cell], _sol[idx_cell], _normals[idx_cell][idx_neighbor] );
-            else
-                _solNew[idx_cell] += _g->Flux( _AxPlus,
-                                               _AxMinus,
-                                               _AyPlus,
-                                               _AyMinus,
-                                               _AzPlus,
-                                               _AzMinus,
-                                               _sol[idx_cell],
-                                               _sol[_neighbors[idx_cell][idx_neighbor]],
-                                               _normals[idx_cell][idx_neighbor] );
+            else {
+                switch( _reconsOrder ) {
+                    // first order solver
+                    case 1:
+                        _solNew[idx_cell] += _g->Flux( _AxPlus,
+                                                       _AxMinus,
+                                                       _AyPlus,
+                                                       _AyMinus,
+                                                       _AzPlus,
+                                                       _AzMinus,
+                                                       _sol[idx_cell],
+                                                       _sol[_neighbors[idx_cell][idx_neighbor]],
+                                                       _normals[idx_cell][idx_neighbor] );
+                        break;
+                    // second order solver
+                    case 2:
+                        // left status of interface
+                        solL = _sol[idx_cell] +
+                               _solDx[idx_cell] * ( _interfaceMidPoints[idx_cell][idx_neighbor][0] - _cellMidPoints[idx_cell][0] ) + 
+                               _solDy[idx_cell] * ( _interfaceMidPoints[idx_cell][idx_neighbor][1] - _cellMidPoints[idx_cell][1] );
+                        // right status of interface
+                        solR = _sol[_neighbors[idx_cell][idx_neighbor]] +
+                               _solDx[_neighbors[idx_cell][idx_neighbor]] * ( _interfaceMidPoints[idx_cell][idx_neighbor][0] - _cellMidPoints[_neighbors[idx_cell][idx_neighbor]][0] ) + 
+                               _solDy[_neighbors[idx_cell][idx_neighbor]] * ( _interfaceMidPoints[idx_cell][idx_neighbor][1] - _cellMidPoints[_neighbors[idx_cell][idx_neighbor]][1] );
+                        // positivity checker (if not satisfied, deduce to first order)
+                        // I manually turned it off here since Pn produces negative solutions essentially
+                        //if( min(solL) < 0.0 || min(solR) < 0.0 ) {
+                        //    solL = _sol[idx_cell];
+                        //    solR = _sol[_neighbors[idx_cell][idx_neighbor]];
+                        //}
+                        // flux evaluation
+                        _solNew[idx_cell] += _g->Flux( _AxPlus,
+                                                       _AxMinus,
+                                                       _AyPlus,
+                                                       _AyMinus,
+                                                       _AzPlus,
+                                                       _AzMinus,
+                                                       solL,
+                                                       solR,
+                                                       _normals[idx_cell][idx_neighbor] );
+                        break;
+                    // default: first order solver
+                    default: 
+                        _solNew[idx_cell] += _g->Flux( _AxPlus,
+                                                       _AxMinus,
+                                                       _AyPlus,
+                                                       _AyMinus,
+                                                       _AzPlus,
+                                                       _AzMinus,
+                                                       _sol[idx_cell],
+                                                       _sol[_neighbors[idx_cell][idx_neighbor]],
+                                                       _normals[idx_cell][idx_neighbor] );
+                }
+            }
         }
     }
 }

code/src/solvers/snsolver.cpp

@@ -55,7 +55,6 @@ void SNSolver::FluxUpdate() {
     // left and right angular flux of interface, used in numerical flux evaluation
     double psiL;
     double psiR;
-    double mass;
 
     // derivatives of angular flux in x and y directions
     VectorVector psiDx( _nCells, Vector( _nq, 0.0 ) );
@@ -98,7 +97,12 @@ void SNSolver::FluxUpdate() {
         //_mesh->ReconstructSlopesS( _nq, psiDx, psiDy, _psi );    // structured reconstruction (not stable currently)
     }
     */
-
+    if( _reconsOrder > 1 ) {
+        _mesh->ReconstructSlopesU( _nq, _psiDx, _psiDy, _sol );    // unstructured reconstruction
+        //_mesh->ReconstructSlopesS( _nq, _psiDx, _psiDy, _psi );    // structured reconstruction (not stable currently)
+    }
+    double psiL;
+    double psiR;
     // Loop over all spatial cells
     for( unsigned idx_cell = 0; idx_cell < _nCells; ++idx_cell ) {
         // Dirichlet cells stay at IC, farfield assumption
@@ -114,45 +118,40 @@ void SNSolver::FluxUpdate() {
                     _solNew[idx_cell][idx_quad] +=
                         _g->Flux( _quadPoints[idx_quad], _sol[idx_cell][idx_quad], _sol[idx_cell][idx_quad], _normals[idx_cell][idx_neighbor] );
                 else {
-                    /*                    switch( reconsOrder ) {
-                                            // first order solver
-                                            case 1:
-                                                psiNew[idx_cells][idx_quad] += _g->Flux( _quadPoints[idx_quad],
-                                                                                         _sol[idx_cells][idx_quad],
-                                                                                         _sol[_neighbors[idx_cells][idx_neighbor]][idx_quad],
-                                                                                         _normals[idx_cells][idx_neighbor] );
-                                                break;
-                                            // second order solver
-                                            case 2:
-                                                // left status of interface
-                                                psiL = _sol[idx_cells][idx_quad] +
-                                                       psiDx[idx_cells][idx_quad] * ( interfaceMidPoints[idx_cells][idx_neighbor][0] -
-                       cellMidPoints[idx_cells][0] ) + psiDy[idx_cells][idx_quad] * ( interfaceMidPoints[idx_cells][idx_neighbor][1] -
-                       cellMidPoints[idx_cells][1] );
-                                                // right status of interface
-                                                psiR = _sol[_neighbors[idx_cells][idx_neighbor]][idx_quad] +
-                                                       psiDx[_neighbors[idx_cells][idx_neighbor]][idx_quad] *
-                                                           ( interfaceMidPoints[idx_cells][idx_neighbor][0] -
-                       cellMidPoints[_neighbors[idx_cells][idx_neighbor]][0] ) + psiDy[_neighbors[idx_cells][idx_neighbor]][idx_quad] * (
-                       interfaceMidPoints[idx_cells][idx_neighbor][1] - cellMidPoints[_neighbors[idx_cells][idx_neighbor]][1] );
-                                                // positivity check (if not satisfied, deduce to first order)
-                                                if( psiL < 0.0 || psiR < 0.0 ) {
-                                                    psiL = _sol[idx_cells][idx_quad];
-                                                    psiR = _sol[_neighbors[idx_cells][idx_neighbor]][idx_quad];
-                                                }
-                                                // flux evaluation
-                                                psiNew[idx_cells][idx_quad] += _g->Flux( _quadPoints[idx_quad], psiL, psiR,
-                       _normals[idx_cells][idx_neighbor] ); break;
-                                            // higher order solver
-                                            case 3: std::cout << "higher order is WIP" << std::endl; break;
-                                            // default: first order solver
-                                            default:
-                                            */
-                    _solNew[idx_cell][idx_quad] += _g->Flux( _quadPoints[idx_quad],
-                                                             _sol[idx_cell][idx_quad],
-                                                             _sol[_neighbors[idx_cell][idx_neighbor]][idx_quad],
-                                                             _normals[idx_cell][idx_neighbor] );
-                    // }
+                        switch( _reconsOrder ) {
+                            // first order solver
+                            case 1:
+                                _solNew[idx_cell][idx_quad] += _g->Flux( _quadPoints[idx_quad],
+                                                                            _sol[idx_cell][idx_quad],
+                                                                            _sol[_neighbors[idx_cell][idx_neighbor]][idx_quad],
+                                                                            _normals[idx_cell][idx_neighbor] );
+                                break;
+                            // second order solver
+                            case 2:
+                                // left status of interface
+                                psiL = _sol[idx_cell][idx_quad] +
+                                        _psiDx[idx_cell][idx_quad] * ( _interfaceMidPoints[idx_cell][idx_neighbor][0] - _cellMidPoints[idx_cell][0] ) + 
+                                        _psiDy[idx_cell][idx_quad] * ( _interfaceMidPoints[idx_cell][idx_neighbor][1] - _cellMidPoints[idx_cell][1] );
+                                // right status of interface
+                                psiR = _sol[_neighbors[idx_cell][idx_neighbor]][idx_quad] +
+                                        _psiDx[_neighbors[idx_cell][idx_neighbor]][idx_quad] * ( _interfaceMidPoints[idx_cell][idx_neighbor][0] - _cellMidPoints[_neighbors[idx_cell][idx_neighbor]][0] ) + 
+                                        _psiDy[_neighbors[idx_cell][idx_neighbor]][idx_quad] * ( _interfaceMidPoints[idx_cell][idx_neighbor][1] - _cellMidPoints[_neighbors[idx_cell][idx_neighbor]][1] );
+                                // positivity check (if not satisfied, deduce to first order)
+                                if( psiL < 0.0 || psiR < 0.0 ) {
+                                    psiL = _sol[idx_cell][idx_quad];
+                                    psiR = _sol[_neighbors[idx_cell][idx_neighbor]][idx_quad];
+                                }
+                                // flux evaluation
+                                _solNew[idx_cell][idx_quad] += _g->Flux( _quadPoints[idx_quad], psiL, psiR, _normals[idx_cell][idx_neighbor] ); break;
+                                // higher order solver
+                                case 3: std::cout << "higher order is WIP" << std::endl; break;
+                                // default: first order solver
+                            default: 
+                                _solNew[idx_cell][idx_quad] += _g->Flux( _quadPoints[idx_quad],
+                                                               _sol[idx_cell][idx_quad],
+                                                               _sol[_neighbors[idx_cell][idx_neighbor]][idx_quad],
+                                                               _normals[idx_cell][idx_neighbor] );
+                    }
                 }
             }
         }

code/src/solvers/solverbase.cpp

@@ -25,10 +25,32 @@ Solver::Solver( Config* settings ) : _settings( settings ) {
     _settings->SetNCells( _nCells );
 
     // build quadrature object and store frequently used params
-    _quadrature = QuadratureBase::CreateQuadrature( settings );
+    _quadrature = QuadratureBase::Create( settings );
     _nq         = _quadrature->GetNq();
     _settings->SetNQuadPoints( _nq );
 
+    // build slope related params
+    _reconstructor = Reconstructor::Create( settings );
+    _reconsOrder = _reconstructor->GetReconsOrder();
+
+    auto nodes         = _mesh->GetNodes();
+    auto cells         = _mesh->GetCells();
+    std::vector<std::vector<Vector>> interfaceMidPoints( _nCells, std::vector<Vector>( _mesh->GetNumNodesPerCell(), Vector( 2, 1e-10 ) ) );
+    for( unsigned idx_cell = 0; idx_cell < _nCells; ++idx_cell ) {
+        for( unsigned k = 0; k < _mesh->GetDim(); ++k ) {
+            for( unsigned j = 0; j < _neighbors[idx_cell].size() - 1; ++j ) {
+                interfaceMidPoints[idx_cell][j][k] = 0.5 * ( nodes[cells[idx_cell][j]][k] + nodes[cells[idx_cell][j + 1]][k] );
+            }
+            interfaceMidPoints[idx_cell][_neighbors[idx_cell].size() - 1][k] =
+                0.5 * ( nodes[cells[idx_cell][_neighbors[idx_cell].size() - 1]][k] + nodes[cells[idx_cell][0]][k] );
+        }
+    }
+    _interfaceMidPoints = interfaceMidPoints;
+    _cellMidPoints = _mesh->GetCellMidPoints();
+
+    _psiDx = VectorVector( _nCells, Vector( _nq, 0.0 ) );
+    _psiDy = VectorVector( _nCells, Vector( _nq, 0.0 ) );
+
     // set time step
     _dE        = ComputeTimeStep( settings->GetCFL() );
     _nEnergies = unsigned( settings->GetTEnd() / _dE );

code/src/toolboxes/interpolation.cpp

@@ -91,19 +91,19 @@ double Interpolation::operator()( double x, double y ) const {
     if( _type == cubic ) {
 
         // find closest values to x and y in table (lower bounds)
-        unsigned xId = IndexOfClosestValue( x, _x );
-        unsigned yId = IndexOfClosestValue( y, _y );
+        int xId = IndexOfClosestValue( x, _x );
+        int yId = IndexOfClosestValue( y, _y );
 
         // store all 16 interpolation points needed
         double points[4][4];
         for( int i = -1; i < 3; ++i ) {
             unsigned idx_y;
             idx_y = yId + i < 0 ? 0 : yId + i;
-            idx_y = yId + i > _data.rows() - 1 ? _data.rows() - 1 : yId + i;
+            idx_y = yId + i > static_cast<int>( _data.rows() - 1 ) ? _data.rows() - 1 : yId + i;
             for( int j = -1; j < 3; ++j ) {
                 unsigned idx_x;
                 idx_x = xId + j < 0 ? 0 : xId + j;
-                idx_x = xId + j > _data.columns() - 1 ? _data.columns() - 1 : xId + j;
+                idx_x = xId + j > static_cast<int>( _data.columns() - 1 ) ? _data.columns() - 1 : xId + j;
 
                 points[i + 1][j + 1] = _data( idx_x, idx_y );
             }

code/src/toolboxes/reconstructor.cpp

 #include "toolboxes/reconstructor.h"
 #include "common/config.h"
 
-Reconstructor::Reconstructor( Config* settings ) {}
+Reconstructor::Reconstructor( Config* settings ) {
+    _reconsOrder = settings->GetReconsOrder();
+}
+
+Reconstructor* Reconstructor::Create( Config* settings ) {
+    return new Reconstructor( settings );
+}
 
 double FortSign( double a, double b ) {
-    if( b > 0.0 ) return abs( a );
-    if( b < 0.0 ) return -abs( a );
+    if( b > 0.0 ) return std::fabs( a );
+    if( b < 0.0 ) return -std::fabs( a );
     return 0.0;
 }
 
-double LMinMod( double sL, double sR ) { return 0.5 * ( FortSign( 1.0, sL ) + FortSign( 1., sR ) ) * fmin( abs( sL ), abs( sR ) ); }
+double LMinMod( double sL, double sR ) { return 0.5 * ( FortSign( 1.0, sL ) + FortSign( 1., sR ) ) * fmin( std::fabs( sL ), std::fabs( sR ) ); }
 
 double LVanLeer( double sL, double sR ) {
 
-    return ( FortSign( 1.0, sL ) + FortSign( 1.0, sR ) ) * abs( sL ) * abs( sR ) / ( abs( sL ) + abs( sR ) + 0.0000001 );
+    return ( FortSign( 1.0, sL ) + FortSign( 1.0, sR ) ) * std::fabs( sL ) * std::fabs( sR ) / ( std::fabs( sL ) + std::fabs( sR ) + 0.0000001 );
 }
 
 double LSuperBee( double sL, double sR ) {
 
-    if( sR >= 0.5 * sL && sR <= 2.0 * sL ) return 0.5 * ( FortSign( 1.0, sL ) + FortSign( 1., sR ) ) * fmax( abs( sL ), abs( sR ) );
-    if( sR < 0.5 * sL && sR > 2.0 * sL ) return ( FortSign( 1.0, sL ) + FortSign( 1., sR ) ) * fmin( abs( sL ), abs( sR ) );
+    if( sR >= 0.5 * sL && sR <= 2.0 * sL ) return 0.5 * ( FortSign( 1.0, sL ) + FortSign( 1., sR ) ) * fmax( std::fabs( sL ), std::fabs( sR ) );
+    if( sR < 0.5 * sL && sR > 2.0 * sL ) return ( FortSign( 1.0, sL ) + FortSign( 1., sR ) ) * fmin( std::fabs( sL ), std::fabs( sR ) );
     return 0.0;
 }
 
 double LVanAlbaba( double sL, double sR ) { return ( sL * sL * sR + sL * sR * sR ) / ( sL * sL + sR * sR + 0.0000001 ); }
 
-double LWENOJS( double x ) { return 0.0; }
+double LWENOJS( double /*x*/ ) { return 0.0; }
 
 double Reconstructor::ReconstructSlopeStruct( double uL, double uC, double uR, double dxL, double dxR, std::string limiter ) const {
     double sL = ( uC - uL ) / dxL;

code/src/solvers/sphericalharmonics.cpp → code/src/toolboxes/sphericalharmonics.cpp

-#include "solvers/sphericalharmonics.h"
+#include "toolboxes/sphericalharmonics.h"
 #include <math.h>
 
 SphericalHarmonics::SphericalHarmonics( unsigned L_degree ) {

code/tests/input/validation_tests/MN_solver/checkerboard_MN.cfg

@@ -18,7 +18,7 @@ PROBLEM = CHECKERBOARD
 % ---- Solver specifications ----
 %
 CFL_NUMBER = 0.5
-TIME_FINAL = 3.2
+TIME_FINAL = 0.4
 SOLVER = MN_SOLVER
 MAX_MOMENT_SOLVER = 2
 ENTROPY_FUNCTIONAL = MAXWELL_BOLTZMANN

code/tests/input/validation_tests/MN_solver/checkerboard_MN_reference.vtk

@@ -2320,23 +2320,23 @@ radiation%20flux%20density 1 1056 double
 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 
 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 
 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 
-0.012884029418 0.01332198066 -0.001175354229 -0.001175354229 -0.001175354229 0.046722187509 0.0022378573236 -0.001175354229 0.041608308258 
--0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 0.008281290878 -0.001175354229 -0.001175354229 -0.001175354229 
-0.0047775072362 -0.001175354229 0.0046949706315 -0.001175354229 0.0050999772269 -0.001175354229 -0.001175354229 -0.001175354229 0.012885237389 
-0.01347064903 -0.001175354229 0.04639207685 0.041579672744 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 0.0026810318544 
--0.001175354229 -0.001175354229 0.0082830531229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 0.0047516101692 
-0.0056955650474 -0.001175354229 0.0046994404757 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 
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--0.001175354229 -0.001175354229 -0.001175354229 0.85204988839 0.85199638633 0.68980279598 0.68927947887 0.67087477349 0.66912582908 
-0.61272173232 0.61213831452 0.6133534161 0.61369427875 0.6136185249 0.61200216845 0.61285461689 0.61342925303 0.73606817489 
-0.73601944613 0.73626518573 0.73582185697 0.79138406505 0.79131698612 0.79107835712 0.79101095225 0.72915753834 0.7280089701 
-0.72911194046 0.72805502925 -0.001175354229 -0.0038733217722 0.016039733942 -0.001175354229 -0.001175354229 0.01052228751 -0.001175354229 
--0.0011257638221 0.0022189461361 -0.001175354229 0.040778283178 -0.001175354229 0.040194665944 -0.001175354229 -0.001175354229 0.0098347709769 
--0.001175354229 0.011667877157 -0.001175354229 -0.005059381161 -0.001175354229 0.012829021376 0.0064114630433 -0.001175354229 -0.001175354229 
-0.012641862507 -0.0039070363941 -0.001175354229 -0.001175354229 0.012055467489 -0.001175354229 0.010471596771 -0.001175354229 -0.001175354229 
-0.0026175353195 0.040758620814 0.0022389643141 -0.001175354229 -0.001175354229 0.039831961741 -0.001175354229 -0.001175354229 -0.001175354229 
-0.014059824509 -0.001175354229 -0.001175354229 0.012785943198 -0.001175354229 -0.001175354229 -0.001175354229 0.0065130215447 0.012626577153 
+-0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 
+-0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 
+-0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 
+-0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 
+-0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 
+-0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 
+-0.001175354229 -0.001175354229 -0.001175354229 0.32218118677 0.32218118677 0.27929540709 0.27926629057 0.27270276389 0.2727027643 
+0.26227966045 0.26227966026 0.26227966063 0.26227966014 0.26227966035 0.26227966054 0.26227966005 0.26227966054 0.30770420705 
+0.30771206519 0.30771206518 0.30770420703 0.32218118677 0.32218118677 0.32218118677 0.32218118677 0.30594486955 0.30594335561 
+0.30594335542 0.30594486977 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 
+-0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 
+-0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 -0.001175354229 
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@@ -2448,34 +2448,34 @@ radiation%20flux%20density 1 565 double
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@@ -2484,14 +2484,14 @@ radiation%20flux%20density 1 565 double
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code/tests/input/validation_tests/PN_solver/checkerboard_PN.cfg

@@ -18,7 +18,7 @@ PROBLEM = CHECKERBOARD
 % ---- Solver specifications ----
 %
 CFL_NUMBER = 0.5
-TIME_FINAL = 3.2
+TIME_FINAL = 0.4
 SOLVER = PN_SOLVER
 MAX_MOMENT_SOLVER = 2
 %

code/tests/input/validation_tests/PN_solver/checkerboard_PN_reference.vtk

@@ -2311,187 +2311,187 @@ CELL_TYPES 1056
 CELL_DATA 1056
 FIELD FieldData 1
 radiation%20flux%20density 1 1056 double
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--0.29952032556 0.00017502977479 0.082162953095 -2.6270163484 0.5234653321 0.0057496428382 -0.24702935277 0.8049690972 2.6310730426 
--0.41804158682 0.75867472335 -0.22949135501 0.53474264455 -3.5887777324 0.11868744547 -1.3432366538 0.18156377352 -0.33764318032 
--0.64573486571 2.0127982757 2.0132214512 -0.73595704861 -3.1816299175 -1.7436149454 2.644739802 1.6466414815 -2.1737299163 
-1.6601832229 -1.7576480632 2.7165974765 -2.2113619794 -3.420304092 -2.8270277583 -2.8151747814 -3.3813679843 -0.4904148507 
--0.50537147341 1.5593351301 1.5701402649 5.2395476777 0.10851871505 5.2569762271 0.11522798402 0.37577515122 -0.46047973334