Initialize at openlb-1-3

5 files changed, 779 insertions, 0 deletions

diff --git a/examples/laminar/poiseuille3d/Makefile b/examples/laminar/poiseuille3d/Makefile
new file mode 100644
index 0000000..a953954
--- /dev/null
+++ b/examples/laminar/poiseuille3d/Makefile
@@ -0,0 +1,105 @@
+#  This file is part of the OpenLB library
+#
+#  Copyright (C) 2007 Mathias Krause
+#  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.
+
+###########################################################################
+## definitions
+
+include definitions.mk
+
+include $(ROOT)/global.mk
+
+OBJECTS    := $(foreach file, $(SRC), $(PWD)/$(file:.cpp=.o))
+DEPS       := $(foreach file, $(SRC), $(PWD)/$(file:.cpp=.d))
+
+###########################################################################
+## all
+
+all : depend compile link
+
+
+###########################################################################
+## dependencies
+
+depend : $(DEPS)
+
+$(PWD)/%.d : %.cpp
+	@echo Create dependencies for $<
+	@$(SHELL) -ec '$(CXX) -M $(CXXFLAGS) $(IDIR) $< \
+                       | sed -e "s!$*\.o!$(PWD)\/$*\.o!1" > .tmpfile; \
+                       cp -f .tmpfile $@;'
+
+###########################################################################
+## compile
+
+compile : $(OBJECTS)
+
+$(PWD)/%.o: %.cpp
+	@echo Compile $<
+	$(CXX) $(CXXFLAGS) $(IDIR) -c $< -o $@
+
+###########################################################################
+## clean
+
+clean : cleanrub cleanobj cleandep
+
+cleanrub:
+	@echo Clean rubbish files
+	@rm -f *~ core .tmpfile tmp/*.* $(OUTPUT)
+	@rm -f tmp/vtkData/*.* tmp/vtkData/data/*.* tmp/imageData/*.* tmp/gnuplotData/*.* tmp/gnuplotData/data/*.*
+
+cleanobj:
+	@echo Clean object files
+	@rm -f $(OBJECTS)
+
+cleandep:
+	@echo Clean dependencies files
+	@rm -f $(DEPS)
+
+cleanbuild:
+	@cd $(ROOT); \
+	 $(MAKE) cleanlib;
+
+###########################################################################
+## update lib
+
+$(ROOT)/$(LIBDIR)/lib$(LIB).a :
+	@cd $(ROOT); \
+	$(MAKE) all
+
+###########################################################################
+## link
+
+link: $(OUTPUT)
+
+$(OUTPUT): $(OBJECTS) $(ROOT)/$(LIBDIR)/lib$(LIB).a
+	@echo Link $@
+	$(CXX) $(foreach file, $(SRC), $(file:.cpp=.o)) $(LDFLAGS) -L$(ROOT)/$(LIBDIR) -l$(LIB) -lz -o $@
+
+###########################################################################
+## include dependencies
+
+ifneq "$(strip $(wildcard *.d))" ""
+   include $(foreach file,$(DEPS),$(file))
+endif
+
+###########################################################################
+###########################################################################
diff --git a/examples/laminar/poiseuille3d/definitions.mk b/examples/laminar/poiseuille3d/definitions.mk
new file mode 100644
index 0000000..f4827a0
--- /dev/null
+++ b/examples/laminar/poiseuille3d/definitions.mk
@@ -0,0 +1,30 @@
+#  This file is part of the OpenLB library
+#
+#  Copyright (C) 2007 Mathias Krause
+#  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.
+
+
+###########################################################################
+###########################################################################
+## DEFINITIONS TO BE CHANGED
+
+ROOT            := ../../..
+SRC             := poiseuille3d.cpp
+OUTPUT          := poiseuille3d
diff --git a/examples/laminar/poiseuille3d/launcher3d.sh b/examples/laminar/poiseuille3d/launcher3d.sh
new file mode 100755
index 0000000..04cfe09
--- /dev/null
+++ b/examples/laminar/poiseuille3d/launcher3d.sh
@@ -0,0 +1,2 @@
+#!/bin/bash
+mpirun -np 4 poiseuille3d 21 0 5
diff --git a/examples/laminar/poiseuille3d/module.mk b/examples/laminar/poiseuille3d/module.mk
new file mode 100644
index 0000000..1190482
--- /dev/null
+++ b/examples/laminar/poiseuille3d/module.mk
@@ -0,0 +1,29 @@
+#  This file is part of the OpenLB library
+#
+#  Copyright (C) 2017 Markus Mohrhard
+#  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.
+
+current_dir := $(dir $(word $(words $(MAKEFILE_LIST)),$(MAKEFILE_LIST)))
+
+include global.mk
+include rules.mk
+include $(addsuffix definitions.mk, $(current_dir))
+
+$(eval $(call sample,$(current_dir)$(OUTPUT),$(addprefix $(current_dir), $(SRC))))
diff --git a/examples/laminar/poiseuille3d/poiseuille3d.cpp b/examples/laminar/poiseuille3d/poiseuille3d.cpp
new file mode 100755
index 0000000..11a1eb1
--- /dev/null
+++ b/examples/laminar/poiseuille3d/poiseuille3d.cpp
@@ -0,0 +1,613 @@
+/*  Lattice Boltzmann sample, written in C++, using the OpenLB
+ *  library
+ *
+ *  Copyright (C) 2018 Marc Haußmann, Mathias J. Krause
+ *  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.
+ */
+
+/* poiseuille3d.cpp:
+ * This example examines a 3D Poseuille flow
+ * It illustrates the computation of error norms.
+ */
+
+
+#include "olb3D.h"
+#include "olb3D.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 MRT
+#ifdef MRT
+#define DESCRIPTOR ForcedMRTD3Q19Descriptor
+#else
+#define DESCRIPTOR  D3Q19<FORCE>
+#endif
+
+typedef enum {forced, nonForced} FlowType;
+
+typedef enum {bounceBack, local, interpolated, bouzidi, freeSlip, partialSlip} BoundaryType;
+
+
+// Parameters for the simulation setup
+FlowType flowType = forced;
+BoundaryType boundaryType = bouzidi;
+const T length  = 2.;         // length of the pie
+const T diameter  = 1.;       // diameter of the pipe
+int N = 21;                   // resolution of the model
+const T physU = 1.;           // physical velocity
+const T Re = 10.;             // Reynolds number
+const T physRho = 1.;         // physical density
+const T tau = 0.8;            // lattice relaxation time
+const T maxPhysT = 20.;       // max. simulation time in s, SI unit
+const T residuum = 1e-5;      // residuum for the convergence check
+const T tuner = 0.97;         // for partialSlip only: 0->bounceBack, 1->freeSlip
+
+// Scaled Parameters
+const T radius  = diameter/2.;            // radius of the pipe
+const T physInterval = 0.0125*maxPhysT;   // interval for the convergence check in s
+
+
+// Stores geometry information in form of material numbers
+void prepareGeometry( UnitConverter<T,DESCRIPTOR> const& converter,
+                      SuperGeometry3D<T>& superGeometry )
+{
+
+  OstreamManager clout(std::cout, "prepareGeometry");
+
+  clout << "Prepare Geometry ..." << std::endl;
+
+  Vector<T, 3> center0(-converter.getPhysDeltaX() * 0.2, radius, radius);
+  Vector<T, 3> center1(length, radius, radius);
+  if (flowType == forced) {
+    center0[0] -= 3.*converter.getPhysDeltaX();
+    center1[0] += 3.*converter.getPhysDeltaX();
+  }
+  IndicatorCylinder3D<T> pipe(center0, center1, radius);
+
+  superGeometry.rename(0, 2);
+
+  superGeometry.rename(2, 1, pipe);
+
+  if (flowType == nonForced) {
+    Vector<T, 3> origin(0, radius, radius);
+    Vector<T, 3> extend = origin;
+
+    // Set material number for inflow
+    origin[0] = -converter.getPhysDeltaX() * 2;
+    extend[0] = converter.getPhysDeltaX() * 2;
+    IndicatorCylinder3D<T> inflow(origin, extend, radius);
+    superGeometry.rename(2, 3, 1, inflow);
+
+    // Set material number for outflow
+    origin[0] = length - 2 * converter.getPhysDeltaX();
+    extend[0] = length + 2 * converter.getPhysDeltaX();
+    IndicatorCylinder3D<T> outflow(extend, origin, radius);
+    superGeometry.rename(2, 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;
+}
+
+// Set up the geometry of the simulation
+void prepareLattice(SuperLattice3D<T, DESCRIPTOR>& sLattice,
+                    UnitConverter<T, DESCRIPTOR>const& converter,
+                    Dynamics<T, DESCRIPTOR>& bulkDynamics,
+                    sOnLatticeBoundaryCondition3D<T, DESCRIPTOR>& onBc,
+                    sOffLatticeBoundaryCondition3D<T, DESCRIPTOR>& offBc,
+                    SuperGeometry3D<T>& superGeometry)
+{
+
+  OstreamManager clout( std::cout,"prepareLattice" );
+  clout << "Prepare Lattice ..." << std::endl;
+
+  const T omega = converter.getLatticeRelaxationFrequency();
+
+  // Material=0 -->do nothing
+  sLattice.defineDynamics( superGeometry, 0, &instances::getNoDynamics<T, DESCRIPTOR>() );
+
+  // Material=1 -->bulk dynamics
+  sLattice.defineDynamics( superGeometry, 1, &bulkDynamics );
+
+  Vector<T, 3> center0(0, radius, radius);
+  Vector<T, 3> center1(length, radius, radius);
+
+  std::vector<T> origin = { length, radius, radius};
+  std::vector<T> axis = { 1, 0, 0 };
+
+  CirclePoiseuille3D<T> poiseuilleU(origin, axis, converter.getCharLatticeVelocity(), radius);
+
+  if (boundaryType == bounceBack) {
+    sLattice.defineDynamics( superGeometry, 2, &instances::getBounceBack<T, DESCRIPTOR>() );
+  }
+  else if (boundaryType == freeSlip) {
+    sLattice.defineDynamics(superGeometry, 2, &instances::getNoDynamics<T, DESCRIPTOR>());
+    onBc.addSlipBoundary( superGeometry, 2 );
+  }
+  else if (boundaryType == partialSlip) {
+    sLattice.defineDynamics(superGeometry, 2, &instances::getNoDynamics<T, DESCRIPTOR>());
+    onBc.addPartialSlipBoundary(tuner, superGeometry, 2 );
+  }
+  else if (boundaryType == bouzidi) {
+    sLattice.defineDynamics(superGeometry, 2, &instances::getNoDynamics<T, DESCRIPTOR>() );
+
+    center0[0] -= 0.5*converter.getPhysDeltaX();
+    center1[0] += 0.5*converter.getPhysDeltaX();
+    if (flowType == forced) {
+      center0[0] -= 3.*converter.getPhysDeltaX();
+      center1[0] += 3.*converter.getPhysDeltaX();
+    }
+    IndicatorCylinder3D<T> pipe(center0, center1, radius);
+    offBc.addZeroVelocityBoundary(superGeometry, 2, pipe);
+  }
+  else {
+    sLattice.defineDynamics( superGeometry, 2, &bulkDynamics );
+    onBc.addVelocityBoundary( superGeometry, 2, omega );
+  }
+
+  if (flowType == nonForced) {
+    if (boundaryType == bouzidi) {
+      sLattice.defineDynamics(superGeometry, 3, &instances::getNoDynamics<T, DESCRIPTOR>() );
+      IndicatorCylinder3D<T> pipe(center0, center1, radius);
+      offBc.addVelocityBoundary(superGeometry, 3, pipe);
+      offBc.defineU(superGeometry,3,poiseuilleU);
+    }
+    else {
+      // Material=3 -->bulk dynamics
+      sLattice.defineDynamics( superGeometry, 3, &bulkDynamics );
+      onBc.addVelocityBoundary( superGeometry, 3, omega );
+    }
+    // Material=4 -->bulk dynamics
+    sLattice.defineDynamics( superGeometry, 4, &bulkDynamics );
+    onBc.addPressureBoundary( superGeometry, 4, omega );
+  }
+
+  if (flowType == forced) {
+    // Initial conditions
+    T D = converter.getLatticeLength(diameter);
+
+    std::vector<T> poiseuilleForce(3, T());
+    poiseuilleForce[0] = 4. * converter.getLatticeViscosity() * converter.getCharLatticeVelocity() / (D * D / 4. );
+    AnalyticalConst3D<T,T> force( poiseuilleForce );
+
+    // Initialize force
+    sLattice.defineField<FORCE>(superGeometry, 1, force);
+    sLattice.defineField<FORCE>(superGeometry, 2, force );
+
+
+    AnalyticalConst3D<T, T> rhoF(1);
+
+    sLattice.defineRhoU(superGeometry, 1, rhoF, poiseuilleU);
+    sLattice.iniEquilibrium(superGeometry, 1, rhoF, poiseuilleU);
+    sLattice.defineRhoU(superGeometry, 2, rhoF, poiseuilleU);
+    sLattice.iniEquilibrium(superGeometry, 2, rhoF, poiseuilleU);
+  }
+  else {
+    // Initial conditions
+    T p0 = 4. * converter.getPhysViscosity() * converter.getCharPhysVelocity() * length / (radius * radius);
+
+    p0 = converter.getLatticePressure(p0);
+    AnalyticalLinear3D<T, T> rho(-p0 / length * descriptors::invCs2<T,DESCRIPTOR>(), 0, 0, p0 * descriptors::invCs2<T,DESCRIPTOR>() + 1);
+
+    std::vector<T> velocity(3, T());
+    AnalyticalConst3D<T, T> uF(velocity);
+
+    // Initialize all values of distribution functions to their local equilibrium
+    sLattice.defineRhoU(superGeometry, 0, rho, uF);
+    sLattice.iniEquilibrium(superGeometry, 0, rho, uF);
+    sLattice.defineRhoU(superGeometry, 1, rho, poiseuilleU);
+    sLattice.iniEquilibrium(superGeometry, 1, rho, poiseuilleU);
+    sLattice.defineRhoU(superGeometry, 2, rho, poiseuilleU);
+    sLattice.iniEquilibrium(superGeometry, 2, rho, poiseuilleU);
+    sLattice.defineRhoU(superGeometry, 3, rho, poiseuilleU);
+    sLattice.iniEquilibrium(superGeometry, 3, rho, poiseuilleU);
+    sLattice.defineRhoU(superGeometry, 4, rho, poiseuilleU);
+    sLattice.iniEquilibrium(superGeometry, 4, rho, poiseuilleU);
+  }
+
+  // Make the lattice ready for simulation
+  sLattice.initialize();
+
+  clout << "Prepare Lattice ... OK" << std::endl;
+}
+
+// Compute error norms
+void error( SuperGeometry3D<T>& superGeometry,
+            SuperLattice3D<T, DESCRIPTOR>& sLattice,
+            UnitConverter<T,DESCRIPTOR> const& converter,
+            Dynamics<T, DESCRIPTOR>& bulkDynamics,
+            SuperLatticePhysWallShearStress3D<T,DESCRIPTOR>& wss)
+{
+  OstreamManager clout( std::cout,"error" );
+
+  int tmp[]= { };
+  T result[2]= { };
+
+  // velocity error
+  const T maxVelocity = converter.getCharPhysVelocity();
+  std::vector<T> axisPoint = {length, radius, radius};
+  std::vector<T> axisDirection = { 1, 0, 0 };
+  CirclePoiseuille3D<T> uSol(axisPoint, axisDirection, maxVelocity, radius);
+  SuperLatticePhysVelocity3D<T,DESCRIPTOR> u( sLattice,converter );
+  auto indicatorF = superGeometry.getMaterialIndicator(1);
+
+  SuperAbsoluteErrorL1Norm3D<T> absVelocityErrorNormL1(u, uSol, indicatorF);
+  absVelocityErrorNormL1(result, tmp);
+  clout << "velocity-L1-error(abs)=" << result[0];
+  SuperRelativeErrorL1Norm3D<T> relVelocityErrorNormL1(u, uSol, indicatorF);
+  relVelocityErrorNormL1(result, tmp);
+  clout << "; velocity-L1-error(rel)=" << result[0] << std::endl;
+
+  SuperAbsoluteErrorL2Norm3D<T> absVelocityErrorNormL2(u, uSol, indicatorF);
+  absVelocityErrorNormL2(result, tmp);
+  clout << "velocity-L2-error(abs)=" << result[0];
+  SuperRelativeErrorL2Norm3D<T> relVelocityErrorNormL2(u, uSol, indicatorF);
+  relVelocityErrorNormL2(result, tmp);
+  clout << "; velocity-L2-error(rel)=" << result[0] << std::endl;
+
+  SuperAbsoluteErrorLinfNorm3D<T> absVelocityErrorNormLinf(u, uSol, indicatorF);
+  absVelocityErrorNormLinf(result, tmp);
+  clout << "velocity-Linf-error(abs)=" << result[0];
+  SuperRelativeErrorLinfNorm3D<T> relVelocityErrorNormLinf(u, uSol, indicatorF);
+  relVelocityErrorNormLinf(result, tmp);
+  clout << "; velocity-Linf-error(rel)=" << result[0] << std::endl;
+
+  // strainRate error
+  CirclePoiseuilleStrainRate3D<T, DESCRIPTOR> sSol( converter, radius );
+  SuperLatticePhysStrainRate3D<T,DESCRIPTOR> s( sLattice,converter );
+
+  SuperAbsoluteErrorL1Norm3D<T> absStrainRateErrorNormL1(s, sSol, indicatorF);
+  absStrainRateErrorNormL1(result, tmp);
+  clout << "strainRate-L1-error(abs)=" << result[0];
+  SuperRelativeErrorL1Norm3D<T> relStrainRateErrorNormL1(s, sSol, indicatorF);
+  relStrainRateErrorNormL1(result, tmp);
+  clout << "; strainRate-L1-error(rel)=" << result[0] << std::endl;
+
+  SuperAbsoluteErrorL2Norm3D<T> absStrainRateErrorNormL2(s, sSol, indicatorF);
+  absStrainRateErrorNormL2(result, tmp);
+  clout << "strainRate-L2-error(abs)=" << result[0];
+  SuperRelativeErrorL2Norm3D<T> relStrainRateErrorNormL2(s, sSol, indicatorF);
+  relStrainRateErrorNormL2(result, tmp);
+  clout << "; strainRate-L2-error(rel)=" << result[0] << std::endl;
+
+  SuperAbsoluteErrorLinfNorm3D<T> absStrainRateErrorNormLinf(s, sSol, indicatorF);
+  absStrainRateErrorNormLinf(result, tmp);
+  clout << "strainRate-Linf-error(abs)=" << result[0];
+  SuperRelativeErrorLinfNorm3D<T> relStrainRateErrorNormLinf(s, sSol, indicatorF);
+  relStrainRateErrorNormLinf(result, tmp);
+  clout << "; strainRate-Linf-error(rel)=" << result[0] << std::endl;
+
+  // wallShearStress error
+  AnalyticalConst3D<T,T> wssSol(4. * converter.getPhysViscosity() * converter.getPhysDensity() * maxVelocity / diameter);
+  SuperLatticeFfromAnalyticalF3D<T,DESCRIPTOR> wssSolLattice (wssSol, sLattice);
+
+  auto indicatorB = superGeometry.getMaterialIndicator(2);
+
+  SuperAbsoluteErrorL1Norm3D<T> absWallShearStressErrorNormL1(wss, wssSol, indicatorB);
+  absWallShearStressErrorNormL1(result, tmp);
+  clout << "wss-L1-error(abs)=" << result[0];
+  SuperRelativeErrorL1Norm3D<T> relWallShearStressErrorNormL1(wss, wssSol, indicatorB);
+  relWallShearStressErrorNormL1(result, tmp);
+  clout << "; wss-L1-error(rel)=" << result[0] << std::endl;
+
+  SuperAbsoluteErrorL2Norm3D<T> absWallShearStressErrorNormL2(wss, wssSol, indicatorB);
+  absWallShearStressErrorNormL2(result, tmp);
+  clout << "wss-L2-error(abs)=" << result[0];
+  SuperRelativeErrorL2Norm3D<T> relWallShearStressErrorNormL2(wss, wssSol, indicatorB);
+  relWallShearStressErrorNormL2(result, tmp);
+  clout << "; wss-L2-error(rel)=" << result[0] << std::endl;
+
+  SuperAbsoluteErrorLinfNorm3D<T> absWallShearStressErrorNormLinf(wss, wssSol, indicatorB);
+  absWallShearStressErrorNormLinf(result, tmp);
+  clout << "wss-Linf-error(abs)=" << result[0];
+  SuperRelativeErrorLinfNorm3D<T> relWallShearStressErrorNormLinf(wss, wssSol, indicatorB);
+  relWallShearStressErrorNormLinf(result, tmp);
+  clout << "; wss-Linf-error(rel)=" << result[0] << std::endl;
+
+  if (flowType == nonForced) {
+    // pressure error
+    T p0 = 4. * converter.getPhysViscosity() * maxVelocity * length / (radius * radius);
+    AnalyticalLinear3D<T, T> pressureSol(-p0 / length, 0, 0, p0);
+    SuperLatticePhysPressure3D<T, DESCRIPTOR> pressure(sLattice, converter);
+
+    SuperAbsoluteErrorL1Norm3D<T> absPressureErrorNormL1(pressure, pressureSol, indicatorF);
+    absPressureErrorNormL1(result, tmp);
+    clout << "pressure-L1-error(abs)=" << result[0];
+    SuperRelativeErrorL1Norm3D<T> relPressureErrorNormL1(pressure, pressureSol, indicatorF);
+    relPressureErrorNormL1(result, tmp);
+    clout << "; pressure-L1-error(rel)=" << result[0] << std::endl;
+
+    SuperAbsoluteErrorL2Norm3D<T> absPressureErrorNormL2(pressure, pressureSol, indicatorF);
+    absPressureErrorNormL2(result, tmp);
+    clout << "pressure-L2-error(abs)=" << result[0];
+    SuperRelativeErrorL2Norm3D<T> relPressureErrorNormL2(pressure, pressureSol, indicatorF);
+    relPressureErrorNormL2(result, tmp);
+    clout << "; pressure-L2-error(rel)=" << result[0] << std::endl;
+
+    SuperAbsoluteErrorLinfNorm3D<T> absPressureErrorNormLinf(pressure, pressureSol, indicatorF);
+    absPressureErrorNormLinf(result, tmp);
+    clout << "pressure-Linf-error(abs)=" << result[0];
+    SuperRelativeErrorLinfNorm3D<T> relPressureErrorNormLinf(pressure, pressureSol, indicatorF);
+    relPressureErrorNormLinf(result, tmp);
+    clout << "; pressure-Linf-error(rel)=" << result[0] << std::endl;
+  }
+}
+
+// Output to console and files
+void getResults( SuperLattice3D<T,DESCRIPTOR>& sLattice, Dynamics<T, DESCRIPTOR>& bulkDynamics,
+                 UnitConverter<T,DESCRIPTOR> const& converter, int iT,
+                 SuperGeometry3D<T>& superGeometry, Timer<T>& timer, bool hasConverged,
+                 SuperLatticePhysWallShearStress3D<T,DESCRIPTOR>& wss)
+{
+
+  OstreamManager clout( std::cout,"getResults" );
+
+  SuperVTMwriter3D<T> vtmWriter( "poiseuille3d" );
+  SuperLatticePhysVelocity3D<T, DESCRIPTOR> velocity( sLattice, converter );
+  SuperLatticePhysPressure3D<T, DESCRIPTOR> pressure( sLattice, converter );
+  vtmWriter.addFunctor( velocity );
+  vtmWriter.addFunctor( pressure );
+  vtmWriter.addFunctor( wss );
+
+  const int vtmIter  = converter.getLatticeTime( maxPhysT/20. );
+  const int statIter = converter.getLatticeTime( maxPhysT/20. );
+
+  if ( iT==0 ) {
+    // Writes the geometry, cuboid no. and rank no. as vti file for visualization
+    SuperLatticeGeometry3D<T, DESCRIPTOR> geometry( sLattice, superGeometry );
+    SuperLatticeCuboid3D<T, DESCRIPTOR> cuboid( sLattice );
+    SuperLatticeRank3D<T, DESCRIPTOR> rank( sLattice );
+
+    vtmWriter.write( geometry );
+    vtmWriter.write( cuboid );
+    vtmWriter.write( rank );
+
+    vtmWriter.createMasterFile();
+  }
+
+  // Writes the vtm files and profile text file
+  if ( iT%vtmIter==0 || hasConverged ) {
+    vtmWriter.write( iT );
+
+    SuperEuklidNorm3D<T, DESCRIPTOR> normVel( velocity );
+    BlockReduction3D2D<T> planeReduction( normVel, {0,0,1}, 600, BlockDataSyncMode::ReduceOnly );
+    // write output as JPEG
+    heatmap::write(planeReduction, iT);
+
+  }
+
+  if ( hasConverged ) {
+    Gnuplot<T> gplot( "centerVelocity" );
+    T D = converter.getLatticeLength( diameter );
+    for ( int iY=0; iY<=D; ++iY ) {
+      T dx = 1. / T(converter.getResolution());
+      T point[3]= {T(),T(),T()};
+      point[0] = length/2.;
+      point[1] = ( T )converter.getPhysLength(iY);
+      point[2] = ( T )radius;
+      const T maxVelocity = converter.getCharPhysVelocity();
+      std::vector<T> axisPoint = {length, radius, radius};
+      std::vector<T> axisDirection = { 1, 0, 0 };
+      CirclePoiseuille3D<T> uSol(axisPoint, axisDirection, maxVelocity, radius);
+      T analytical[3] = {T(),T(),T()};
+      uSol( analytical,point );
+      SuperLatticePhysVelocity3D<T, DESCRIPTOR> velocity( sLattice, converter );
+      AnalyticalFfromSuperF3D<T> intpolateVelocity( velocity, true, 1 );
+      T numerical[3] = {T(),T(),T()};
+      intpolateVelocity( numerical,point );
+      gplot.setData( iY*dx, {analytical[0],numerical[0]}, {"analytical","numerical"} );
+    }
+    // Create PNG file
+    gplot.writePNG();
+  }
+
+  // Writes output on the console
+  if ( iT%statIter==0 || hasConverged ) {
+    // Timer console output
+    timer.update( iT );
+    timer.printStep();
+
+    // Lattice statistics console output
+    sLattice.getStatistics().print( iT,converter.getPhysTime( iT ) );
+
+    // Error norms
+    error( superGeometry, sLattice, converter, bulkDynamics, wss );
+  }
+}
+
+int main( int argc, char* argv[] )
+{
+
+  // === 1st Step: Initialization ===
+  olbInit( &argc, &argv );
+  singleton::directories().setOutputDir( "./tmp/" );
+  OstreamManager clout( std::cout,"main" );
+
+  if (argc > 1) {
+    if (argv[1][0]=='-'&&argv[1][1]=='h') {
+      OstreamManager clout( std::cout,"help" );
+      clout<<"Usage: program [Resolution] [FlowType] [BoundaryType]"<<std::endl;
+      clout<<"FlowType: 0=forced, 1=nonForced"<<std::endl;
+      clout<<"BoundaryType: 0=bounceBack, 1=local, 2=interpolated, 3=bouzidi, 4=freeSlip, 5=partialSlip"<<std::endl;
+      clout<<"Default: FlowType=forced, Resolution=21, BoundaryType=bouzidi"<<std::endl;
+      return 0;
+    }
+  }
+
+  if (argc > 1) {
+    N = atoi(argv[1]);
+    if (N < 1) {
+      std::cerr << "Fluid domain is too small" << std::endl;
+      return 1;
+    }
+  }
+
+  if (argc > 2) {
+    int flowTypeNumber = atoi(argv[2]);
+    if (flowTypeNumber < 0 || flowTypeNumber > (int)nonForced) {
+      std::cerr << "Unknown fluid flow type" << std::endl;
+      return 2;
+    }
+    flowType = (FlowType) flowTypeNumber;
+  }
+
+  if (argc > 3) {
+    int boundaryTypeNumber = atoi(argv[3]);
+    if (boundaryTypeNumber < 0 || boundaryTypeNumber > (int) partialSlip) {
+      std::cerr << "Unknown boundary type" << std::endl;
+      return 3;
+    }
+    boundaryType = (BoundaryType) boundaryTypeNumber;
+  }
+
+  UnitConverterFromResolutionAndRelaxationTime<T, DESCRIPTOR> const converter(
+    int {N},                  // resolution: number of voxels per charPhysL
+    (T)   tau,                // latticeRelaxationTime: relaxation time, have to be greater than 0.5!
+    (T)   diameter,           // charPhysLength: reference length of simulation geometry
+    (T)   physU,              // charPhysVelocity: maximal/highest expected velocity during simulation in __m / s__
+    (T)   diameter*physU/Re,  // physViscosity: physical kinematic viscosity in __m^2 / s__
+    (T)   physRho             // physDensity: physical density in __kg / m^3__
+  );
+  // Prints the converter log as console output
+  converter.print();
+  // Writes the converter log in a file
+  converter.write("poiseuille3d");
+
+
+  // === 2nd Step: Prepare Geometry ===
+
+  Vector<T, 3> center0(0, radius, radius);
+  Vector<T, 3> center1(length, radius, radius);
+  IndicatorCylinder3D<T> pipe(center0, center1, radius);
+  IndicatorLayer3D<T> extendedDomain(pipe, converter.getPhysDeltaX());
+
+  // Instantiation of a cuboidGeometry with weights
+#ifdef PARALLEL_MODE_MPI
+  const int noOfCuboids = 2*singleton::mpi().getSize();
+#else // ifdef PARALLEL_MODE_MPI
+  const int noOfCuboids = 6;
+#endif // ifdef PARALLEL_MODE_MPI
+  CuboidGeometry3D<T> cuboidGeometry(extendedDomain, converter.getPhysDeltaX(), noOfCuboids);
+  if (flowType == forced) {
+    // Periodic boundaries in x-direction
+    cuboidGeometry.setPeriodicity( true, false, false );
+  }
+
+  // Instantiation of a loadBalancer
+  HeuristicLoadBalancer<T> loadBalancer(cuboidGeometry);
+
+  // Instantiation of a superGeometry
+  SuperGeometry3D<T> superGeometry(cuboidGeometry, loadBalancer, 2);
+
+  prepareGeometry(converter, superGeometry);
+
+  // === 3rd Step: Prepare Lattice ===
+  SuperLattice3D<T, DESCRIPTOR> sLattice( superGeometry );
+
+  std::unique_ptr<Dynamics<T, DESCRIPTOR>> bulkDynamics;
+
+#if defined(MRT)
+  if (flowType == forced) {
+    bulkDynamics.reset(new ForcedMRTdynamics<T, DESCRIPTOR>( converter.getLatticeRelaxationFrequency(), instances::getBulkMomenta<T, DESCRIPTOR>() ));
+  }
+  else {
+    bulkDynamics.reset(new MRTdynamics<T, DESCRIPTOR>( converter.getLatticeRelaxationFrequency(), instances::getBulkMomenta<T, DESCRIPTOR>() ));
+  }
+#else
+  if (flowType == forced) {
+    bulkDynamics.reset(new ForcedBGKdynamics<T, DESCRIPTOR>( converter.getLatticeRelaxationFrequency(), instances::getBulkMomenta<T, DESCRIPTOR>() ));
+  }
+  else {
+    bulkDynamics.reset(new BGKdynamics<T, DESCRIPTOR>( converter.getLatticeRelaxationFrequency(), instances::getBulkMomenta<T, DESCRIPTOR>() ));
+  }
+#endif
+
+
+  // choose between local and non-local boundary condition
+  sOnLatticeBoundaryCondition3D<T, DESCRIPTOR> sOnBoundaryCondition( sLattice );
+  sOffLatticeBoundaryCondition3D<T, DESCRIPTOR> sOffBoundaryCondition(sLattice);
+  createBouzidiBoundaryCondition3D<T, DESCRIPTOR>(sOffBoundaryCondition);
+
+  if (boundaryType == local) {
+    createLocalBoundaryCondition3D<T, DESCRIPTOR> (sOnBoundaryCondition);
+  }
+  else {
+    createInterpBoundaryCondition3D<T, DESCRIPTOR> ( sOnBoundaryCondition );
+  }
+
+  prepareLattice(sLattice, converter, *bulkDynamics, sOnBoundaryCondition, sOffBoundaryCondition, superGeometry);
+
+  // set up size-increased indicator and instantiate wall shear stress functor (wss)
+  Vector<T, 3> center0Extended(-converter.getPhysDeltaX() * 0.2, radius, radius);
+  Vector<T, 3> center1Extended(length, radius, radius);
+  if (flowType == forced) {
+    center0Extended[0] -= 4.*converter.getPhysDeltaX();
+    center1Extended[0] += 4.*converter.getPhysDeltaX();
+  }
+  IndicatorCylinder3D<T> pipeExtended(center0Extended, center1Extended, radius);
+  IndicatorLayer3D<T> indicatorExtended (pipeExtended, 0.9*converter.getConversionFactorLength()*N/11.);
+  SuperLatticePhysWallShearStress3D<T,DESCRIPTOR> wss(sLattice, superGeometry, 2, converter, indicatorExtended);
+
+  // === 4th Step: Main Loop with Timer ===
+  clout << "starting simulation..." << endl;
+  Timer<T> timer( converter.getLatticeTime( maxPhysT ), superGeometry.getStatistics().getNvoxel() );
+  util::ValueTracer<T> converge( converter.getLatticeTime( physInterval ), residuum );
+  timer.start();
+
+  for ( int iT = 0; iT < converter.getLatticeTime( maxPhysT ); ++iT ) {
+    if ( converge.hasConverged() ) {
+      clout << "Simulation converged." << endl;
+      getResults( sLattice, *bulkDynamics, converter, iT, superGeometry, timer, converge.hasConverged(), wss );
+
+      break;
+    }
+
+    // === 5th Step: Definition of Initial and Boundary Conditions ===
+    // in this application no boundary conditions have to be adjusted
+
+    // === 6th Step: Collide and Stream Execution ===
+    sLattice.collideAndStream();
+
+    // === 7th Step: Computation and Output of the Results ===
+    getResults( sLattice, *bulkDynamics, converter, iT, superGeometry, timer, converge.hasConverged(), wss  );
+    converge.takeValue( sLattice.getStatistics().getAverageEnergy(), true );
+  }
+
+  timer.stop();
+  timer.printSummary();
+}