Initialize at openlb-1-3

7 files changed, 683 insertions, 0 deletions

diff --git a/examples/laminar/powerLaw2d/Makefile b/examples/laminar/powerLaw2d/Makefile
new file mode 100644
index 0000000..a953954
--- /dev/null
+++ b/examples/laminar/powerLaw2d/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/powerLaw2d/definitions.mk b/examples/laminar/powerLaw2d/definitions.mk
new file mode 100644
index 0000000..137f8c5
--- /dev/null
+++ b/examples/laminar/powerLaw2d/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             := powerLaw2d.cpp
+OUTPUT          := powerLaw2d
diff --git a/examples/laminar/powerLaw2d/input-model.xml b/examples/laminar/powerLaw2d/input-model.xml
new file mode 100644
index 0000000..f4bed5b
--- /dev/null
+++ b/examples/laminar/powerLaw2d/input-model.xml
@@ -0,0 +1,17 @@
+<Param>
+		  <geometry>
+					 <N> 40 </N>
+					 <lx> 2 </lx>
+					 <ly> 1 </ly>
+		  </geometry>
+		  <dynamics>
+					 <maxU> MAXU </maxU> <!-- Velocity profile does not change if maxU is changed. Try 0.1, 1 or 10 as an example. -->
+					 <Re> 10 </Re>
+					 <tau> 0.8 </tau>
+					 <n> 0.2 </n>
+		  </dynamics>
+		  <time>
+					 <Tmax> 20 </Tmax>
+					 <Tprint> 1 </Tprint>
+		  </time>
+</Param>
diff --git a/examples/laminar/powerLaw2d/input.xml b/examples/laminar/powerLaw2d/input.xml
new file mode 100644
index 0000000..68c5080
--- /dev/null
+++ b/examples/laminar/powerLaw2d/input.xml
@@ -0,0 +1,17 @@
+<Param>
+		  <geometry>
+					 <N> 40 </N>
+					 <lx> 2 </lx>
+					 <ly> 1 </ly>
+		  </geometry>
+		  <dynamics>
+					 <maxU> .1 </maxU> <!-- Velocity profile does not change if maxU is changed. Try 0.1, 1 or 10 as an example. -->
+					 <Re> 10 </Re>
+					 <tau> 0.8 </tau>
+					 <n> 0.2 </n>
+		  </dynamics>
+		  <time>
+					 <Tmax> 20 </Tmax>
+					 <Tprint> 1 </Tprint>
+		  </time>
+</Param>
diff --git a/examples/laminar/powerLaw2d/module.mk b/examples/laminar/powerLaw2d/module.mk
new file mode 100644
index 0000000..1190482
--- /dev/null
+++ b/examples/laminar/powerLaw2d/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/powerLaw2d/powerLaw2d.cpp b/examples/laminar/powerLaw2d/powerLaw2d.cpp
new file mode 100644
index 0000000..fd5e833
--- /dev/null
+++ b/examples/laminar/powerLaw2d/powerLaw2d.cpp
@@ -0,0 +1,456 @@
+/*  Lattice Boltzmann sample, written in C++, using the OpenLB
+ *  library
+ *
+ *  Copyright (C) 2016 Vojtech Cvrcek, 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.
+ */
+
+/* powerLaw2d.cpp:
+ * This example examines a steady flow of a non-newtonian fluid in a channel.
+ * At the inlet, a profile for non-newtonian fluid is imposed on the velocity,
+ * where as the outlet implements an outflow condition grad_x p = 0.
+ * The power law model is for n=1 and m=charNu in fact the classical poiseuille flow.
+ * One can validate the error with using functors in void error.
+ *
+ *
+ */
+
+#include "olb2D.h"
+#include "olb2D.hh"   // include full template code
+
+#include <vector>
+#include <cmath>
+#include <iostream>
+#include <fstream>
+
+using namespace olb;
+using namespace olb::descriptors;
+using namespace olb::graphics;
+using namespace olb::util;
+using namespace std;
+
+typedef double T;
+#define DESCRIPTOR DynOmegaD2Q9Descriptor
+
+// Parameters for the simulation setup
+int N = 40;            // resolution of the model
+T Re = 10.;      // Reynolds number
+T tau = 0.8;
+T lx = 2.;             // channel lenght
+T ly = 1.;             // channel width
+T maxU = 1;     // Max velocity
+T Tmax = 20;      // max. phys. time in s
+T Tprint = 1;      // Phys time at which the status of the system is print
+// set the changes for n and m in powerLawBGKdynamics.h
+T n = .2;              // parameter in power law model (n=1 Newtonian fluid)
+bool bcTypePeriodic = false; //true works only with one core
+
+const T residuum = 1e-5;      // residuum for the convergence check
+
+void prepareGeometry( PowerLawUnitConverter<T,DESCRIPTOR> const& converter,
+                      SuperGeometry2D<T>& superGeometry ) {
+  OstreamManager clout( std::cout,"prepareGeometry" );
+  clout << "Prepare Geometry ..." << std::endl;
+
+  Vector<T,2> extend( lx, ly );
+  Vector<T,2> origin;
+
+  superGeometry.rename( 0,2 );
+  superGeometry.rename( 2,1,1,1 );
+
+  // Set material number for inflow
+  extend[0] = 1.2*converter.getConversionFactorLength();
+  origin[0] = -converter.getConversionFactorLength();
+  IndicatorCuboid2D<T> inflow( extend, origin );
+  if (bcTypePeriodic)
+    superGeometry.rename( 1,3,inflow );
+  else
+    superGeometry.rename( 2,3,1,inflow );
+  // Set material number for outflow
+  origin[0] = lx-.5*converter.getConversionFactorLength();
+  IndicatorCuboid2D<T> outflow( extend, origin );
+  if (bcTypePeriodic)
+    superGeometry.rename( 1,4,outflow );
+  else
+    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.getStatistics().print();
+
+  clout << "Prepare Geometry ... OK" << std::endl;
+  return;
+}
+
+// Set up the geometry of the simulation
+void prepareLattice( SuperLattice2D<T,DESCRIPTOR>& sLattice,
+                     PowerLawUnitConverter<T,DESCRIPTOR> const& converter,
+                     Dynamics<T, DESCRIPTOR>& bulkDynamics,
+                     Dynamics<T, DESCRIPTOR>& inDynamics,
+                     Dynamics<T, DESCRIPTOR>& outDynamics,
+                     sOnLatticeBoundaryCondition2D<T,DESCRIPTOR>& sBoundaryCondition,
+                     SuperGeometry2D<T>& superGeometry ) {
+
+  OstreamManager clout( std::cout,"prepareLattice" );
+  clout << "Prepare Lattice ..." << std::endl;
+
+  const T omega = converter.getLatticeRelaxationFrequency();
+
+  // Material=0 -->do nothing
+  sLattice.defineDynamics( superGeometry.getMaterialIndicator(0), &instances::getNoDynamics<T, DESCRIPTOR>() );
+
+  // Material=1 -->bulk dynamics
+  sLattice.defineDynamics( superGeometry.getMaterialIndicator(1), &bulkDynamics );
+
+  // Material=2 -->bounce back
+  sLattice.defineDynamics( superGeometry.getMaterialIndicator(2), &instances::getBounceBack<T, DESCRIPTOR>() );
+
+  // Material=3 -->bulk dynamics (inflow)
+  if (bcTypePeriodic)
+    sLattice.defineDynamics( superGeometry.getMaterialIndicator(3), &inDynamics );
+  else {
+    sLattice.defineDynamics( superGeometry.getMaterialIndicator(3), &bulkDynamics );
+    // Setting of the boundary conditions
+    sBoundaryCondition.addVelocityBoundary( superGeometry, 3, omega );
+  }
+
+  // Material=4 -->bulk dynamics (outflow)
+  if (bcTypePeriodic)
+    sLattice.defineDynamics( superGeometry.getMaterialIndicator(4), &outDynamics );
+  else {
+    sLattice.defineDynamics( superGeometry.getMaterialIndicator(4), &bulkDynamics );
+    // Setting of the boundary conditions
+    sBoundaryCondition.addPressureBoundary( superGeometry, 4, omega );
+  }
+  clout << "Prepare Lattice ... OK" << std::endl;
+}
+
+
+void setBoundaryValues( SuperLattice2D<T, DESCRIPTOR>& sLattice,
+                        PowerLawUnitConverter<T,DESCRIPTOR> const& converter,
+                        int iT, SuperGeometry2D<T>& superGeometry ) {
+
+  OstreamManager clout( std::cout,"setBoundaryValues" );
+
+  // Set initial and steady boundary conditions
+  if ( iT==0 ) {
+
+    // Define the analytical solutions for pressure and velocity
+    T maxVelocity = converter.getCharLatticeVelocity();
+    T distance2Wall = converter.getConversionFactorLength()/2.;
+
+    T p0 = converter.getPhysConsistencyCoeff()*pow( converter.getCharPhysVelocity(),n )*pow( ( n + 1. )/n,n )*pow( 2./( ly-distance2Wall*2 ),n + 1. );
+
+    AnalyticalLinear2D<T,T> rho( converter.getLatticeDensityFromPhysPressure( -p0 ) - 1., 0, converter.getLatticeDensityFromPhysPressure(  p0*(lx + distance2Wall*2.)/2. ) );
+
+    PowerLaw2D<T> u( superGeometry, 3, maxVelocity, distance2Wall, ( n + 1. )/n );
+
+    // Set the analytical solutions for pressure and velocity
+    AnalyticalConst2D<T,T> omega0( converter.getLatticeRelaxationFrequency() );
+    sLattice.defineField<descriptors::OMEGA>( superGeometry, 1, omega0 );
+    sLattice.defineField<descriptors::OMEGA>( superGeometry, 3, omega0 );
+    sLattice.defineField<descriptors::OMEGA>( superGeometry, 4, omega0 );
+
+    // Set the analytical solutions for pressure and velocity
+    // Initialize all values of distribution functions to their local equilibrium
+
+    sLattice.defineRhoU( superGeometry, 1, rho, u );
+    sLattice.iniEquilibrium( superGeometry, 1, rho, u );
+
+    sLattice.iniEquilibrium( superGeometry, 3, rho, u );
+    sLattice.defineRhoU( superGeometry, 3, rho, u );
+
+    sLattice.iniEquilibrium( superGeometry, 4, rho, u );
+    sLattice.defineRhoU( superGeometry, 4, rho, u );
+
+    // Make the lattice ready for simulation
+    sLattice.initialize();
+  }
+}
+
+// Compute error norms
+void error( SuperGeometry2D<T>& superGeometry,
+            SuperLattice2D<T, DESCRIPTOR>& sLattice,
+            PowerLawUnitConverter<T,DESCRIPTOR> const& converter,
+            Dynamics<T, DESCRIPTOR>& bulkDynamics ) {
+  OstreamManager clout( std::cout,"error" );
+
+  int input[1] = { };
+  T result[1]  = { };
+
+  T distance2Wall = converter.getConversionFactorLength()/2.;
+
+  PowerLaw2D<T> uSol( superGeometry,3,converter.getCharPhysVelocity(),distance2Wall,( n + 1. )/n );
+  SuperLatticePhysVelocity2D<T,DESCRIPTOR> u( sLattice,converter );
+
+  T p0 = converter.getPhysConsistencyCoeff()*pow( converter.getCharPhysVelocity(),n )*pow( ( n + 1. )/n,n )*pow( 2./( ly-distance2Wall*2 ),n + 1. );
+  AnalyticalLinear2D<T,T> pressureSol( -p0, 0, p0*(lx + distance2Wall*2.)/2. );
+  SuperLatticePhysPressure2D<T,DESCRIPTOR> pressure( sLattice,converter );
+
+  auto indicatorF = superGeometry.getMaterialIndicator(1);
+
+  // velocity error
+  SuperAbsoluteErrorL1Norm2D<T> absVelocityErrorNormL1(u, uSol, indicatorF);
+  absVelocityErrorNormL1(result, input);
+  clout << "velocity-L1-error(abs)=" << result[0];
+  SuperRelativeErrorL1Norm2D<T> relVelocityErrorNormL1(u, uSol, indicatorF);
+  relVelocityErrorNormL1(result, input);
+  clout << "; velocity-L1-error(rel)=" << result[0] << std::endl;
+
+  SuperAbsoluteErrorL2Norm2D<T> absVelocityErrorNormL2(u, uSol, indicatorF);
+  absVelocityErrorNormL2(result, input);
+  clout << "velocity-L2-error(abs)=" << result[0];
+  SuperRelativeErrorL2Norm2D<T> relVelocityErrorNormL2(u, uSol, indicatorF);
+  relVelocityErrorNormL2(result, input);
+  clout << "; velocity-L2-error(rel)=" << result[0] << std::endl;
+
+  SuperAbsoluteErrorLinfNorm2D<T> absVelocityErrorNormLinf(u, uSol, indicatorF);
+  absVelocityErrorNormLinf(result, input);
+  clout << "velocity-Linf-error(abs)=" << result[0];
+  SuperRelativeErrorLinfNorm2D<T> relVelocityErrorNormLinf(u, uSol, indicatorF);
+  relVelocityErrorNormLinf(result, input);
+  clout << "; velocity-Linf-error(rel)=" << result[0] << std::endl;
+
+  // pressure error
+  SuperAbsoluteErrorL1Norm2D<T> absPressureErrorNormL1(pressure, pressureSol, indicatorF);
+  absPressureErrorNormL1(result, input);
+  clout << "pressure-L1-error(abs)=" << result[0];
+  SuperRelativeErrorL1Norm2D<T> relPressureErrorNormL1(pressure, pressureSol, indicatorF);
+  relPressureErrorNormL1(result, input);
+  clout << "; pressure-L1-error(rel)=" << result[0] << std::endl;
+
+  SuperAbsoluteErrorL2Norm2D<T> absPressureErrorNormL2(pressure, pressureSol, indicatorF);
+  absPressureErrorNormL2(result, input);
+  clout << "pressure-L2-error(abs)=" << result[0];
+  SuperRelativeErrorL2Norm2D<T> relPressureErrorNormL2(pressure, pressureSol, indicatorF);
+  relPressureErrorNormL2(result, input);
+  clout << "; pressure-L2-error(rel)=" << result[0] << std::endl;
+
+  SuperAbsoluteErrorLinfNorm2D<T> absPressureErrorNormLinf(pressure, pressureSol, indicatorF);
+  absPressureErrorNormLinf(result, input);
+  clout << "pressure-Linf-error(abs)=" << result[0];
+  SuperRelativeErrorLinfNorm2D<T> relPressureErrorNormLinf(pressure, pressureSol, indicatorF);
+  relPressureErrorNormLinf(result, input);
+  clout << "; pressure-Linf-error(rel)=" << result[0] << std::endl;
+}
+
+// Output to console and files
+void getResults( SuperLattice2D<T, DESCRIPTOR>& sLattice,
+                 Dynamics<T, DESCRIPTOR>& bulkDynamics,
+                 PowerLawUnitConverter<T,DESCRIPTOR> const& converter, int iT,
+                 SuperGeometry2D<T>& superGeometry, Timer<double>& timer ) {
+  OstreamManager clout( std::cout,"getResults" );
+
+  SuperVTMwriter2D<T> vtmWriter( "powerLaw2d" );
+  SuperLatticePhysVelocity2D<T, DESCRIPTOR> velocity( sLattice, converter );
+  SuperLatticePhysPressure2D<T, DESCRIPTOR> pressure( sLattice, converter );
+
+  vtmWriter.addFunctor( velocity );
+  vtmWriter.addFunctor( pressure );
+
+  if ( iT==0 ) {
+    SuperLatticeCuboid2D<T, DESCRIPTOR> cuboid( sLattice );
+    SuperLatticeGeometry2D<T, DESCRIPTOR> geometry( sLattice,superGeometry );
+    SuperLatticeRank2D<T, DESCRIPTOR> rank( sLattice );
+    vtmWriter.write( geometry );
+    vtmWriter.write( cuboid );
+    vtmWriter.write( rank );
+    vtmWriter.createMasterFile();
+  }
+
+  if ( iT%converter.getLatticeTime( Tprint )==0 ) {
+    vtmWriter.write( iT );
+
+    SuperEuklidNorm2D<T, DESCRIPTOR> normVel( velocity );
+    BlockReduction2D2D<T> planeReduction( normVel, 600, BlockDataSyncMode::ReduceOnly );
+    // write output of velocity as JPEG
+    heatmap::write(planeReduction, iT);
+  }
+
+  // Writes output on the console
+  if ( iT%converter.getLatticeTime( Tprint )==0 ) {
+    timer.update( iT );
+    timer.printStep();
+    sLattice.getStatistics().print( iT,converter.getPhysTime( iT ) );
+    error( superGeometry, sLattice, converter, bulkDynamics );
+  }
+  return;
+}
+
+
+int main( int argc, char* argv[] ) {
+
+  // === 1st Step: Initialization ===
+  olbInit( &argc, &argv );
+  singleton::directories().setOutputDir( "./tmp/" );
+  OstreamManager clout( std::cout,"main" );
+
+  /*
+  if ( argc > 1 ) {
+    N = atoi( argv[1] );
+  }
+  if ( argc > 2 ) {
+    n = atof( argv[2] );
+  }
+  */
+
+  singleton::directories().setOutputDir( "./tmp/" );
+
+  XMLreader config("input.xml");
+  config["geometry"]["N"].read(N);
+  config["geometry"]["lx"].read(lx);
+  config["geometry"]["ly"].read(ly);
+  config["dynamics"]["maxU"].read(maxU);
+  config["dynamics"]["Re"].read(Re);
+  config["dynamics"]["tau"].read(tau);
+  config["dynamics"]["n"].read(n);
+  config["time"]["Tmax"].read(Tmax);
+  config["time"]["Tprint"].read(Tprint);
+
+  /*
+  T physDeltaX = (ly/N);
+  T m = ly*maxU*pow( maxU/(2*ly),1-n )/Re;
+  T physViscosity = m*pow( maxU/(2*ly),n-1 );
+  T physDeltaT = (tau - 0.5) / DESCRIPTOR::invCs2 * pow(physDeltaX,2) / physViscosity;
+  PowerLawUnitConverter<T, DESCRIPTOR> const converter(
+    (T)   physDeltaX,
+    (T)   physDeltaT,
+   (T)   ly,
+   (T)   maxU,
+   (T)   m,
+   (T)   n,     // power-law index
+    (T)   1.0    // physDensity: physical density in __kg / m^3__
+  );
+  */
+  PowerLawUnitConverterFrom_Resolution_RelaxationTime_Reynolds_PLindex<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)   ly,     // charPhysLength: reference length of simulation geometry
+  (T)   maxU,     // charPhysVelocity: maximal/highest expected velocity during simulation in __m / s__
+  (T)   Re,        // Reynolds number
+  (T)   n,     // power-law index
+  (T)   1.0    // 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("powerLaw2d");
+
+
+  // === 2rd Step: Prepare Geometry ===
+  // Instantiation of a cuboidGeometry with weights
+
+  Vector<T,2> extend( lx, ly );
+  Vector<T,2> origin;
+  IndicatorCuboid2D<T> cuboid( extend, origin );
+
+#ifdef PARALLEL_MODE_MPI
+  CuboidGeometry2D<T> cuboidGeometry( cuboid, converter.getConversionFactorLength(), singleton::mpi().getSize() );
+#else
+  CuboidGeometry2D<T> cuboidGeometry( cuboid, converter.getConversionFactorLength(), 7 );
+#endif
+
+  // Periodic boundaries in x-direction
+  if (bcTypePeriodic)
+    cuboidGeometry.setPeriodicity( true, false );
+
+  //cuboidGeometry.printExtended();
+
+  HeuristicLoadBalancer<T> loadBalancer( cuboidGeometry );
+  SuperGeometry2D<T> superGeometry( cuboidGeometry, loadBalancer, 2 );
+  prepareGeometry( converter, superGeometry );
+
+  // === 3rd Step: Prepare Lattice ===
+  SuperLattice2D<T, DESCRIPTOR> sLattice( superGeometry );
+
+  T distance2Wall = converter.getConversionFactorLength()/2.;
+  T p0 = converter.getPhysConsistencyCoeff()*pow( converter.getCharPhysVelocity(),n )*pow( ( n + 1. )/n,n )*pow( 2./( ly-distance2Wall*2 ),n + 1. );
+
+  clout << "Dimensionalized version-1." << std::endl;
+  PowerLawBGKdynamics<T, DESCRIPTOR> bulkDynamics( converter.getLatticeRelaxationFrequency(), instances::getBulkMomenta<T, DESCRIPTOR>(), converter.getLatticeConsistencyCoeff(), n );
+
+  PeriodicPressureDynamics<T, DESCRIPTOR, PowerLawBGKdynamics<T,DESCRIPTOR>> outDynamics( bulkDynamics,converter.getLatticeDensityFromPhysPressure( p0*(lx + distance2Wall*2.))-1,1,0);
+  PeriodicPressureDynamics<T, DESCRIPTOR, PowerLawBGKdynamics<T,DESCRIPTOR>> inDynamics( bulkDynamics,-converter.getLatticeDensityFromPhysPressure( p0*(lx + distance2Wall*2. ))+1,-1,0);
+  std::cout << -converter.getLatticeDensityFromPhysPressure( p0 )+1 << std::endl;
+
+  sOnLatticeBoundaryCondition2D<T, DESCRIPTOR> sBoundaryCondition( sLattice );
+  createLocalBoundaryCondition2D<T, DESCRIPTOR, PowerLawBGKdynamics<T,DESCRIPTOR> > ( sBoundaryCondition );
+
+  prepareLattice( sLattice, converter, bulkDynamics, inDynamics, outDynamics, sBoundaryCondition, superGeometry );
+
+  // === 4th Step: Main Loop with Timer ===
+  Timer<double> timer( converter.getLatticeTime( Tmax ), superGeometry.getStatistics().getNvoxel() );
+  util::ValueTracer<T> converge( converter.getLatticeTime( 0.1*Tprint ), residuum );
+  timer.start();
+
+  for ( int iT=0; iT<converter.getLatticeTime( Tmax ); ++iT ) {
+    if ( converge.hasConverged() ) {
+      clout << "Simulation converged." << endl;
+      getResults( sLattice, bulkDynamics, converter, iT, superGeometry, timer );
+
+      break;
+    }
+
+    // === 5th Step: Definition of Initial and Boundary Conditions ===
+    setBoundaryValues( sLattice, converter, iT, superGeometry );
+    // === 7th Step: Computation and Output of the Results ===
+    getResults( sLattice, bulkDynamics, converter, iT, superGeometry, timer );
+    converge.takeValue( sLattice.getStatistics().getAverageEnergy(), true );
+    // === 6th Step: Collide and Stream Execution ===
+    sLattice.collideAndStream();
+
+    if (bcTypePeriodic)
+      sLattice.stripeOffDensityOffset ( sLattice.getStatistics().getAverageRho()-(T)1 );
+  }
+  timer.stop();
+  timer.printSummary();
+
+  // === 7th Step: Gnuplot ===
+  Gnuplot<T> gplot( "centerVelocity" );
+  T Ly = converter.getLatticeLength( ly );
+  for ( int iY=0; iY<=Ly; ++iY ) {
+    T dx = 1. / T(converter.getResolution());
+    // const T maxVelocity = converter.getPhysVelocity( converter.getCharLatticeVelocity() );
+    T point[2]= {T(),T()};
+    point[0] = .9*lx;
+    point[1] = ( T )iY/Ly;
+    // const T radius = ly/2.;
+    std::vector<T> axisPoint( 2,T() );
+    axisPoint[0] = lx/2.;
+    axisPoint[1] = ly/2.;
+    std::vector<T> axisDirection( 2,T() );
+    axisDirection[0] = 1;
+    axisDirection[1] = 0;
+    T distance2Wall = converter.getConversionFactorLength()/2.;
+    PowerLaw2D<T> uSol( superGeometry,3,converter.getCharPhysVelocity(),distance2Wall,( n + 1. )/n );
+    //Poiseuille2D<T> uSol( axisPoint, axisDirection, maxVelocity, radius ); // <---
+    T analytical[2] = {T(),T()};
+    uSol( analytical,point );
+    SuperLatticePhysVelocity2D<T, DESCRIPTOR> velocity( sLattice, converter );
+    AnalyticalFfromSuperF2D<T> intpolateVelocity( velocity, true );
+    T numerical[2] = {T(),T()};
+    intpolateVelocity( numerical,point );
+    gplot.setData( iY*dx, {analytical[0],numerical[0]}, {"analytical","numerical"} );
+  }
+  // Create PNG file
+  gplot.writePNG();
+}
diff --git a/examples/laminar/powerLaw2d/run.sh b/examples/laminar/powerLaw2d/run.sh
new file mode 100755
index 0000000..190f65d
--- /dev/null
+++ b/examples/laminar/powerLaw2d/run.sh
@@ -0,0 +1,29 @@
+#!/bin/bash
+
+# Script to run the example with three different values for maxU and collect the output.
+
+APP=powerLaw2d
+NP=2
+
+if [ ! -f $APP ]; then make; fi
+
+for N in `seq 1 3`; do
+
+		  case $N in
+					 1) MAXU=1;   DIR="out_u1e+0" ;;
+					 2) MAXU=0.1; DIR="out_u1e-1" ;;
+					 3) MAXU=10;  DIR="out_u1e+1" ;;
+		  esac
+
+		  if [ ! -d $DIR ]; then mkdir $DIR; fi
+		  
+		  sed "s/MAXU/$MAXU/g" input-model.xml > $DIR/input.xml
+		  cp $APP $DIR/
+
+		  cd $DIR
+
+		  mpirun -np $NP $APP 2>&1 | tee log.log \
+					 && cp tmp/gnuplotData/centerVelocity.png ../u_$DIR".png"
+
+		  cd ..
+done