# firemodels/fds

FDS Verification : Add CC Poiseuille 2D Verification test case.

marcosvanella committed Aug 13, 2018
1 parent d1d8cfa commit 9a2714635c1485e07420ed9cba4310f9d0634b42
 @@ -2747,6 +2747,49 @@ \subsection{Immersed boundary method on manufactured solution around rotated cub %See figures~\ref{}a-c. \subsection{Poiseuille flow in channel created by two GEOMs} Consider a gas with density $\rho=1.165$ kg/m$^3$, and molecular viscosity $\mu=0.025$ kg/m/s, being advected through a 2D channel of height $H=1$ m and length $L=10$ m, by means of a constant force field along the channel direction $F_x=1$ N/m$^3$. This force field is equivalent to a pressure drop $dp/dx=-1$ Pa/m. The analytical solution for the friction factor in this laminar flow is: % \begin{equation} f_{an} = 24/Re_H \end{equation} % where in our case $Re_H= \rho \overline{u} H/ \mu \simeq 155$, being the analytical value for the bulk velocity $\overline{u}=3.\hat{3}$ m/s. The (Moody) friction factor formula for pressure losses is: % \begin{equation} \Delta p / L = f \frac{L}{H} \frac{1}{2} \rho \overline{u}^2 \end{equation} % which can be used to compute the simulation error in $f$, as a function of the mean velocity evaluated on the numerical mesh. To evaluate the solution quality of the CC-IBM scheme we consider three sets of test cases. See figure~\ref{Fig:PoiseSketch}. % % figure \begin{figure}[h] \centering \includegraphics[trim = 60mm 34mm 60mm 42mm, clip, width=0.75\linewidth]{../../../fig/fds/Poiseuille_cc_Sketch.png} \caption{Poiseuille flow created by two geometries $\Omega_1, \Omega_2$: Location of channel walls respect to Cartesian grid lines (in blue).} \label{Fig:PoiseSketch} \end{figure} % We define as $h$ the distance from the lower geometry wall to the closest grid line within it. The we consider discretizations with ${10,20,40,80}$ cells along the $z$ direction and cases: grid aligned $h=0$, grid dependent $h=\Delta z /3$, and fixed $h=\Delta z_{10}/11$, where $\Delta z_{10}$ is the wall normal cell size in the coarsest discretization used. Friction factor errors computed as $|f-f_{an}|$ are shown in figures~\ref{Fig:PoiseConvg}a,b. Second order convergence of this error measure in all cases can be seen. There is more noise on the fixed geometry case $h=\Delta z_{10}/11$, because the cut-cell size ratios and interpolation coefficients are changing from grid to grid. These error fluctuations are not seen when $h=\Delta z /3$, and cut-cells keep same sizes and interpolation coefficients respect to the Cartesian grids. % % figure \begin{figure}[h] \centering \includegraphics[trim = 5mm 0mm 5mm 0mm, clip, width=0.49\linewidth]{../FDS_Verification_Guide/SCRIPT_FIGURES/geom_poiseuille_convergence_theta0a.pdf} \includegraphics[trim = 5mm 0mm 5mm 0mm, clip, width=0.49\linewidth]{../FDS_Verification_Guide/SCRIPT_FIGURES/geom_poiseuille_convergence_theta0na.pdf} \caption{Poiseuille flow created by two geometries: Convergence trends on friction factor (Moody) for $h=0$, grid dependent $h=\Delta z/3$ and fixed $h=\Delta z_{10}/11$. Fluctuations on the friction factor error in the last case are produced by changes in cut-cell aspect ratios and velocity interpolation stencils as grids are refined.} \label{Fig:PoiseConvg} \end{figure} % \subsection{Conservation test of isothermal helium plume around sphere}
 @@ -66,6 +66,7 @@ disp('turb_model...'); turb_model disp('jet_decay...'); jet_decay disp('wall_model...'); wall_model disp('wall_model_cc...'); wall_model_cc disp('pyrolysis...'); pyrolysis disp('birch_tga...'); birch_tga disp('water_ice_water...'); water_ice_water
 @@ -0,0 +1,107 @@ % CC script that follows McDermott poiseuille_convergence.m close all clear all plot_style dpdx = -1; L = 1; N = [10,20,40,80]; outdir = '../../Verification/Complex_Geometry/'; % Aligned case theta=0: [f(1),Re(1)] = friction_factor_calc(dpdx,L,[outdir,'geom_poiseuille_N10a_theta0_devc.csv']); [f(2),Re(2)] = friction_factor_calc(dpdx,L,[outdir,'geom_poiseuille_N20a_theta0_devc.csv']); [f(3),Re(3)] = friction_factor_calc(dpdx,L,[outdir,'geom_poiseuille_N40a_theta0_devc.csv']); [f(4),Re(4)] = friction_factor_calc(dpdx,L,[outdir,'geom_poiseuille_N80a_theta0_devc.csv']); [f2(1),Re2(1)] = friction_factor_calc(dpdx,L,[outdir,'geom_poiseuille_N10nah_theta0_devc.csv']); [f2(2),Re2(2)] = friction_factor_calc(dpdx,L,[outdir,'geom_poiseuille_N20nah_theta0_devc.csv']); [f2(3),Re2(3)] = friction_factor_calc(dpdx,L,[outdir,'geom_poiseuille_N40nah_theta0_devc.csv']); [f2(4),Re2(4)] = friction_factor_calc(dpdx,L,[outdir,'geom_poiseuille_N80nah_theta0_devc.csv']); % plot convergence for Poiseuille flow aligned case theta=0 (mu = 0.025) dz = L./N; error = abs(f-24./Re); error2= abs(f2-24./Re2); figure set(gca,'Units',Plot_Units) set(gca,'Position',[Plot_X Plot_Y Plot_Width Plot_Height]) H(1)=loglog(dz,error,'b*-','Linewidth',1.); hold on H(2)=loglog(dz,error2,'rx-','Linewidth',1.); hold on H(3)=loglog(dz,.12*dz,'k--','Linewidth',1.); H(4)=loglog(dz,.4*dz.^2,'k-','Linewidth',1.); set(gca,'FontName',Font_Name) set(gca,'FontSize',Title_Font_Size) axis([0.01 0.2 0.0000005 0.01]) xlabel('Grid Spacing, {\it\deltaz} (m)','Interpreter',Font_Interpreter,'Fontname','Times') ylabel('Friction Factor Error') h = legend(H,'FDS, h=0','FDS, h=\Deltaz/3','{\itO}({\it\deltaz})','{\itO}({\it\deltaz}^2)','Location','Southeast'); set(h,'Interpreter',Font_Interpreter) % add Git revision if file is available Git_Filename = [outdir,'geom_poiseuille_N10a_theta0_git.txt']; addverstr(gca,Git_Filename,'loglog') % print to pdf set(gcf,'Visible',Figure_Visibility); set(gcf,'Units',Paper_Units); set(gcf,'PaperUnits',Paper_Units); set(gcf,'PaperSize',[Paper_Width Paper_Height]); set(gcf,'Position',[0 0 Paper_Width Paper_Height]); print(gcf,'-dpdf','../../Manuals/FDS_Verification_Guide/SCRIPT_FIGURES/geom_poiseuille_convergence_theta0a') % NOT aligned case theta=0 clear f Re f2 Re2 H [f(1),Re(1)] = friction_factor_calc(dpdx,L,[outdir,'geom_poiseuille_N10na_theta0_devc.csv']); [f(2),Re(2)] = friction_factor_calc(dpdx,L,[outdir,'geom_poiseuille_N20na_theta0_devc.csv']); [f(3),Re(3)] = friction_factor_calc(dpdx,L,[outdir,'geom_poiseuille_N40na_theta0_devc.csv']); [f(4),Re(4)] = friction_factor_calc(dpdx,L,[outdir,'geom_poiseuille_N80na_theta0_devc.csv']); % plot convergence for Poiseuille flow not aligned case theta=0 (mu = 0.025) dz = L./N; error = abs(f-24./Re); figure set(gca,'Units',Plot_Units) set(gca,'Position',[Plot_X Plot_Y Plot_Width Plot_Height]) H(1)=loglog(dz,error,'b*-','Linewidth',1.); hold on H(2)=loglog(dz,.05*dz,'k--','Linewidth',1.); H(3)=loglog(dz,.4*dz.^2,'k-','Linewidth',1.); set(gca,'FontName',Font_Name) set(gca,'FontSize',Title_Font_Size) axis([0.01 0.2 0.0000005 0.01]) xlabel('Grid Spacing, {\it\deltaz} (m)','Interpreter',Font_Interpreter,'Fontname','Times') ylabel('Friction Factor Error') h = legend(H,'FDS, h=\Deltaz_{10}/11','{\itO}({\it\deltaz})','{\itO}({\it\deltaz}^2)','Location','Southeast'); set(h,'Interpreter',Font_Interpreter) % add Git revision if file is available Git_Filename = [outdir,'geom_poiseuille_N10na_theta0_git.txt']; addverstr(gca,Git_Filename,'loglog') % print to pdf set(gcf,'Visible',Figure_Visibility); set(gcf,'Units',Paper_Units); set(gcf,'PaperUnits',Paper_Units); set(gcf,'PaperSize',[Paper_Width Paper_Height]); set(gcf,'Position',[0 0 Paper_Width Paper_Height]); print(gcf,'-dpdf','../../Manuals/FDS_Verification_Guide/SCRIPT_FIGURES/geom_poiseuille_convergence_theta0na')
 @@ -0,0 +1,4 @@ % CC version of McDermott wall_model.m % poiseuille_convergence_cc % Convergence for 2D Poiseuille flow
 @@ -1,7 +1,7 @@ &HEAD CHID='geom_poiseuille_N10na_theta0', TITLE='Poiseuille flow in 2D, GEOM channel at 0 degree slope respect to mesh. Mesh not aligned case.' / # 10 cells in channel height (from 0 to 1): Domain shifted up by 1/11*DZ10: &MESH IJK=10,1,12, XB=0,10,-.5,.5,-0.090909090909091,1.109090909090909 / &MESH IJK=10,1,12, XB=0,10,-.5,.5,-0.109090909090909,1.090909090909091 / &TIME T_END=100.0 / needs to be roughtly (.5*H)^2/VISCOSITY (here H=1) &DUMP NFRAMES=100, SIG_FIGS=6, SIG_FIGS_EXP=4 / @@ -23,7 +23,7 @@ &SLCF PBY=0, QUANTITY='DENSITY', CELL_CENTERED=.TRUE. / &SLCF PBY=0, QUANTITY='VISCOSITY', CELL_CENTERED=.TRUE. / &DEVC XB=5.0,5.0, -0.5,0.5, 0.0,1.0, QUANTITY='U-VELOCITY', STATISTICS='AREA INTEGRAL' / &DEVC XB=5.0,5.0, -0.5,0.5, -0.109090909090909,1.090909090909091, QUANTITY='U-VELOCITY', STATISTICS='AREA INTEGRAL' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='U-VELOCITY' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='VISCOSITY' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='DENSITY' /
 @@ -0,0 +1,31 @@ &HEAD CHID='geom_poiseuille_N10nah_theta0', TITLE='Poiseuille flow in 2D, GEOM channel at 0 degree slope respect to mesh. Mesh not aligned case.' / # 10 cells in channel height (from 0 to 1): GEOMs shifted up by 1/3*DZ10: &MESH IJK=10,1,12, XB=0,10,-.5,.5,-0.1,1.1 / &TIME T_END=100.0 / needs to be roughtly (.5*H)^2/VISCOSITY (here H=1) &DUMP NFRAMES=100, SIG_FIGS=6, SIG_FIGS_EXP=4 / &MISC DNS=.TRUE., NOISE=.FALSE. / &WIND STRATIFICATION=.FALSE., FORCE_VECTOR(1)=1 / &SPEC ID='AIR', VISCOSITY=0.025, BACKGROUND=.TRUE. / &VENT MB='XMIN', SURF_ID='PERIODIC' / &VENT MB='XMAX', SURF_ID='PERIODIC' / &GEOM XB=-1,11,-.5,.5,-0.1,0.033333333333333/ &GEOM XB=-1,11,-.5,.5, 1.033333333333333,1.1/ &SLCF PBY=0, QUANTITY='VELOCITY', VECTOR=.TRUE. / &SLCF PBY=0, QUANTITY='H', CELL_CENTERED=.TRUE. / &SLCF PBY=0, QUANTITY='DENSITY', CELL_CENTERED=.TRUE. / &SLCF PBY=0, QUANTITY='VISCOSITY', CELL_CENTERED=.TRUE. / &DEVC XB=5.0,5.0, -0.5,0.5, -0.1,1.1, QUANTITY='U-VELOCITY', STATISTICS='AREA INTEGRAL' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='U-VELOCITY' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='VISCOSITY' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='DENSITY' / &TAIL /
 @@ -1,7 +1,7 @@ &HEAD CHID='geom_poiseuille_N20na_theta0', TITLE='Poiseuille flow in 2D, GEOM channel at 0 degree slope respect to mesh. Mesh not aligned case.' / # 20 cells in channel height (from 0 to 1): Domain shifted up by 1/11*DZ10: &MESH IJK=10,1,24, XB=0,10,-.5,.5,-0.090909090909091,1.109090909090909 / &MESH IJK=10,1,24, XB=0,10,-.5,.5,-0.109090909090909,1.090909090909091 / &TIME T_END=100.0 / needs to be roughtly (.5*H)^2/VISCOSITY (here H=1) &DUMP NFRAMES=100, SIG_FIGS=6, SIG_FIGS_EXP=4 / @@ -23,7 +23,7 @@ &SLCF PBY=0, QUANTITY='DENSITY', CELL_CENTERED=.TRUE. / &SLCF PBY=0, QUANTITY='VISCOSITY', CELL_CENTERED=.TRUE. / &DEVC XB=5.0,5.0, -0.5,0.5, 0.0,1.0, QUANTITY='U-VELOCITY', STATISTICS='AREA INTEGRAL' / &DEVC XB=5.0,5.0, -0.5,0.5, -0.109090909090909,1.090909090909091, QUANTITY='U-VELOCITY', STATISTICS='AREA INTEGRAL' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='U-VELOCITY' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='VISCOSITY' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='DENSITY' /
 @@ -0,0 +1,31 @@ &HEAD CHID='geom_poiseuille_N20nah_theta0', TITLE='Poiseuille flow in 2D, GEOM channel at 0 degree slope respect to mesh. Mesh not aligned case.' / # 20 cells in channel height (from 0 to 1): GEOMs shifted up by 1/3*DZ20: &MESH IJK=10,1,24, XB=0,10,-.5,.5,-0.1,1.1 / &TIME T_END=100.0 / needs to be roughtly (.5*H)^2/VISCOSITY (here H=1) &DUMP NFRAMES=100, SIG_FIGS=6, SIG_FIGS_EXP=4 / &MISC DNS=.TRUE., NOISE=.FALSE. / &WIND STRATIFICATION=.FALSE., FORCE_VECTOR(1)=1 / &SPEC ID='AIR', VISCOSITY=0.025, BACKGROUND=.TRUE. / &VENT MB='XMIN', SURF_ID='PERIODIC' / &VENT MB='XMAX', SURF_ID='PERIODIC' / &GEOM XB=-1,11,-.5,.5,-0.1,0.016666666666667/ &GEOM XB=-1,11,-.5,.5, 1.016666666666667,1.1/ &SLCF PBY=0, QUANTITY='VELOCITY', VECTOR=.TRUE. / &SLCF PBY=0, QUANTITY='H', CELL_CENTERED=.TRUE. / &SLCF PBY=0, QUANTITY='DENSITY', CELL_CENTERED=.TRUE. / &SLCF PBY=0, QUANTITY='VISCOSITY', CELL_CENTERED=.TRUE. / &DEVC XB=5.0,5.0, -0.5,0.5, -0.1,1.1, QUANTITY='U-VELOCITY', STATISTICS='AREA INTEGRAL' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='U-VELOCITY' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='VISCOSITY' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='DENSITY' / &TAIL /
 @@ -1,7 +1,7 @@ &HEAD CHID='geom_poiseuille_N40na_theta0', TITLE='Poiseuille flow in 2D, GEOM channel at 0 degree slope respect to mesh. Mesh not aligned case.' / # 40 cells in channel height (from 0 to 1): Domain shifted up by 1/11*DZ10: &MESH IJK=10,1,48, XB=0,10,-.5,.5,-0.090909090909091,1.109090909090909 / &MESH IJK=10,1,48, XB=0,10,-.5,.5,-0.109090909090909,1.090909090909091 / &TIME T_END=100.0 / needs to be roughtly (.5*H)^2/VISCOSITY (here H=1) &DUMP NFRAMES=100, SIG_FIGS=6, SIG_FIGS_EXP=4 / @@ -23,7 +23,7 @@ &SLCF PBY=0, QUANTITY='DENSITY', CELL_CENTERED=.TRUE. / &SLCF PBY=0, QUANTITY='VISCOSITY', CELL_CENTERED=.TRUE. / &DEVC XB=5.0,5.0, -0.5,0.5, 0.0,1.0, QUANTITY='U-VELOCITY', STATISTICS='AREA INTEGRAL' / &DEVC XB=5.0,5.0, -0.5,0.5, -0.109090909090909,1.090909090909091, QUANTITY='U-VELOCITY', STATISTICS='AREA INTEGRAL' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='U-VELOCITY' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='VISCOSITY' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='DENSITY' /
 @@ -0,0 +1,31 @@ &HEAD CHID='geom_poiseuille_N40nah_theta0', TITLE='Poiseuille flow in 2D, GEOM channel at 0 degree slope respect to mesh. Mesh not aligned case.' / # 40 cells in channel height (from 0 to 1): GEOMs shifted up by 1/3*DZ40: &MESH IJK=10,1,48, XB=0,10,-.5,.5,-0.1,1.1 / &TIME T_END=100.0 / needs to be roughtly (.5*H)^2/VISCOSITY (here H=1) &DUMP NFRAMES=100, SIG_FIGS=6, SIG_FIGS_EXP=4 / &MISC DNS=.TRUE., NOISE=.FALSE. / &WIND STRATIFICATION=.FALSE., FORCE_VECTOR(1)=1 / &SPEC ID='AIR', VISCOSITY=0.025, BACKGROUND=.TRUE. / &VENT MB='XMIN', SURF_ID='PERIODIC' / &VENT MB='XMAX', SURF_ID='PERIODIC' / &GEOM XB=-1,11,-.5,.5,-0.1,0.008333333333333/ &GEOM XB=-1,11,-.5,.5, 1.008333333333333,1.1/ &SLCF PBY=0, QUANTITY='VELOCITY', VECTOR=.TRUE. / &SLCF PBY=0, QUANTITY='H', CELL_CENTERED=.TRUE. / &SLCF PBY=0, QUANTITY='DENSITY', CELL_CENTERED=.TRUE. / &SLCF PBY=0, QUANTITY='VISCOSITY', CELL_CENTERED=.TRUE. / &DEVC XB=5.0,5.0, -0.5,0.5, -0.1,1.1, QUANTITY='U-VELOCITY', STATISTICS='AREA INTEGRAL' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='U-VELOCITY' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='VISCOSITY' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='DENSITY' / &TAIL /
 @@ -1,7 +1,7 @@ &HEAD CHID='geom_poiseuille_N80na_theta0', TITLE='Poiseuille flow in 2D, GEOM channel at 0 degree slope respect to mesh. Mesh not aligned case.' / # 80 cells in channel height (from 0 to 1): Domain shifted up by 1/11*DZ10: &MESH IJK=10,1,96, XB=0,10,-.5,.5,-0.090909090909091,1.109090909090909 / &MESH IJK=10,1,96, XB=0,10,-.5,.5,-0.109090909090909,1.090909090909091 / &TIME T_END=100.0 / needs to be roughtly (.5*H)^2/VISCOSITY (here H=1) &DUMP NFRAMES=100, SIG_FIGS=6, SIG_FIGS_EXP=4 / @@ -23,7 +23,7 @@ &SLCF PBY=0, QUANTITY='DENSITY', CELL_CENTERED=.TRUE. / &SLCF PBY=0, QUANTITY='VISCOSITY', CELL_CENTERED=.TRUE. / &DEVC XB=5.0,5.0, -0.5,0.5, 0.0,1.0, QUANTITY='U-VELOCITY', STATISTICS='AREA INTEGRAL' / &DEVC XB=5.0,5.0, -0.5,0.5, -0.109090909090909,1.090909090909091, QUANTITY='U-VELOCITY', STATISTICS='AREA INTEGRAL' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='U-VELOCITY' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='VISCOSITY' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='DENSITY' /
 @@ -0,0 +1,31 @@ &HEAD CHID='geom_poiseuille_N80nah_theta0', TITLE='Poiseuille flow in 2D, GEOM channel at 0 degree slope respect to mesh. Mesh not aligned case.' / # 80 cells in channel height (from 0 to 1): GEOMs shifted up by 1/3*DZ80: &MESH IJK=10,1,96, XB=0,10,-.5,.5,-0.1,1.1 / &TIME T_END=100.0 / needs to be roughtly (.5*H)^2/VISCOSITY (here H=1) &DUMP NFRAMES=100, SIG_FIGS=6, SIG_FIGS_EXP=4 / &MISC DNS=.TRUE., NOISE=.FALSE. / &WIND STRATIFICATION=.FALSE., FORCE_VECTOR(1)=1 / &SPEC ID='AIR', VISCOSITY=0.025, BACKGROUND=.TRUE. / &VENT MB='XMIN', SURF_ID='PERIODIC' / &VENT MB='XMAX', SURF_ID='PERIODIC' / &GEOM XB=-1,11,-.5,.5,-0.1,0.004166666666667/ &GEOM XB=-1,11,-.5,.5, 1.004166666666667,1.1/ &SLCF PBY=0, QUANTITY='VELOCITY', VECTOR=.TRUE. / &SLCF PBY=0, QUANTITY='H', CELL_CENTERED=.TRUE. / &SLCF PBY=0, QUANTITY='DENSITY', CELL_CENTERED=.TRUE. / &SLCF PBY=0, QUANTITY='VISCOSITY', CELL_CENTERED=.TRUE. / &DEVC XB=5.0,5.0, -0.5,0.5, -0.1,1.1, QUANTITY='U-VELOCITY', STATISTICS='AREA INTEGRAL' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='U-VELOCITY' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='VISCOSITY' / &DEVC XYZ=5.0,0.0,0.5, QUANTITY='DENSITY' / &TAIL /
 @@ -89,6 +89,10 @@ $QFDS -d Complex_Geometry geom_poiseuille_N10na_theta0.fds$QFDS -d Complex_Geometry geom_poiseuille_N20na_theta0.fds $QFDS -d Complex_Geometry geom_poiseuille_N40na_theta0.fds$QFDS -d Complex_Geometry geom_poiseuille_N80na_theta0.fds $QFDS -d Complex_Geometry geom_poiseuille_N10nah_theta0.fds$QFDS -d Complex_Geometry geom_poiseuille_N20nah_theta0.fds $QFDS -d Complex_Geometry geom_poiseuille_N40nah_theta0.fds$QFDS -d Complex_Geometry geom_poiseuille_N80nah_theta0.fds $QFDS -d Complex_Geometry geom_bad_inconsistent_normals.fds$QFDS -d Complex_Geometry geom_bad_non_manifold_edge.fds
 @@ -75,3 +75,7 @@ $QFDS -d Complex_Geometry geom_bad_self_intersection.fds #$QFDS -d Complex_Geometry geom_poiseuille_N20na_theta0.fds # $QFDS -d Complex_Geometry geom_poiseuille_N40na_theta0.fds #$QFDS -d Complex_Geometry geom_poiseuille_N80na_theta0.fds # $QFDS -d Complex_Geometry geom_poiseuille_N10nah_theta0.fds #$QFDS -d Complex_Geometry geom_poiseuille_N20nah_theta0.fds # $QFDS -d Complex_Geometry geom_poiseuille_N40nah_theta0.fds #$QFDS -d Complex_Geometry geom_poiseuille_N80nah_theta0.fds