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pois2D_july31_halfWayBB.m
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%pois2D_july12.m
% for Pouiseuille flow, I want to be able to measure
% 1. Numerical convergence
% 2. Stabilization rate
% compare both for Zou/He and Regularized BCs
% compare both for LBGK and MRT
% provide parabolic inlet velocity profile for convergence testing.
% provide uniform inlet velocity profile to show flow development.
clear
clc
close('all')
location = 'office';
% 'home', 'office', 'hamming'
dynamics = 1;
% 1 =LBGK
% 2 = RBGK <--- not working
% 3 = MRT
BC_type = 1;
% 1 = Zhou/He
% 2 = Regularized
Num_ts = 20000;
ts_rep_freq = 1000;
plot_freq = Num_ts+1;
Re = 10;
dt = 1e-3/256;
Ny_divs = 480;
obst_type = 'none';
% 'none'
sim_name = 'pois2D_convergence';
ts_num=0;
Lx_p = 10;
Ly_p = 1;
switch obst_type
case 'none'
Lo = Ly_p;
end
fluid = 4;
switch fluid
case 1
rho_p = 1260;
nu_p = 1.49/rho_p;
case 2
rho_p = 965.3;
nu_p = 0.06/rho_p;
case 3
rho_p = 1000;
nu_p = 1e-3/rho_p;
case 4
rho_p = 1000;
nu_p = 0.001;
end
% non-dimensionalize and set up LBM lattice
Uo = nu_p*Re/Lo;
To = Lo/Uo;
Uavg = Uo;
Ld = 1; Td = 1; Ud = (To/Lo)*Uavg;
nu_d = 1/Re;
dx = 1/(Ny_divs-1);
u_lbm = (dt/dx)*Ud;
nu_lbm=(dt/(dx^2))*nu_d;
omega = get_BGK_Omega(nu_lbm);
u_conv_fact = (dt/dx)*(To/Lo);
t_conv_fact = (dt*To);
l_conv_fact = dx*Lo;
p_conv_fact = ((l_conv_fact/t_conv_fact)^2)*(1/3); % <--for EOS type methods...
rho_lbm = rho_p;
rho_out = rho_lbm;
Ny = ceil((Ny_divs-1)*(Ly_p/Lo))+1 + 1; % <--- one extra lattice point in the Y direction
Nx = ceil((Ny_divs-1)*(Lx_p/Lo))+1;
dy_p = Ly_p/(Ny-2);
% generate LBM lattice
xm = 0; xp = Lx_p;
ym = 0-dy_p/2; yp = Ly_p+dy_p/2;
[gcoord,~,~]=RecMesh(xm,xp,ym,yp,Nx,Ny);
[nnodes,~]=size(gcoord);
x_space = linspace(xm,xp,Nx);
y_space = linspace(ym,yp,Ny);
[X,Y]=meshgrid(x_space,y_space);
[w,ex,ey,bb_spd]=D2Q9_lattice_parameters();
%stream_tgt = genTargetVecD2Q9r2(Nx,Ny);
LatticeSize = [Nx Ny];
LatticeSpeeds = [ex; ey];
stm = genStreamTgtMat(LatticeSize,LatticeSpeeds);
numSpd=9;
M = getMomentMatrix('D2Q9');
switch dynamics
case 1
S = omega.* eye(numSpd);
case 2
% TRT model as described in Kevin Tubbs' dissertation section 3.4
S = zeros(numSpd);
S(2,2)= omega;
S(3,3)=omega;
S(8,8)=omega;
S(9,9)=omega;
t_s = (1/2)+1/(12*((1/omega)-0.5));
S(5,5)=1/t_s;
S(7,7)=1/t_s;
case 3
% parameters taken from
% Chinese Physics Vol 15 No 8 Aug 2006
% Simulating high Reynolds number flow in 2D lid driven cavity by
% MRT etc...
S = zeros(numSpd);
S(2,2)=1.1;
S(3,3)=1.0;
S(5,5)=1.2;
S(7,7)=1.2;
S(8,8)=omega;
S(9,9)=omega;
end
omega_op = M\(S*M);
% set node lists
snl=find((gcoord(:,2)==ym) | (gcoord(:,2)==yp));
inl=find(gcoord(:,1)==xm);
inl=setxor(inl,intersect(snl,inl)); % eliminate solid nodes from inlet list
onl=find(gcoord(:,1)==xp);
onl=setxor(onl,intersect(snl,onl)); % eliminate solid nodes from outlet list
% modify for obstructions
switch obst_type
case 'none'
% nothing to do here...
end
Umax = (3/2)*u_lbm;
by = Ly_p/2;
ux_p_in = Umax*(1-((gcoord(inl,2)-by)/by).^2);
uy_p_in = zeros(length(ux_p_in),1);
ux_theory = [0;ux_p_in;0]; ux_theory = (ux_theory')./u_conv_fact;
pltX = ceil(2*Nx/4);
pltX_xcoord= x_space(pltX);
pltX_list = find(gcoord(:,1)==pltX_xcoord);
[fIn,fOut,rho,ux,uy]=Initialize_F_zero(gcoord,ex,ey,w,rho_lbm);
fEq = zeros(nnodes,numSpd);
v_data = zeros(Num_ts,1);
v_data_LP = ceil(Ny/2)*Nx+ceil(Nx/2);
u_data = zeros(Num_ts,1);
p_ref = rho_out*p_conv_fact;
fprintf('Number of Lattice-points = %d.\n',nnodes);
fprintf('Number of time-steps = %d. \n',Num_ts);
fprintf('LBM viscosity = %g. \n',nu_lbm);
fprintf('LBM relaxation parameter (omega) = %g. \n',omega);
fprintf('LBM flow Mach number = %g. \n',u_lbm);
input_string = sprintf('Do you wish to continue? [Y/n] \n');
run_dec = input(input_string,'s');
if ((run_dec ~= 'n') && (run_dec ~= 'N'))
fprintf('Ok! Cross your fingers!! \n');
% add paths for Jacket libraries
switch location
case 'home'
addpath('/usr/local/jacket/engine');
base_path='/home/srblair/Dropbox/matlab/jacketSDK/';
case 'office'
base_path='/home/srblair/Dropbox/matlab/jacketSDK/';
addpath('/usr/local/jacket/engine');
case 'hamming'
end
addpath(strcat(base_path,'channel2D_RegVwPe_LBGK_ts'));
addpath(strcat(base_path,'channel2D_RegVwPe_MRT_ts'));
addpath(strcat(base_path,'channel2D_RegVwPe_RBGK_ts'));
addpath(strcat(base_path,'channel2D_VW_PE_LBGK_ts'));
addpath(strcat(base_path,'channel2D_VW_PE_LBGK_DPts'));
addpath(strcat(base_path,'channel2D_VW_PE_LBGK_MPts'));
addpath(strcat(base_path,'channel2D_VW_PE_MRT_ts'));
addpath(strcat(base_path,'channel2D_VW_PE_MRT_DPts'));
% send data to the GPU
fIn = gsingle(fIn);
fOut = gsingle(fOut);
fEq = gsingle(fEq);
ux_p_h = zeros(nnodes,1); ux_p_h(inl)=ux_p_in; ux_p_h(onl)=ux_p_in;
ux_p = gsingle(ux_p_h);
%rho = gzeros(nnodes,1);
%ux = gzeros(nnodes,1);
%uy = gzeros(nnodes,1);
inl_i = zeros(nnodes,1); inl_i(inl)=1; inl_d = gint32(inl_i);
onl_i = zeros(nnodes,1); onl_i(onl)=1; onl_d = gint32(onl_i);
snl_i = zeros(nnodes,1); snl_i(snl)=1; snl_d = gint32(snl_i);
omega_op = gsingle(omega_op);
% prep stuff for writing to vtk
uz_h = zeros(nnodes,1);
gcoord_z = zeros(nnodes,1);
%stm_d = gint32(stm);
%bb_spd_d = gint32(bb_spd);
%commence time stepping
tic;
for ts = 1:Num_ts
% say something comforting about my progress...
if(mod(ts,ts_rep_freq)==0)
fprintf('Executing time step number %d.\n',ts);
end
switch BC_type
case 1
switch dynamics
case 1
if(mod(ts,2)==1)
channel2D_VW_PE_LBGK_ts(fOut,fIn,inl_d,onl_d,snl_d,ux_p,rho_out,nu_lbm,int32(Nx),int32(Ny));
else
channel2D_VW_PE_LBGK_ts(fIn,fOut,inl_d,onl_d,snl_d,ux_p,rho_out,nu_lbm,int32(Nx),int32(Ny));
end
case 2
case 3
if(mod(ts,2)==1)
channel2D_VW_PE_MRT_ts(fOut,fIn,inl_d,onl_d,snl_d,ux_p,rho_out,omega_op,int32(Nx),int32(Ny));
else
channel2D_VW_PE_MRT_ts(fIn,fOut,inl_d,onl_d,snl_d,ux_p,rho_out,omega_op,int32(Nx),int32(Ny));
end
end
case 2
switch dynamics
case 1
if(mod(ts,2)==1)
channel2D_RegVwPe_LBGK_ts(fOut,fIn,inl_d,onl_d,snl_d,ux_p,rho_out,nu_lbm,int32(Nx),int32(Ny));
else
channel2D_RegVwPe_LBGK_ts(fIn,fOut,inl_d,onl_d,snl_d,ux_p,rho_out,nu_lbm,int32(Nx),int32(Ny));
end
case 2
case 3
if(mod(ts,2)==1)
channel2D_RegVwPe_MRT_ts(fOut,fIn,inl_d,onl_d,snl_d,ux_p,rho_out,omega_op,int32(Nx),int32(Ny));
else
channel2D_RegVwPe_MRT_ts(fIn,fOut,inl_d,onl_d,snl_d,ux_p,rho_out,omega_op,int32(Nx),int32(Ny));
end
end
end
if(mod(ts,plot_freq)==0)
% plot something....
if(mod(ts,2)==1)
rho = sum(fOut,2);
ux = ((fOut*ex')./rho)./u_conv_fact;
uy = ((fOut*ey')./rho)./u_conv_fact;
else
rho = sum(fIn,2);
ux = ((fIn*ex')./rho)./u_conv_fact;
uy = ((fIn*ey')./rho)./u_conv_fact;
end
pressure = rho*p_conv_fact - p_ref;
ux(snl)=0;
uy(snl)=0;
% gather data from the GPU
ux_h = double(ux);
uy_h = double(uy);
pressure_h = double(pressure);
% write to VTK file
pv_fileStub = sprintf('_pressureAndVelocity%d.vtk',ts_num);
pv_fileName = strcat(sim_name,pv_fileStub);
save_velocityAndPressureVTK_binaryR2(pressure_h,ux_h,uy_h,uz_h,...
gcoord(:,1),gcoord(:,2),gcoord_z,pv_fileName,[Nx Ny 1]);
ts_num=ts_num+1;
end
end
ex_time = toc;
fprintf('LPU/sec = %g.\n',Num_ts*nnodes/ex_time);
rho = sum(fIn,2);
ux = ((fIn*ex')./rho)./u_conv_fact;
uy = ((fIn*ey')./rho)./u_conv_fact;
pressure = rho*p_conv_fact - p_ref;
% gather data from the GPU
ux_h = double(ux);
uy_h = double(uy);
pressure_h = double(pressure);
% plot velocity profile and compare against theory
ux_lbm = ux_h(pltX_list);
figure(1)
plot(ux_theory,y_space,'-r',ux_h(pltX_list),gcoord(pltX_list,2),'xb');
rel_err = norm(ux_theory - ux_lbm',2)/norm(ux_theory,2);
fprintf('Relative error = %g.\n',rel_err);
fprintf('Grid Resolution = %d.\n',Ny_divs);
fprintf('dx = %g.\n',dx);
fprintf('dt = %g.\n',dt);
fprintf('omega = %g.\n',omega);
% figure(2)
% plot(1:Num_ts,u_data,'LineWidth',2);
% grid on
% title('\bf{Horizontal Velocity Fluctuation x/Lx = 0.75 vs Time Step, Re = 10}','FontSize',12);
% xlabel('\bf{Time Step}','FontSize',12);
% ylabel('\bf{Umax (m/sec)}','FontSize',12);
else
fprintf('Run aborted. Better luck next time!\n');
end