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SmolBuoy_RK3CN2_pBC_GPU.m
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SmolBuoy_RK3CN2_pBC_GPU.m
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%% Time Stepping solver for the Full Smoluchowski Equation (RK3-CN2)
% Loosely based on Spherefun, this solve uses Double Fourier Sphere (DFS)
% method to tranform the orientational space and time-marched in the DFS
% space. Time stepping is semi-implicit, with Advection terms in RK3 and
% Laplacian term in CN2. Implicit matrix inversion is done using the
% Spherefun Helmholtz Solver (only slightly modified to remove
% chebfun-based activiities).
%% Setting up
% RK3 coeff and constants
alpha=[4/15 1/15 1/6];
gamma=[8/15 5/12 3/4];
rho=[0 -17/60 -5/12];
% Preparing Constants
K2 = (1/(dt*diff_const)); % Helmholtz frequency for BDF1
WK2= Re/dt;
%% Initialising Matrices
[settings,Mvor,Mgyro,Minert,Mlap,Rdx,Rd2x,Mp1,Mp3,Mp1p3,~]=all_mat_gen(settings);
% mats=struct('Mint',settings.Mint,'S_profile',S_profile,'Mvor',Mvor,'Mgyro',Mgyro,'Mlap',Mlap,...
% 'Mp1',Mp1,'Mp3',Mp3,'Rdx',Rdx,'Rd2x',Rd2x); settings_CPU=settings; % If CPU PS is used.
Mint=gpuArray(settings.Mint);
MintSq=gpuArray(settings.MintSq);
Kp=settings.Kp;
% GPU stuff
S_profile=gpuArray(S_profile);
Kp=gpuArray(Kp);
mKp_alpha1=gpuArray(-(Kp/alpha(1)));
mKp_alpha2=gpuArray(-(Kp/alpha(2)));
mKp_alpha3=gpuArray(-(Kp/alpha(3)));
mK2_alpha1=gpuArray(-K2/alpha(1));malpha1_K2=1/mK2_alpha1;
mK2_alpha2=gpuArray(-K2/alpha(2));malpha2_K2=1/mK2_alpha2;
mK2_alpha3=gpuArray(-K2/alpha(3));malpha3_K2=1/mK2_alpha3;
gamma_alpha1=gpuArray(gamma(1)/alpha(1)/diff_const);
gamma_alpha2=gpuArray(gamma(2)/alpha(2)/diff_const);
gamma_alpha3=gpuArray(gamma(3)/alpha(3)/diff_const);
rho_alpha2=gpuArray(rho(2)/alpha(2)/diff_const);
rho_alpha3=gpuArray(rho(3)/alpha(3)/diff_const);
mWK2_alpha1=gpuArray(-WK2/alpha(1));malpha1_WK2=1/mWK2_alpha1;
mWK2_alpha2=gpuArray(-WK2/alpha(2));malpha2_WK2=1/mWK2_alpha2;
mWK2_alpha3=gpuArray(-WK2/alpha(3));malpha3_WK2=1/mWK2_alpha3;
Wgamma_alpha1=gpuArray(gamma(1)/alpha(1)*Re);
Wgamma_alpha2=gpuArray(gamma(2)/alpha(2)*Re);
Wgamma_alpha3=gpuArray(gamma(3)/alpha(3)*Re);
Wrho_alpha2=gpuArray(rho(2)/alpha(2)*Re);
Wrho_alpha3=gpuArray(rho(3)/alpha(3)*Re);
% Advection
% Mvor=gpuArray(complex(adv_vor_mat(settings)));
% Mgyro=gpuArray(complex(settings.beta*adv_gyro_mat(settings)));
%For strange behaviour in MATLAB ver < R2020
Mvor=gpuArray(sparse(complex(full(Mvor))));
Mgyro=gpuArray(sparse(complex(full(Mgyro))));
%Laplacian
Mlap=gpuArray(sparse(complex(Mlap)));
helm=helmholtz_genGPU( n, m);
helm_inv_k1=helmholtz_precalGPU( -K2/alpha(1),helm);
helm_inv_k2=helmholtz_precalGPU( -K2/alpha(2),helm);
helm_inv_k3=helmholtz_precalGPU( -K2/alpha(3),helm);
Whelm_inv_k1=gpuArray(inv(Rd2x-WK2/alpha(1)*eye(N_mesh)));
Whelm_inv_k2=gpuArray(inv(Rd2x-WK2/alpha(2)*eye(N_mesh)));
Whelm_inv_k3=gpuArray(inv(Rd2x-WK2/alpha(3)*eye(N_mesh)));
%Dz
Rdx=gpuArray(Rdx);
Rd2x=gpuArray(Rd2x);
%p1
Mp1 = gpuArray(complex(Mp1));
%p3
Mp3 = gpuArray(complex(Mp3));
%p1p3
Mp1p3 = gpuArray(complex(Mp1p3));
%Swimming and sedimentation
MSwim=Vc*Mp1-(Vsmax-Vsmin)*Mp1p3;
% mats=struct('Mint',Mint,'S_profile',S_profile,'Mvor',Mvor,'Mgyro',Mgyro,'Mlap',Mlap,...
% 'Mp1',Mp1,'Mp3',Mp3,'Rdx',Rdx,'Rd2x',Rd2x); % If GPU PS is used.
%% Initialise Recorded values
cell_den=NaN(floor(nsteps/saving_rate3),N_mesh);
W_prof=NaN(floor(nsteps/saving_rate3),N_mesh);
% PS=PS_RunTime'x','inv',mats,settings_CPU,saving_rate1,saving_rate2);
% PS=PS_RunTime('x','invGPU_w_fdt',mats,settings,saving_rate1,saving_rate2);
% PS=PS_RunTime_Svar('x','inv',mats,settings_CPU,saving_rate1,saving_rate2);
% PS=PS_RunTime_Svar('x','invGPU_w_fdt',mats,settings,saving_rate1,saving_rate2);
%% Time-Stepping (RK3-CN2)
ucoeff=gpuArray(complex(ucoeff0));
W_profile=gpuArray(W_profile);
adv_p_coeff =gpuArray(complex(zeros(n*m,N_mesh)));
adv_comb_coeff =gpuArray(complex(zeros(n*m,N_mesh)));
ucoeff_previous2=complex(NaN(n*m,N_mesh,3));
cell_den_loc=real(Mint*ucoeff*2*pi);
Nint_loc=sum(cell_den_loc,2)*dx;
for i = 1:nsteps
%% RK step 1
% k=1;
dxu_coeff=ucoeff*Rdx;
dx2u_coeff=ucoeff*Rd2x;
adv_coeff=S_profile.*(Mvor*ucoeff)+Mgyro*ucoeff;
adv_coeff=adv_coeff+Minert*ucoeff;
adv_coeff=adv_coeff-Mint'*(Mint*adv_coeff)/MintSq;
lap_coeff=Mlap*ucoeff;
lap_coeff=lap_coeff-Mint'*(Mint*lap_coeff)/MintSq;
swim_coeff=MSwim*dxu_coeff;
DT_coeff=DT*dx2u_coeff;
adv_p_coeff=adv_coeff+swim_coeff-DT_coeff;
rhs_coeff = mK2_alpha1*ucoeff-lap_coeff+gamma_alpha1*adv_p_coeff...
+mKp_alpha1*(int_const-Nint_loc)*(Mint'.*ucoeff);
F=permute(reshape(rhs_coeff,helm.n,helm.m,N_mesh),[2 1 3]);
int_constj = pagefun(@mtimes,malpha1_K2*helm.enG,F(:,helm.k,:));
F = pagefun(@mtimes,malpha1_K2*helm.L2G, F);
F(helm.floorm+1,helm.k,:)=int_constj;
CFS = helm_inv_k1*reshape(F,helm.n*helm.m,N_mesh);
ucoeff=reshape(permute(reshape(CFS,helm.m,helm.n,N_mesh),[2 1 3]),helm.n*helm.m,N_mesh);
Wadv_coeff=Ri*(cell_den_loc-Nint_loc/channel_width);
Wlap_coeff=W_profile*Rd2x;
Wadv_p_coeff=Wadv_coeff;
Wrhs_coeff=mWK2_alpha1*W_profile-Wlap_coeff+Wgamma_alpha1*Wadv_p_coeff;
W_profile= Wrhs_coeff*Whelm_inv_k1;
S_profile= W_profile*Rdx/2;
cell_den_loc=real(Mint*ucoeff*2*pi);
Nint_loc=sum(cell_den_loc,2)*dx;
%% RK step 2
% k=2;
dxu_coeff=ucoeff*Rdx;
dx2u_coeff=ucoeff*Rd2x;
adv_coeff=S_profile.*(Mvor*ucoeff)+Mgyro*ucoeff;
adv_coeff=adv_coeff+Minert*ucoeff;
adv_coeff=adv_coeff-Mint'*(Mint*adv_coeff)/MintSq;
lap_coeff=Mlap*ucoeff;
lap_coeff=lap_coeff-Mint'*(Mint*lap_coeff)/MintSq;
swim_coeff=MSwim*dxu_coeff;
DT_coeff=DT*dx2u_coeff;
adv_comb_coeff=adv_coeff+swim_coeff-DT_coeff;
rhs_coeff = mK2_alpha2*ucoeff-lap_coeff+gamma_alpha2*adv_comb_coeff+rho_alpha2*adv_p_coeff...
+mKp_alpha2*(int_const-Nint_loc)*(Mint'.*ucoeff);
F=permute(reshape(rhs_coeff,helm.n,helm.m,N_mesh),[2 1 3]);
int_constj = pagefun(@mtimes,malpha2_K2*helm.enG,F(:,helm.k,:));
F = pagefun(@mtimes,malpha2_K2*helm.L2G, F);
F(helm.floorm+1,helm.k,:)=int_constj;
CFS = helm_inv_k2*reshape(F,helm.n*helm.m,N_mesh);
ucoeff=reshape(permute(reshape(CFS,helm.m,helm.n,N_mesh),[2 1 3]),helm.n*helm.m,N_mesh);
Wadv_coeff=Ri*(cell_den_loc-Nint_loc/channel_width);
Wlap_coeff=W_profile*Rd2x;
Wadv_comb_coeff=Wadv_coeff;
Wrhs_coeff=mWK2_alpha2*W_profile-Wlap_coeff+Wgamma_alpha2*Wadv_comb_coeff+Wrho_alpha2*Wadv_p_coeff;
W_profile= Wrhs_coeff*Whelm_inv_k2;
S_profile= W_profile*Rdx/2;
cell_den_loc=real(Mint*ucoeff*2*pi);
Nint_loc=sum(cell_den_loc,2)*dx;
%% RK step 3
% k=3;
dxu_coeff=ucoeff*Rdx;
dx2u_coeff=ucoeff*Rd2x;
adv_p_coeff=adv_comb_coeff;
adv_coeff=S_profile.*(Mvor*ucoeff)+Mgyro*ucoeff;
adv_coeff=adv_coeff+Minert*ucoeff;
adv_coeff=adv_coeff-Mint'*(Mint*adv_coeff)/MintSq;
lap_coeff=Mlap*ucoeff;
lap_coeff=lap_coeff-Mint'*(Mint*lap_coeff)/MintSq;
swim_coeff=MSwim*dxu_coeff;
DT_coeff=DT*dx2u_coeff;
adv_comb_coeff=adv_coeff+swim_coeff-DT_coeff;
rhs_coeff = mK2_alpha3*ucoeff-lap_coeff+gamma_alpha3*adv_comb_coeff+rho_alpha3*adv_p_coeff...
+mKp_alpha3*(int_const-Nint_loc)*(Mint'.*ucoeff);
F=permute(reshape(rhs_coeff,helm.n,helm.m,N_mesh),[2 1 3]);
int_constj = pagefun(@mtimes,malpha3_K2*helm.enG,F(:,helm.k,:));
F = pagefun(@mtimes,malpha3_K2*helm.L2G, F);
F(helm.floorm+1,helm.k,:)=int_constj;
CFS = helm_inv_k3*reshape(F,helm.n*helm.m,N_mesh);
ucoeff=reshape(permute(reshape(CFS,helm.m,helm.n,N_mesh),[2 1 3]),helm.n*helm.m,N_mesh);
Wadv_coeff=Ri*(cell_den_loc-Nint_loc/channel_width);
Wlap_coeff=W_profile*Rd2x;
Wadv_comb_coeff=Wadv_coeff;
Wrhs_coeff=mWK2_alpha3*W_profile-Wlap_coeff+Wgamma_alpha3*Wadv_comb_coeff+Wrho_alpha3*Wadv_p_coeff;
W_profile= Wrhs_coeff*Whelm_inv_k3;
S_profile= W_profile*Rdx/2;
cell_den_loc=real(Mint*ucoeff*2*pi);
Nint_loc=sum(cell_den_loc,2)*dx;
%% Saving for Post-Processing
% Saving full Psi and it time derivative
% PS=PS.RunTimeCall(ucoeff,i);
% PS=PS.RunTimeCall(ucoeff,S_profile,i);
% Saving Cell Density
if ( mod(i, saving_rate3) == 0 )
cell_den(i/saving_rate3,:)=gather(cell_den_loc);
W_prof(i/saving_rate3,:)=gather(W_profile);
disp([num2str(i) '/' num2str(nsteps)]);
if any(isnan(cell_den(i/saving_rate3,:)))
disp('NaN detected in cell_den');
break;
end
end
end