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Merge pull request #6 from RDycore/donghui/swe-roe-dev
Code Verification for ex1.
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| clear;close all;clc | ||
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| % Run several simulations before runing the following scripts | ||
| % mpiexec -n 40 ./ex1 -hd 5.0 -save 2 -b -dx 10 -dy 10 -dt 0.0005 | ||
| % mpiexec -n 40 ./ex1 -hd 5.0 -save 2 -b -dx 2 -dy 2 -dt 0.0005 | ||
| % mpiexec -n 40 ./ex1 -hd 5.0 -save 2 -b -dx 1 -dy 1 -dt 0.0005 | ||
| % mpiexec -n 40 ./ex1 -hd 5.0 -save 2 -b -dx 0.5 -dy 0.5 -dt 0.0005 | ||
| % mpiexec -n 40 ./ex1 -hd 5.0 -save 2 -b -dx 0.2 -dy 0.2 -dt 0.0005 | ||
| % mpiexec -n 40 ./ex1 -hd 5.0 -save 2 -b -dx 0.1 -dy 0.1 -dt 0.0005 | ||
| % mpiexec -n 40 ./ex1 -hd 5.0 -save 2 -b -dx 0.05 -dy 0.05 -dt 0.0005 | ||
| % mpiexec -n 40 ./ex1 -hd 5.0 -save 2 -b -dx 0.02 -dy 0.02 -dt 0.0005<-- assuming this is exact solution | ||
| % mpiexec -n 40 ./ex1 -hd 5.0 -save 2 -b -dx 0.01 -dy 0.01 -dt 0.0005<-- unstable, smaller time step is needed, but too expensive | ||
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| % User need to provide petsc directory | ||
| addpath('/Users/xudo627/developments/petsc/share/petsc/matlab/'); | ||
| Lx = 200; % [m] | ||
| Ly = 200; % [m] | ||
| dof = 3; | ||
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| filename = 'outputs/ex1_Nx_10000_Ny_10000_dt_0.000500_14400.dat'; | ||
| data = PetscBinaryRead(filename); | ||
| strs = strsplit(filename,'_'); | ||
| for i = 1 : length(strs) | ||
| if strcmp(strs{i},'Nx') | ||
| Nx = str2num(strs{i+1}); | ||
| elseif strcmp(strs{i},'Ny') | ||
| Ny = str2num(strs{i+1}); | ||
| elseif strcmp(strs{i},'dt') | ||
| dt = str2num(strs{i+1}); | ||
| end | ||
| end | ||
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| figure; | ||
| data = reshape(data, [dof, length(data)/dof]); | ||
| hexact = reshape(data(1,:),[Nx Ny]); | ||
| uexact = reshape(data(1,:),[Nx Ny]); | ||
| vexact = reshape(data(1,:),[Nx Ny]); | ||
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| imagesc(hexact); colorbar; caxis([0 10]); colormap(jet); | ||
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| Nxexact = 10000; | ||
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| dx = []; | ||
| Nxs = [20 40 100 200 400 1000 2000]; | ||
| err_L1 = NaN(length(Nxs),3); | ||
| err_L2 = NaN(length(Nxs),3); | ||
| err_Max = NaN(length(Nxs),3); | ||
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| k = 1; | ||
| for Nx = Nxs | ||
| disp(['Nx = ' num2str(Nx)]); | ||
| Ny = Nx; | ||
| dx = [dx; Lx/Nx]; | ||
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| bu = 29 / dx(k); | ||
| bd = 104 / dx(k); | ||
| bl = 94 / dx(k); | ||
| br = 106 / dx(k); | ||
| ii = 1 : Nx; jj = 1 : Ny; | ||
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| filename = ['outputs/ex1_Nx_' num2str(Nx) '_Ny_' num2str(Ny) '_dt_0.000500_14400.dat']; | ||
| data = PetscBinaryRead(filename); | ||
| data = reshape(data, [dof, length(data)/dof]); | ||
| h = reshape(data(1,:),[Nx Ny]); | ||
| u = reshape(data(1,:),[Nx Ny]); | ||
| v = reshape(data(1,:),[Nx Ny]); | ||
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| h(ii <= bu,jj < br & jj > bl) = NaN; | ||
| h(ii > bd ,jj < br & jj > bl) = NaN; | ||
| u(ii <= bu,jj < br & jj > bl) = NaN; | ||
| u(ii > bd ,jj < br & jj > bl) = NaN; | ||
| v(ii <= bu,jj < br & jj > bl) = NaN; | ||
| v(ii > bd ,jj < br & jj > bl) = NaN; | ||
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| scale_factor = Nxexact / Nx; | ||
| hexact_tmp = convert_res(hexact,1,scale_factor) ./ scale_factor^2; | ||
| uhexact_tmp = convert_res(uexact.*hexact,1,scale_factor) ./ scale_factor^2; | ||
| vhexact_tmp = convert_res(vexact.*hexact,1,scale_factor) ./ scale_factor^2; | ||
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| for i = 1 : 3 | ||
| if i == 1 | ||
| err = abs(h - hexact_tmp); | ||
| elseif i == 2 | ||
| err = abs(u.*h - uhexact_tmp); | ||
| elseif i == 3 | ||
| err = abs(v.*h - vhexact_tmp); | ||
| end | ||
| err_L1(k,i) = nansum(abs(err(:)))/(Nx*Ny); | ||
| err_L2(k,i) = sqrt(nansum(err(:).^2)/(Nx*Ny)); | ||
| err_Max(k,i) = max(abs(err(:))); | ||
| end | ||
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| k = k + 1; | ||
| end | ||
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| figure; set(gcf,'Position',[10 10 900 300]); | ||
| varnames = {'h','uh','vh'}; | ||
| for i = 1 : 3 | ||
| subplot(1,3,i); | ||
| loglog(dx, err_L1(:,i) ,'bo-','LineWidth',2); hold on; grid on; | ||
| loglog(dx, err_L2(:,i) ,'g*-','LineWidth',2); | ||
| loglog(dx, err_Max(:,i),'rx-','LineWidth',2); | ||
| ydum = ylim; | ||
| loglog([dx(end) dx(1)], ydum(1).*[1, dx(1)/dx(end)],'k--','LineWidth',2); | ||
| title(varnames{i},'FontSize',15,'FontWeight','bold'); | ||
| if i == 1 | ||
| leg = legend('1-norm','2-norm','max-norm','first order'); | ||
| end | ||
| end | ||
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| function Z = convert_res(A,u,d) | ||
| %u = 5; %upsampling factor | ||
| %d = 12; %downsampling factor | ||
| t = d/u; %reduction factor | ||
| [m,n]=size(A); | ||
| L1=speye(m); L2=speye(round(m/t))/u; | ||
| R1=speye(n); R2=speye(round(n/t))/u; | ||
| L=repelem(L2,1,d) * repelem(L1,u,1); | ||
| R=(repelem(R2,1,d) * repelem(R1,u,1)).'; | ||
| Z= L*(A*R); | ||
| end | ||
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