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c85255c5af
All of these code samples currently are mis-identified in my repositories. I'm donating them to the cause.
50 lines
1.6 KiB
Matlab
50 lines
1.6 KiB
Matlab
clear all
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tic
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% initialize integration time T, f(x,t), discretization size n ----------------
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T = 8;
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x_min=0;
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x_max=2;
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y_min=0;
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y_max=1;
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n=50; % how many points per one measure unit (both in x and in y)
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ds=1/(n-1);
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x_res=(x_max-x_min)*n;
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y_res=(y_max-y_min)*n;
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grid_x=linspace(x_min,x_max,x_res);
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grid_y=linspace(y_min,y_max,y_res);
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advected_x=zeros(x_res,y_res);
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advected_y=zeros(x_res,y_res);
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% integrate all initial points for t in [0,T] --------------------------------
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parfor i = 1:x_res
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for j = 1:y_res
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[t,X] = ode45(@dg,[0,T],[grid_x(i),grid_y(j)]);
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% store advected positions as they would appear in (x,y) coords ------
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advected_x(i,j) = X(length(X(:,1)),1);
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advected_y(i,j) = X(length(X(:,2)),2);
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end
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end
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%% Compute FTLE
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sigma=zeros(x_res,y_res);
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% at each point in interior of grid, store FTLE ------------------------------
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for i = 2:x_res-1
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for j = 2:y_res-1
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% compute Jacobian phi -----------------------------------------------
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phi(1,1) = (advected_x(i+1,j)-advected_x(i-1,j))/(2*ds);
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phi(1,2) = (advected_x(i,j-1)-advected_x(i,j+1))/(2*ds);
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phi(2,1) = (advected_y(i+1,j)-advected_y(i-1,j))/(2*ds);
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phi(2,2) = (advected_y(i,j-1)-advected_y(i,j+1))/(2*ds);
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% find max eigenvalue of phi'*phi ------------------------------------
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lambda_max = max(abs(eig(phi'*phi)));
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% store FTLE ---------------------------------------------------------
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sigma(i,j) = log(lambda_max)/abs(2*T);
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end
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end
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toc
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%% plot FTLE field ------------------------------------------------------------
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figure
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contourf(grid_x,grid_y,sigma');
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colorbar('location','EastOutside');
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axis equal
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shading flat
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