MATLAB: Mapping 3D velocity data onto a uniform grid

cfdmeshgrid

I am trying to map 3D velocity data from a non-uniform computational fluid dynamics (CFD) mesh grid onto a uniform Cartesian grid. The CFD data is generated using adaptive meshing, and therefore local grid density changes with every time step. However, I need results from each time step on the same Cartesian grid for input into another program.

I have created a uniform grid using meshgrid and then tried interp3 for mapping the data to the new grid. However, I haven't been successful in this approach because of difficulties interpolating from a non-uniform grid. Is there a more appropriate function that I could try?

Best Answer

Try this

[Xq,Yq,Zq] = meshgrid(min(x):0.001:max(x),min(y):0.001:max(y),min(z):0.001:max(z));
Uq = griddata(x,y,z,u,Xq,Yq,Zq);
Vq = griddata(x,y,z,v,Xq,Yq,Zq);
Wq = griddata(x,y,z,w,Xq,Yq,Zq);
quiver3(Xq(:),Yq(:),Zq(:),Uq(:),Vq(:),Wq(:))

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MATLAB: How to generate a coneplot with a non-uniform grid

The function CONEPLOT(X,Y,Z,U,V,W,Cx,Cy,Cz) plots velocity vectors as cones at the points (Cx,Cy,Cz) in the vector field defined by U,V,W. The arrays X,Y,Z define the coordinates for U,V,W and must be monotonic and 3D plaid (as if produced by MESHGRID). You should be able to use a grid that is non-uniformly distributed, as long as it meets these requirements. The following simple example demonstrates the use of a non-uniformly distributed grid:

[x,y,z]=meshgrid([0 10 15 30 60],[0 10 30 50 60],[-10 -8 0 2 10]); % non-uniform

[u,v,w]=meshgrid([0 5 11 12 20],[0 5 13 15 20],[0 7 19 20 25]); % non-uniform
cx=1;
cy=2;
cz=3;
surf(peaks)
h1=coneplot(x,y,z,u,v,w,cx,cy,cz)
set(h1, 'FaceColor', 'blue', 'EdgeColor', 'none')

MATLAB: Resampling non-uniformly sampled 2D Surface

Not a single function, however there are a group of functions that used in concert can do it.

Try this example:

x = sort(rand(1, 10))*10;                           % Latitude Vector
y = sort(rand(1, 12))*10;                           % Longitude Vector
[X,Y] = meshgrid(x, y);                             % Create Matrices

Z = sin(X*pi/2) .* cos(Y*pi/2);                     % Create Matrices
figure
surf(x, y, Z)
xlabel('x')
ylabel('y')
zlabel('Z')
title('Surface With Non-Uniform Grid Spacing')
xv = linspace(min(x), max(x), 40);                  % Create New Uniformly-Spaced Vector From Original ‘x’
yv = linspace(min(y), max(y), 50);                  % Create New Uniformly-Spaced Vector Vector From Original ‘y’
[Xq,Yq] = ndgrid(xv, yv);                           % Create Interpolation Matrices With Uniform Grid Spacing
Zq = griddata(X(:),Y(:),Z(:), Xq, Yq, 'natural');   % Interpolate Matrices To New Regular Grid
figure
surf(Xq, Yq, Zq)
xlabel('Xq')
ylabel('Yq')
zlabel('Zq')
title('Interpolated Surface With Uniform Grid Spacing')

Best Answer

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MATLAB: How to generate a coneplot with a non-uniform grid

MATLAB: Resampling non-uniformly sampled 2D Surface

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