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Make a grid for a non-rectangular geometry

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Ann St
Ann St 2015-4-25
评论： Jeremy Ahner 2022-7-15
I have a code that makes a grid for a rectangular geometry. Then it solves equations at each grid point. I want to make the geometry a little more complex (like in the diagram attached--a tank with an outlet attached to it), but don't know how. There is probably information out there about this, but I am not experienced in using Matlab and probably am not using the right search terms. If someone could help, I would be very grateful.
Here is the code I have:
Nx = 20; Ny = Nx; % Number of nodes in x and y direction.
% Lx and Ly are the lengths of each side of the rectangle.
% Grid
x = linspace(0,Lx,Nx); y = linspace(0,Ly,Ny);
delta_x = Lx/(Nx-1); delta_y = Ly/(Ny-1); % Spacing between nodes
% Initial condition
psi = zeros(Nx,Ny); var_store = zeros(Nx,Ny); omega = zeros(Nx,Ny);
How can I modify this to make it appropriate for the shape I want?

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回答（2 个）

KSSV
KSSV 2018-11-8
L = 10; % length
H1 = 5 ;
H2 = 7 ;
%
% Full rectangle
M = 500 ;
x1 = linspace(0,L,M)' ;
y1 = linspace(0,H1,M)' ;
[X1,Y1] = meshgrid(x1,y1) ;
%
N = nnz(x1>=4 & x1<=7);
% Create top notch rectangle from x = 4 t0 7
x2 = linspace(4,7,N)' ;
y2 = linspace(H1,H2,N)' ;
[X2,Y2] = meshgrid(x2,y2) ;
% Merge the double nodes present
idx = knnsearch([X1(end,:)' Y1(end,:)'],[X2(1,:)' Y2(1,:)']) ;
X2(1,:) = X1(end,idx) ;
Y2(1,:) = Y1(end,idx) ;
figure
hold on
plot(X1,Y1,'.r')
plot(X2,Y2,'.b')
Peter
Peter 2022-2-22
Another answer for this is to leave the nominal XY grid defining the mesh, but use NaN outside of the prefered geometry.

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