Make a grid for a non-rectangular geometry

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?

[Khatereh Danaei]

Hi dear, I have a question exactly like you. do you find any answer? thank you.

Answer 1

[KSSV]

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')

Answer 2

[Peter]

Another answer for this is to leave the nominal XY grid defining the mesh, but use NaN outside of the prefered geometry.

[Jeremy Ahner]

How would you go about assigning NaN values outside of the geometry?