Defining an implicit function over a specific interval

Hi guys;

I have a 2-D (fluid) flow domain with the inlet and outlet as shown in Fig. attached as Geometry. My origin is in the lower left corner.

I have numerically calculated the stream function for this flow domain, which is obviously an implicit function of x and y. I have a few questions:

First, how can I specifically define my implicit function for only my flow domain (which is a trapezoidal region in the space). When I try to plot a sample streamline, the actual implicit function goes beyond my flow domain as seen in the Fig. attached as streamline. In fact, I need to define my implicit function only within my flow domain and get rid of the rest.

Specifically, I need a mesh grid of a trapezoidal shape with its node located at (0,0) (0.008,0) (0.008,0.000641) (0,0.0012).

I though maybe I could do it with meshgrid, but I could not find a way to mesh my trapezoidal domain.

Looking at the attached Fig. named ROI, I only want my function defined at the section marked by a check mark and get rid of the rest.

Second, I need to mesh my flow domain into fine grids, then do some mathematical calculation on it. Specifically, since I have the velocity profile both in x and y direction, I need to calculate shear stress along each streamline. So, I need to know how to discretize my domain for further post-processing.

Please let me know if you need further clarification on my question.

Thanks

Answer 1

[KSSV]

You can genearte, grid in your interested domain using transfinite interpolation. Have a look on the following file exchange functions:

https://in.mathworks.com/matlabcentral/fileexchange/40681-transfinite-interpolation

https://in.mathworks.com/matlabcentral/fileexchange/40618-grid-generation

[mohammad faghih]

I will take a look at them and will let you know if I still have some questions. Thanks a lot

[mohammad faghih]

Apart from the meshing and CFD question I have. I still need to know a basic thing in MATLAB.

Is it possible to define an implicit function over only a trapezoidal space? For example, we know a circle has an implicit function as x^2+y^2=R^2, right? But what if I want to define it only for 0<x<R and 0<y<R. You know that this interval of 0<x<R and 0<y<R would correspond to a square in space, right? So, how would I define a trapezoidal space within which my function is defined.

[KSSV]

% Trapezium coordinates
P1 = [0 0] ;
P2 = [8 0] ;
P3 = [8 0.641] ;
P4 = [0 1.2] ;
P5 = P1 ;
T = [P1; P2; P3;P4;P5] ;
N = 100 ;
x = linspace(min(T(:,1)),max(T(:,1)),N) ;
y = linspace(min(T(:,2)),max(T(:,2)),N) ;
[X,Y] = meshgrid(x,y) ;
idx = inpolygon(X(:),Y(:),T(:,1),T(:,2)) ;
% TRapizum coordinates
tx = X(idx) ; ty = Y(idx) ;
figure
hold on
plot(T(:,1),T(:,2),'r')
hold on
plot(tx,ty,'.b')

Now define, your function on (tx,ty)