Pressure Field From Velocity Field

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Mat576
Mat576 2022-9-6
编辑： Torsten 2022-9-6
I have a velocity field in MATLAB as two 641x861 arrays (Vx and Vy) and I need to convert it to a pressure field to determine the pressure difference / gradient between two points. I've tried a handful of approaches (pressure Poisson, Euler equation, etc.) but am struggling with the fact that I already have the velocity field over time and don't need to find u* / v*, u^n+1 / v^n+1.
Right now, I'm trying to use the attached equations but the pressure field values don't seem correct. Do I need to set up a separate mesh even though I already have the velocity at specific points? I assumed that I could use the size of my Vx and Vy arrays as my mesh. I'm also unsure how to appropriately integrate the partial derivatives over a path.
Here's my current code:
imin = 2; imax = m;
jmin = 2; jmax = n;
Px = zeros(imax,jmax);
Py = zeros(imax,jmax);
dx = 1;
dy = 1;
for j = jmin:jmax
for i = imin:imax
Px(i,j) = -rho*(Vx(i,j)*((Vx(i+1,j)-Vx(i-1,j))*0.5*dx)+Vy(i,j)*((Vx(i,j+1)-Vx(i,j-1))*0.5*dy));
Py(i,j) = -rho*(Vx(i,j)*((Vy(i+1,j)-Vy(i-1,j))*0.5*dx)+Vy(i,j)*((Vy(i,j+1)-Vy(i,j-1))*0.5*dy));
end
end
Should I be going about this a different way? Thank you in advance for any feedback!
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Mat576
Mat576 2022-9-6
Thanks for your response. Do you have any insight on how to go about taking the integral of dP/dx and dP/dy over a path? I'm not sure which method is appropriate given that it's discrete data and a partial derivative.
Torsten
Torsten 2022-9-6
编辑：Torsten 2022-9-6
Solve the Pressure Poisson Equation (1.1.3.1) in the domain:
http://www.thevisualroom.com/poisson_for_pressure.html
You will have to know pressure on the boundaries and your velocity field must be divergence-free.

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