How do i write the code for navierstokes equation in matlab/comsol?

The idea is to write the code for the navierstokes equation with the laplacian velocity and pressure term

[KSSV]

You want it in comsol? So this is not the forum. You want in MATLAB? What have you attempted?

Answer 1

[Precise Simulation]

The incompressible Navier-Stokes equations is also available as a built-in pre-defined Navier-Stokes physics mode in the FEATool FEM Matlab toolbox. In this case the equations are in 2D defined as

rho_ns*u' - miu_ns*(2*ux_x + uy_y + vx_y) + rho_ns*(u*ux_t + v*uy_t) + p_x = Fx_ns
rho_ns*v' - miu_ns*(vx_x + uy_x + 2*vy_y) + rho_ns*(u*vx_t + v*vy_t) + p_y = Fy_ns
ux_t + vy_t = 0

the Navier-Stokes equations in axisymmetry (2D cylindrical coordinates) and 3D are defined similarly.

Answer 2

[Bartholomew Osegbe]

I have attempted the weak method fem.equ.weak = { ... { ... {'(-eta*ux)*test(ux)+(-eta*uy)*test(uy)-test(u)*px'} ... {'(-eta*vx)*test(vx)+(-eta*vy)*test(vy)-test(v)*py'} ... {'-test(px)*u-test(py)*v'} ... } ... }; but I have errors and when I sourced online I found a code that uses the poisson equation but just wanted a simple code with a laplacian velocity and pressure term.

Answer 3

[Ameer Hamza]

You may find these FEX submission useful:

1) https://www.mathworks.com/matlabcentral/fileexchange/47183-navier-stokes-solver.

2) https://www.mathworks.com/matlabcentral/fileexchange/60868-2d-steady-navier-stokes.

Answer 4

[Bartholomew Osegbe]

Thank you all for your answers, I do appreciate it.