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misabel February 10, 2010 07:06

4th order Runge-Kutte & uncoupled method Navier Stokes equations
Hello CFD's users!

I have programmed a code in order to solve Navier-Stokes equations with Finite Element Method. In order to solve it, I use an uncoupled method (first I calculate the velocity, secondly, the PPE to obtain the pressure), to make time discretization I have applied 4th explicit Runge Kutta method.

But I don't know if I am applying rightly Runge-Kutta with the uncoupled method.

I do:

1) Calculate velocity u_n+1 doing:

1.a) k1=incrT*(-Advection_Term(n,u_n)-Difusion_Term(n,u_n)-Gradient*p_n)

1.b) k2=incrT*(-Advection_Term(n+1/2,u_n+k1/2 )-Difusion_Term(n+1/2,u_n+k1/2 )-Gradient*p_n)

1.c) k3=incrT*(-Advection_Term(n+1/2,u_n+k2/2 )-Difusion_Term(n+1/2,u_n+k2/2 )-Gradient*p_n)

1.c) k4=incrT*(-Advection_Term(n+1,u_n+k3 )-Difusion_Term(n+1,u_n+k3 )-Gradient*p_n)

In that way, we have Mu_n+1=Mu_n+k1/6+k2/3+k3/3+k4/6, where M is the mass matrix.

2) Calculate pressure p_n+1 with velocity u_n+1, throughout the Pressure Poisson Equations (PPE).

I would like to know if I am doing it in the right way, does it make sense?

Thanks in advance!
Best regards!

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