# 4th order Runge-Kutte & uncoupled method Navier Stokes equations

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 February 10, 2010, 06:06 4th order Runge-Kutte & uncoupled method Navier Stokes equations #1 New Member   Isabel Join Date: Mar 2009 Posts: 4 Rep Power: 17 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! Isi

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