
[Sponsors] 
March 13, 2009, 13:02 
Sod Shock Tube problem

#1 
Guest
Posts: n/a

Hi all,
I'm trying to model the Sod Shock Tube Riemann Problem using a Riemann decomposition method. The theory is outlined in EF Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, section 3.1. The problem consists of an area of density, pressure of 1 and initial velocity of 0.75 on the left of a membrane, and an area with density of 0.125, and pressure of 0.1 with a speed of 0 on the right. At time zero the membrane is removed. I'm using a Riemann method to solve the problem, first for the Riemann variables, which is the matrix of right eigenvectors (of the Jacobian matrix of the flux) premultiplied by the variables (rho, rho.u, E)^T where the right eigenvectors are  1 , 1 , 1   ua , u , u+a   H ua , 0.5u^2 , H+ua  a = soundspeed, H = (E + p)/rho, p = pressure, E = total energy = rho.(0.5u^2 + specific internal energy). The eigenvalues of this system are (ua, u, u+a). For the next timestep. If the eigenvalue is greater than zero, we take INITOUTPUT(i,k) = INITOUTPUT(i,k)*(1  EIG(i,k)*(DT/DX)) + EIG(i,k)*(DT/DX)*(INITOUTPUT(i1,k). If the eigenvalue is less than zero, we take INITOUTPUT(i,k) = INITOUTPUT(i,k)*(1 + (DT/DX)*(EIG(i,k))  EIG(i,k)*(DT/DX)*INITOUTPUT(i+1,k). Where INITOUTPUT(i,k) are the Riemann variables, i is the x variable. Then we use a newton solver to solve the nonlinear relationship between the Riemann variables and the original variables, (rho, rho.u, E). Regardless of the timestep or grid spacing, I seem to get the density decreasing smoothly towards the discontinuity over time, then sharply reducing to much lower than the original 0.125 on the right hand side just after the discontinuity and only then going back to the original 0.125. The solution to this problem is well known and not this. I'm using reflective boundary conditions for the near wall rho(0) = rho(1), u(0) = u(1), E(0)=E(1) and the same on the far wall. Can anyone help? I would really appreciate it. 

March 13, 2009, 14:41 
Re: Sod Shock Tube problem

#2 
Guest
Posts: n/a


March 13, 2009, 16:33 
Re: Sod Shock Tube problem

#3 
Guest
Posts: n/a

Thanks, but I want to generate my own code. This is part of a project for a PhD.


March 17, 2009, 08:45 
Try without the initial velocity

#4 
New Member
Join Date: Mar 2009
Posts: 4
Rep Power: 7 
Hi
Have you tried the test without the initial velocity? Try that first, and you should also have open boundary on both sides. Try ul=0. The star values are shown on pg 133. Looks like you get a rarefaction wave on the right side of the discont. 

July 7, 2009, 13:24 

#5 
Member
Nishant Kumar
Join Date: Jun 2009
Posts: 32
Rep Power: 7 
Hi,
I am dealing with kind of the same problem. Were you able to figure it out? Reply me at babuu.nishu@gmail.com Thanks 

Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
analytical solution of 1D shock tube problem  ma  Main CFD Forum  9  August 5, 2014 19:04 
HLL Riemann Shock Tube Matlab Problem  Luke F  Main CFD Forum  1  July 7, 2009 13:44 
How to slove shock tube problem with Harten's TVD  xialiuyu  Main CFD Forum  0  June 17, 2007 00:57 
shock tube validation  AB  Main CFD Forum  3  December 10, 2004 08:31 
shock problem  arief  Main CFD Forum  10  October 22, 1998 19:22 