Sunday, March 4, 2012

Sod's 1D Shock Tube Solution

I have nearly completed my 2D gas dynamics code. A rotated Roe-HLL approximate Reimann solver is implemented on a structured trapezoidal grid with MUSCL upwind reconstruction and UMIST limiter to ensure a 2nd order TVD scheme. A RK-4 algorithm is used for time integration. Here is the output computed for Sod's Shock Tube Problem as a test case where P1=10,000 Pa and P2=100,000 Pa at t=.002 seconds. These results are consistent with the exact solutions.

Constants:
MM =  30 g/mol
Specific heat ratio = 1.4
Initial temp = 298 K

 Grid:
nx = 800
xmax = 4 m
nt =  10,000
tmax = .01 sec

I am still trying to work out some bugs in its application to 2D axisymmetric flows.

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