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May 2, 2005, 09:15 
I wish to test the numerical m

#1 
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Marco Kupiainen
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I wish to test the numerical methods in OpenFOAM on a well known hyperbolic testproblem, namely the psystem:
[v u]_t + [u A*v^gamma]_x = 0 I have written a piece of code that solves this in 1D, using the OpenFOAM spacediscretizationoperator div. The timestepping is made with a 2:nd order TVD RungeKutta. My question is the following: The convectionspecific schemes calculate the interpolation based on the flux of the flow velocity. What should I consider as the flow velocity here? 

May 2, 2005, 11:27 
I have solved the "shallowwat

#2 
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I have solved the "shallowwater" equations in various ways but never the "psystem". In the former the choice of flux variable is obvious but in the later it is definitely not obvious. What physical problem can the "psystem" be applied to?


May 2, 2005, 12:31 
The psystem is a model for is

#3 
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Marco Kupiainen
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The psystem is a model for isentropic (=constant entropy) or polytropic gas given in a Lagrangian coordinate system.
v is the specific volume i.e. 1/rho and u is the velocity, and p=A*v^gamma is the pressure (A>0 and gamma=1.4 typically for air). I have defined both v and u as volScalarFields, and by this choice I can use the linear interpolation scheme. However since I want to solve a Riemann problem I want to test all the different TVD methods already implemented in OpenFOAM. What is the easiest solution to this? 

May 2, 2005, 12:34 
If u is the velocity then you

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If u is the velocity then you should construct a flux from it somehow, ideally by constructing a pressure equation and getting the flux from that but if that is not appropriate then by linear interpolation.


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