# Solving the Psystem

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 May 2, 2005, 09:15 I wish to test the numerical m #1 Member   Marco Kupiainen Join Date: Mar 2009 Posts: 31 Rep Power: 10 I wish to test the numerical methods in OpenFOAM on a well known hyperbolic test-problem, namely the p-system: [v u]_t + [-u A*v^-gamma]_x = 0 I have written a piece of code that solves this in 1D, using the OpenFOAM space-discretization-operator div. The time-stepping is made with a 2:nd order TVD Runge-Kutta. My question is the following: The convection-specific 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 "shallow-wat #2 Senior Member   Join Date: Mar 2009 Posts: 854 Rep Power: 15 I have solved the "shallow-water" equations in various ways but never the "p-system". In the former the choice of flux variable is obvious but in the later it is definitely not obvious. What physical problem can the "p-system" be applied to?

 May 2, 2005, 12:31 The p-system is a model for is #3 Member   Marco Kupiainen Join Date: Mar 2009 Posts: 31 Rep Power: 10 The p-system 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 #4 Senior Member   Join Date: Mar 2009 Posts: 854 Rep Power: 15 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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