Interpolated pressure laws in two-fluid simulations and hyperbolicity

Philippe Helluy, Jonathan Jung
IRMA, University of Strasbourg
hal-00957043, (7 March 2014)


   title={Interpolated pressure laws in two-fluid simulations and hyperbolicity},

   author={HELLUY, Philippe and JUNG, Jonathan},



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We consider a two-fluid compressible flow. Each fluid obeys a stiffened gas pressure law. The continuous model is well defined without considering mixture regions. However, for numerical applications it is often necessary to consider artificial mixtures, because the two-fluid interface is diffused by the numerical scheme. We show that classic pressure law interpolations lead to a non-convex hyperbolicity domain and failure of well-known numerical schemes. We propose a physically relevant pressure law interpolation construction and show that it leads to a necessary modification of the pure phase pressure laws. We also propose a numerical scheme that permits to approximate the stiffened gas model without artificial mixture.
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