Chapter

Analysis and Numerics for Conservation Laws

pp 137-162

Riemann Problem for the Euler Equation with Non-Convex Equation of State including Phase Transitions

  • Wolfgang DahmenAffiliated withInstitut für Geometrie und Praktische Mathematik, RWTH Aachen
  • , Siegfried MüllerAffiliated withInstitut für Geometrie und Praktische Mathematik, RWTH Aachen
  • , Alexander VoßAffiliated withInstitut für Geometrie und Praktische Mathematik, RWTH Aachen

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Summary

An exact Riemann solver is developed for the investigation of non-classical wave phenomena in BZT fluids and fluids which undergo a phase transition. Here we outline the basic construction principles of this Riemann solver employing a general equation of state that takes negative nonlinearity and phase transition into account. This exact Riemann solver is a useful validation tool for numerical schemes, in particular, when applied to the aforementioned fluids. As an application, we present some numerical results where we consider flow fields exhibiting non-classical wave phenomena due to BZT fluids and phase transition.