Pressure Linearization Method for the Computation of Real Fluids
Abstract
We present a method for the numerical solution of the Euler equations
for fluids governed by a general equation of state, in the framework of finite volume
schemes. In the evolution step, the idea is to replace the original pressure law with
a locally-parameterized linear one. Then, the original EOS is used in the projection
step to update the cell values of the pressure. A validation of the proposed scheme
is provided by its interpretation as a relaxation method for the Euler equations. In
the present paper we specialize our approach to a Roe-type method, and some two-dimensional
numerical results are presented. Finally, we propose a modification of
our scheme that allows us to ensure the invariance of the pressure and the velocity
across contact discontinuities, for those cases in which difficulties arise in updating
the pressure through the original nonlinear equation of state, as a consequence of
the cell-based discretization of finite volume methods.