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A hybrid scheme to compute contact discontinuities in one-dimensional Euler systems. (English) Zbl 1137.65419

Summary: The present paper is devoted to the computation of single phase or two phase flows using the single-fluid approach. Governing equations rely on Euler equations which may be supplemented by conservation laws for mass species. Emphasis is given on numerical modelling with help of Godunov scheme or an approximate form of Godunov scheme called VFRoe-ncv based on velocity and pressure variables. Three distinct classes of closure laws to express the internal energy in terms of pressure, density and additional variables are exhibited. It is shown first that a standard conservative formulation of above mentioned schemes enables to predict “perfectly” unsteady contact discontinuities on coarse meshes, when the equation of state (EOS) belongs to the first class. On the basis of previous work issuing from literature, an almost conservative though modified version of the scheme is proposed to deal with EOS in the second or third class. Numerical evidence shows that the accuracy of approximations of discontinuous solutions of standard Riemann problems is strengthened on coarse meshes, but that convergence towards the right shock solution may be lost in some cases involving complex EOS in the third class. Hence, a blend scheme is eventually proposed to benefit from both properties (“perfect” representation of contact discontinuities on coarse meshes, and correct convergence on finer meshes). Computational results based on an approximate Godunov scheme are provided and discussed.

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
76M12 Finite volume methods applied to problems in fluid mechanics
76M15 Boundary element methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
80A10 Classical and relativistic thermodynamics

Software:

Thetis; CHEMKIN
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References:

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