Path-conservative in-cell discontinuous reconstruction schemes for non conservative hyperbolic systems

Entropy Conservative and Entropy Stable Schemes for Nonconservative Hyperbolic Systems

The vanishing viscosity limit of nonconservative hyperbolic systems depends heavily on the specific form of the viscosity. Numerical approximations, such as the path consistent schemes of [C. Parés, SIAM J. Numer. Anal., 41 (2007), pp. 169–185], may not converge to the physically relevant solutions of the system. We construct entropy stable path consistent (ESPC) schemes to approximate nonconse...

FORCE schemes on unstructured meshes I: Conservative hyperbolic systems

In this paper we propose a new high order accurate centered path-conservative method on unstructured triangular and tetrahedral meshes for the solution of multidimensional non-conservative hyperbolic systems, as they typically arise in the context of compressible multi-phase flows. Our path-conservative centered scheme is an extension of the centered method recently proposed in [36] for conserv...

On the Riemann Problem for Non-conservative Hyperbolic Systems

A new comment on the computation of non-conservative products using Roe-type path conservative schemes

We are interested in the numerical approximation of the discontinuous solutions of non conservative hyperbolic systems. We more precisely consider a non conservative formulation of the usual gas dynamics equations and show how to slightly modify the so-called Roe-type path-conservative schemes to properly capture the underlying shock discontinuities. Numerical evidences are proposed. The presen...

Comparison of two Conservative Schemes for Hyperbolic Interface Problems

We recall two conservative schemes recently proposed for the numerical solution of hyperbolic interface problems. Then, we compare the two schemes on a piston problem and a shock tube problem.