Corrected Nonconservative Schemes

Abstract

Derivatives of discontinuities being Dirac singularities, it is usually not possible to multiply them by discontinuous functions. However in the context of conservation laws we have shown in a recent paper that it can be done. We shall make use of this new framework to revisit some upwind methods, mostly characteristic schemes, and show that they can be corrected to be conservative and to work on difficult problems such as Euler’s equations for fluids. Numerous numerical results are given.

Keywords

Upwinding, Non-conservative / Finite volume method / Compressible Euler / 35A25 / 65N99

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