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arXiv · 1312.4481

Conservative and non-conservative methods based on hermite weighted essentially-non-oscillatory reconstruction for Vlasov equations

Chang Yang·Francis Filbet
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Abstract

We introduce a WENO reconstruction based on Hermite interpolation both for semi-Lagrangian and finite difference methods. This WENO reconstruction technique allows to control spurious oscillations. We develop third and fifth order methods and apply them to non-conservative semi-Lagrangian schemes and conservative finite difference methods. Our numerical results will be compared to the usual semi-Lagrangian method with cubic spline reconstruction and the classical fifth order WENO finite difference scheme. These reconstructions are observed to be less dissipative than the usual weighted essentially non- oscillatory procedure. We apply these methods to transport equations in the context of plasma physics and the numerical simulation of turbulence phenomena.

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Chang Yang, Francis Filbet. 2013-12-16. Conservative and non-conservative methods based on hermite weighted essentially-non-oscillatory reconstruction for Vlasov equations. https://doi.org/10.1016/j.jcp.2014.08.048

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