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arXiv · 1503.03239

Local principle satisfying high order total variation diminishing approximation for non-sonic data extrema

Ritesh Kumar Dubey·Biswarup Biswas·Vikas Gupta
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Abstract

The main contribution of this work is to construct higher than second order accurate total variation diminishing (TVD) schemes which can preserve high accuracy at non-sonic extrema with out induced local oscillations. It is done in the framework of local maximum principle (LMP) and non-conservative formulation. The representative uniformly second order accurate schemes are converted in to their non-conservative form using the ratio of consecutive gradient. These resulting schemes are analyzed for their non-linear LMP/TVD stability bounds using the local maximum principle. Based on the bounds, second order accurate hybrid numerical schemes are constructed using a shock detector. Numerical results are presented to show that such hybrid schemes yield TVD approximation with second or higher order convergence rate for smooth solution with extrema.

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Ritesh Kumar Dubey, Biswarup Biswas, Vikas Gupta. 2015-03-11. Local principle satisfying high order total variation diminishing approximation for non-sonic data extrema. https://arxiv.org/abs/1503.03239

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