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Modified third and fifth order WENO schemes for inviscid compressible flows

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Abstract

The weighted essentially non-oscillatory schemes are well known for their shock captu- ring abilities due to their properties resulting from weighted combination reconstruction taken such that less weight is given to less smooth stencils. In this article, contrary to this property, the analysis has been done by adding extra weight to less smooth substencils of the domain that in turn adds the useful information which plays a vital role in improving resolution of the solution mainly at discontinuities or sharp gradients. The theoretical aspects have been supported with scalar, one-dimensional as well as two-dimensional test problems for third- and fifth-order schemes. Numerical solutions obtained by the proposed third-order scheme are comparable to the numerical solutions obtained using some of the native fifth-order WENO schemes.

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  1. Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, India

    Naga Raju Gande & Ashlesha A. Bhise

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  1. Naga Raju Gande
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  2. Ashlesha A. Bhise
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Correspondence to Naga Raju Gande.

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Gande, N.R., Bhise, A.A. Modified third and fifth order WENO schemes for inviscid compressible flows. Numer Algor 88, 249–279 (2021). https://doi.org/10.1007/s11075-020-01039-9

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