A new mapped WENO scheme using order-preserving mapping

TL;DR

This paper introduces an order-preserving mapped WENO scheme that effectively reduces spurious oscillations and maintains high resolution in long-time simulations by ensuring the mapping function preserves the order of nonlinear weights.

Contribution

The paper proposes a novel mapped WENO scheme with order-preserving mapping functions, improving stability and resolution over existing schemes.

Findings

The new scheme prevents spurious oscillations near discontinuities.

It maintains high resolution at long output times.

It outperforms previous mapped WENO schemes in stability and accuracy.

Abstract

Existing mapped WENO schemes can hardly prevent spurious oscillations while preserving high resolutions at long output times. We reveal in this paper the essential reason for such phenomena. It is actually caused by that the mapping function in these schemes can not preserve the order of the nonlinear weights of the stencils. The nonlinear weights may be increased for non-smooth stencils and be decreased for smooth stencils. It is then indicated to require the set of mapping functions to be Order-Preserving in mapped WENO schemes. Therefore, we propose a new mapped WENO scheme with a set of mapping functions to be order-preserving which exhibits a remarkable advantage over the mapped WENO schemes in references. For long output time simulations, the new scheme has the capacity to attain high resolutions and avoid spurious oscillations near discontinuities meanwhile.