A High Order Accuracy Corrected Hermite-ENO Scheme

doi:10.19596/j.cnki.1001-246x.7819

Abstract

Abstract: A kind of sixth order accuracy ENO scheme with 3 units based on corrected Hermite polynomials, named CHENO scheme, is proposed for one-dimensional hyperbolic conservation laws. Space discrete of CHENO scheme is based on finite volume formulation. In space layer, it chooses templates with Newton difference method in ENO scheme. Reconstruction of function and its first derivative in the half node based on Hermite interpolation are corrected to improve accuracy to sixth order by Taylor expansion. We proposed a discontinuous recognition method to control oscillation in discontinuous points. In time layer, both function and its first derivative of CHENO scheme are evolved in time by using 3rd TVD Runge-Kutta schemes. Major advantage of CHENO scheme is higher order accuracy and compactness. Numerical experiments on one-dimensional hyperbolic conservation laws validated feasibility of CHENO scheme.

Key words: hyperbolic conservation laws, ENO and WENO schemes, corrected Hermite interpolation, discontinuous recognition method

CLC Number:

O241.82

GUO Zitao, FENG Renzhong. A High Order Accuracy Corrected Hermite-ENO Scheme[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 36(2): 141-152.

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