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An optimized compact reconstruction weighted essentially non‐oscillatory scheme for advection problems
Author(s) -
Liu Bijin,
Yu ChingHao,
An Ruidong
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22716
Subject(s) - mathematics , dissipation , burgers' equation , classification of discontinuities , convection–diffusion equation , advection , mathematical analysis , oscillation (cell signaling) , flux limiter , heat equation , euler's formula , euler equations , partial differential equation , physics , thermodynamics , genetics , biology
This paper presents an optimized compact reconstruction weighted essentially non‐oscillatory scheme without dissipation errors (OCRWENO‐LD) for solving advection problems. The construction procedure of this optimized scheme without dissipation errors is as follows: (1) We first design a high‐order compact difference scheme with four general weights connecting four low‐order compact stencils. The four general weights are determined by applying the Taylor series expansions. (2) These general weights are optimized to the new weights which are derived from the WENO concept and modified wavenumber approach. (3) No dissipation errors are found for the developed OCRWENO‐LD scheme through Fourier analysis. The proposed high‐resolution scheme demonstrates its capability in exhibiting high‐accuracy in smooth regions and avoiding numerical oscillation near discontinuities when simulating the wave equation, Burgers' equation, one‐dimensional Euler equation, porous medium equation, and convection–diffusion Buckley–Leverett equation.