An optimized compact reconstruction weighted essentially non‐oscillatory scheme for advection problems. Issue 3 (12th December 2020)

• Record Type: Journal Article
• Authors: Liu, Bijin; Yu, Ching‐Hao; An, Ruidong
• Is Part Of: Numerical methods for partial differential equations. Volume 37:Issue 3(2021)
• Page Start: 2317
• Page End: 2356
• Publication Date: 2020-12-12
• Subjects: compact stencils -- dissipation errors -- Fourier analysis -- high‐resolution -- non‐oscillation; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22716
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: 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.