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A Slope Constrained 4th Order Multi-Moment Finite Volume Method with WENO Limiter

Part of: Shock waves and blast waves Partial differential equations, initial value and time-dependent initial-boundary value problems Compressible fluids and gas dynamics, general

Published online by Cambridge University Press:  15 October 2015

Ziyao Sun ,
Honghui Teng  and
Feng Xiao
Ziyao Sun
Affiliation:
Department of Energy Sciences, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama, 226-8502, Japan
Honghui Teng
Affiliation:
State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China
Feng Xiao*
Affiliation:
Department of Energy Sciences, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama, 226-8502, Japan
*
*Corresponding author. Email addresses: sun.z.ab@m.titech.ac.jp (Z. Sun), hhteng@imech.ac.cn (H. Teng), xiao@es.titech.ac.jp (F. Xiao)
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Abstract

This paper presents a new and better suited formulation to implement the limiting projection to high-order schemes that make use of high-order local reconstructions for hyperbolic conservation laws. The scheme, so-called MCV-WENO4 (multi-moment Constrained finite Volume with WENO limiter of 4th order) method, is an extension of the MCV method of Ii & Xiao (2009) by adding the 1st order derivative (gradient or slope) at the cell center as an additional constraint for the cell-wise local reconstruction. The gradient is computed from a limiting projection using the WENO (weighted essentially non-oscillatory) reconstruction that is built from the nodal values at 5 solution points within 3 neighboring cells. Different from other existing methods where only the cell-average value is used in the WENO reconstruction, the present method takes account of the solution structure within each mesh cell, and thus minimizes the stencil for reconstruction. The resulting scheme has 4th-order accuracy and is of significant advantage in algorithmic simplicity and computational efficiency. Numerical results of one and two dimensional benchmark tests for scalar and Euler conservation laws are shown to verify the accuracy and oscillation-less property of the scheme.

Keywords

Multi-moment finite volume methodWENOflux reconstructioncompressible flowconservative methodoscillation-suppressing

MSC classification

Secondary: 65M08: Finite volume methods 65M70: Spectral, collocation and related methods 76L05: Shock waves and blast waves 76N15: Gas dynamics, general
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 4 , October 2015 , pp. 901 - 930
Copyright
Copyright © Global-Science Press 2015 

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