An adaptive TVD limiter
type: Item
instance of: scholarly article
title: An adaptive TVD limiter
zbMATH Open document ID: 0841.65077
author: Uon Jan Payne
author: Yih-Nen Jeng
published in: Journal of Computational Physics
publication date: 1996-07-14T00:00:00Z
review text: When solving nonlinear hyperbolic conservation laws numerically one introduces limiters to enforce that the schemes are total variational diminishing, TVD, and of at least second order in regions of smooth solutions. In this work adaptive TVD limiters are studied which are based on a limiter approximating the upper boundary of the TVD range and that of the third-order upwind TVD scheme. The adaptive limiter switches to a compressive one near a discontinuity, to the third-order TVD scheme's limiter in smooth regions, and to a weighted averaged scheme in the transition region between smooth and high gradient solutions. The analysis is mainly done on a scalar one-dimensional conservation law. Following \textit{A. Harten}'s idea of a subcell resolution scheme [J. Comput. Phys. 83, No. 1, 148-184 (1989; Zbl 0696.65078)] the authors propose new rules for switching the limiters such that the discontinuities are better captured. Numerical examples show that the proposed scheme works very well for one-dimensional scalar equations but become less effective in one- and two-dimensional Euler equations of gas dynamics.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 758629
zbMATH Keywords: numerical examples
zbMATH Keywords: switching of limiter
zbMATH Keywords: compressive limiter
zbMATH Keywords: diffusive limiter
zbMATH Keywords: nonlinear hyperbolic conservation laws
zbMATH Keywords: total variational diminishing
zbMATH Keywords: adaptive TVD limiters
zbMATH Keywords: third-order upwind TVD scheme
zbMATH Keywords: discontinuity
zbMATH Keywords: Euler equations of gas dynamics
reviewed by: Rolf Jeltsch
MaRDI profile type: Publication
full work available at URL: jcph.1995.1095
OpenAlex ID: W2030463848
DOI: 10.1006/JCPH.1995.1095
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description: scientific article; zbMATH DE number 758629