Pressure-based adaption indicator for compressible euler equations

We consider the Euler equations of gas dynamics and develop a new adaption indicator, which is based on the weak local residual measured for the nonconservative pressure variable. We demonstrate that the proposed indicator is capable of automatically detecting discontinuities and distinguishing betw...

Full description

Saved in:
Bibliographic Details
Published in:Numerical methods for partial differential equations 2015-11, Vol.31 (6), p.1844-1874
Main Authors: Dewar, Jeremy, Kurganov, Alexander, Leopold, Maren
Format: Article
Language:English
Subjects:
adaption indicator
Algorithms
Compressibility
Contact
Discontinuity
Euler equations
Euler equations of gas dynamics
Eulers equations
finite-volume methods
Indicators
Mathematical models
Robustness
scheme adaption algorithm
Two dimensional
weak local residual
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider the Euler equations of gas dynamics and develop a new adaption indicator, which is based on the weak local residual measured for the nonconservative pressure variable. We demonstrate that the proposed indicator is capable of automatically detecting discontinuities and distinguishing between the shock and contact waves when they are isolated from each other. We then use the developed indicator to design a scheme adaption algorithm, according to which nonlinear limiters are used only in the vicinity of shocks. The new adaption algorithm is realized using a second‐order limited and a high‐order nonlimited central‐upwind scheme. We demonstrate robustness and high resolution of the designed method on a number of one‐ and two‐dimensional numerical examples. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1844–1874, 2015
ISSN:0749-159X
1098-2426
DOI:10.1002/num.21970