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Title: Additive semi-implicit Runge-Kutta methods for computing high-speed nonequilibrium reactive flows

Abstract

This paper is concerned with time-stepping numerical methods for computing stiff semi-discrete systems of ordinary differential equations for transient hypersonic flows with thermo-chemical non-equilibrium. The stiffness of the equations is mainly caused by the viscous flux terms across the boundary layers and by the source terms modeling finite-rate thermo-chemical processes. Implicit methods are needed to treat the stiff terms while more efficient explicit methods can still be used for the nonstiff terms in the equations. This paper studies three different semi-implicit Runge-Kutta methods for additively split differential equations in the form of u{prime} = f(u) + g(u), where f is treated by explicit Runge-Kutta methods and g is simultaneously treated by three implicit Runge-Kutta methods: a diagonally implicit Runge-Kutta method and two linearized implicit Runge-Kutta methods. The coefficients of up to third-order accurate additive semi-implicit Runge-Kutta methods have been derived such that the methods are both high-order accurate and strongly A-stable for the implicit terms. The results of two numerical tests on the stability and accuracy properties of these methods are also presented in the paper. 26 refs., 10 figs., 2 tabs.

Authors:
 [1]
  1. Univ. of California, Los Angeles, CA (United States)
Publication Date:
OSTI Identifier:
508264
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 128; Journal Issue: 1; Other Information: PBD: 1 Oct 1996
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING NOT INCLUDED IN OTHER CATEGORIES; 66 PHYSICS; 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; HYPERSONIC FLOW; DIFFERENTIAL EQUATIONS; RUNGE-KUTTA METHOD; CHEMICAL REACTIONS; BOUNDARY LAYERS

Citation Formats

Zhong, Xiaolin. Additive semi-implicit Runge-Kutta methods for computing high-speed nonequilibrium reactive flows. United States: N. p., 1996. Web. doi:10.1006/jcph.1996.0193.
Zhong, Xiaolin. Additive semi-implicit Runge-Kutta methods for computing high-speed nonequilibrium reactive flows. United States. https://doi.org/10.1006/jcph.1996.0193
Zhong, Xiaolin. Tue . "Additive semi-implicit Runge-Kutta methods for computing high-speed nonequilibrium reactive flows". United States. https://doi.org/10.1006/jcph.1996.0193.
@article{osti_508264,
title = {Additive semi-implicit Runge-Kutta methods for computing high-speed nonequilibrium reactive flows},
author = {Zhong, Xiaolin},
abstractNote = {This paper is concerned with time-stepping numerical methods for computing stiff semi-discrete systems of ordinary differential equations for transient hypersonic flows with thermo-chemical non-equilibrium. The stiffness of the equations is mainly caused by the viscous flux terms across the boundary layers and by the source terms modeling finite-rate thermo-chemical processes. Implicit methods are needed to treat the stiff terms while more efficient explicit methods can still be used for the nonstiff terms in the equations. This paper studies three different semi-implicit Runge-Kutta methods for additively split differential equations in the form of u{prime} = f(u) + g(u), where f is treated by explicit Runge-Kutta methods and g is simultaneously treated by three implicit Runge-Kutta methods: a diagonally implicit Runge-Kutta method and two linearized implicit Runge-Kutta methods. The coefficients of up to third-order accurate additive semi-implicit Runge-Kutta methods have been derived such that the methods are both high-order accurate and strongly A-stable for the implicit terms. The results of two numerical tests on the stability and accuracy properties of these methods are also presented in the paper. 26 refs., 10 figs., 2 tabs.},
doi = {10.1006/jcph.1996.0193},
url = {https://www.osti.gov/biblio/508264}, journal = {Journal of Computational Physics},
number = 1,
volume = 128,
place = {United States},
year = {1996},
month = {10}
}