Additive Semi-Implicit Runge–Kutta Methods for Computing High-Speed Nonequilibrium Reactive Flows

✍ Scribed by Xiaolin Zhong

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 411 KB
• Volume: 128
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.0193

✦ Synopsis

fine-grid spacing is used in the direction normal to the wall.

Finite difference approximation to the viscous equations

This paper is concerned with time-stepping numerical methods for computing stiff semi-discrete systems of ordinary differential with these small-size grids lead to stiff systems of ordinary equations for transient hypersonic flows with thermo-chemical nondifferential equations. The source terms are stiff because equilibrium. The stiffness of the equations is mainly caused by the the chemical and thermal nonequilibrium processes have a viscous flux terms across the boundary layers and by the source wide range of time scales, some of which are much smaller terms modeling finite-rate thermo-chemical processes. Implicit than the transient flow ones. As a result, if explicit methods methods are needed to treat the stiff terms while more efficient explicit methods can still be used for the nonstiff terms in the equa-are used to integrate the stiff governing equations, the comtions. This paper studies three different semi-implicit Runge-Kutta putations will become very inefficient because the time-step methods for additively split differential equations in the form of sizes dictated by the stability requirements are much smaller

, where f is treated by explicit Runge-Kutta methods than those required by the accuracy considerations.

and g is simultaneously treated by three implicit Runge-Kutta meth-In order to remove the stability restriction on the explicit ods: a diagonally implicit Runge-Kutta method and two linearized implicit Runge-Kutta methods. The coefficients of up to third-order methods, implicit methods need to be used. For computing accurate additive semi-implicit Runge-Kutta methods have been multidimensional reactive flow, global implicit methods derived such that the methods are both high-order accurate and are seldom used because it takes a prohibitively large strongly A-stable for the implicit terms. The results of two numerical amount of computer time and large memory to convert tests on the stability and accuracy properties of these methods are full implicit equations. Practical implicit methods for multialso presented in the paper.