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research-article

Hyperbolic Runge-Kutta Method using Genetic Algorithm

[+] Author and Article Information
Arun Govind Neelan

Department of Aerospace Engineering, Indian Institute of Space Science and Technology - Thiruvananthapuram, Kerala-695547, India
arungovindneelan@gmail.com

Manoj Nair

Department of Aerospace Engineering, Indian Institute of Space Science and Technology - Thiruvananthapuram, Kerala-695547, India
manojtnair.iist@gmail.com

1Corresponding author.

ASME doi:10.1115/1.4040708 History: Received November 29, 2017; Revised June 20, 2018

Abstract

A family of Runge-Kutta (RK) methods designed for better stability is proposed. Authors have optimized the stability of RK method by increasing the stability region by trading some of the higher order terms in the Taylor series. For flow involving shocks, compromising a few higher order terms will not affect convergence rate, that is justified with an example. Though this kind of analysis began about three decades ago, most of the papers dealt with classical optimization and ended-up in relatively non-optimal values. Here, authors have overcome that by using Evolutionary Algorithm(EA) and the result is refined using Multi-Section Method(MSM). The schemes designed based on this procedure have better stability than the classical RK methods, strong stability RK methods(SSPRK) and low dispersive and dissipative RK methods(LDDRK) of the same number of stages. Authors have tested the schemes on a variety of test cases and found some significant improvement.

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