Convergence of a Finite Difference Scheme for a Flame/Smoldering-Front Evolution Equation and Its Application to Wavenumber Selection-Reference-Cited by-同舟云学术

Convergence of a Finite Difference Scheme for a Flame/Smoldering-Front Evolution Equation and Its Application to Wavenumber Selection

Published:2022-11-11 Issue:2 Volume:23 Page:545-563
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Kobayashi Shunsuke¹^ORCID,Yazaki Shigetoshi²

Affiliation:

1. Faculty of Engineering , University of Miyazaki , 1-1 Gakuen Kibanadainishi , Miyazaki 889-2192 ; and RIKEN iTHEMS, 2-1 Hirosawa, Wako-shi, Saitama 351-0198 , Japan

2. Department of Mathematics , School of Science and Technology , Meiji University , 1-1-1 Higashi-Mita, Tama-ku , Kawasaki-shi , Kanagawa 214-8571 , Japan

Abstract

Abstract In this paper, we propose a finite difference scheme combined with the Crank–Nicolson-type discretization of the Kuramoto–Sivashinsky equation defined on an expanding circle, and show the existence, uniqueness, and second-order error estimate of the scheme. The equation is obtained as a perturbed graph equation from the circle solution to an interfacial curvature-dependent equation. The graph representation can provide guidelines for understanding the wavenumber selection of solutions to the interfacial equation. Indeed, the linearized stability analysis shows a relation between the parameters and the wavenumbers. Our proposed scheme can realize the relation with second-order accuracy.

Funder

Japan Society for the Promotion of Science

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/cmam-2022-0046/pdf

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