双物种凯勒-西格尔模型的高效数值方案及其三维爆破现象研究

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Acta Applicandae Mathematicae Pub Date : 2024-04-10 DOI:10.1007/s10440-024-00647-0

Xueling Huang, Jie Shen

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引用次数: 0

摘要

本文考虑对一个双物种 Keller-Segel 模型进行数值逼近和模拟。该模型具有能量耗散规律、质量守恒和两个物种种群密度的约束或正向保留。我们构建了一类基于广义标量辅助变量松弛的高效数值方案，无条件地保留了离散模型的基本特性。我们进行了一系列数值测试来验证这些方案的特性，并研究了抛物线-椭圆形和抛物线-抛物线形式的三维领域模型的炸毁现象。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Efficient Numerical Schemes for a Two-Species Keller-Segel Model and Investigation of Its Blowup Phenomena in 3D

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Efficient Numerical Schemes for a Two-Species Keller-Segel Model and Investigation of Its Blowup Phenomena in 3D

We consider in this paper numerical approximation and simulation of a two-species Keller-Segel model. The model enjoys an energy dissipation law, mass conservation and bound or positivity preserving for the population density of two species. We construct a class of very efficient numerical schemes based on the generalized scalar auxiliary variable with relaxation which preserve unconditionally the essential properties of the model at the discrete level. We conduct a sequence of numerical tests to validate the properties of these schemes, and to study the blow-up phenomena of the model in a three-dimensional domain in parabolic-elliptic form and parabolic-parabolic form.

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来源期刊

Acta Applicandae Mathematicae 数学-应用数学

CiteScore

2.80

自引率

6.20%

发文量

审稿时长

16.2 months

期刊介绍： Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods. Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.