An optimized algorithm for numerical solution of coupled Burgers equations

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-06-26 DOI:10.1016/j.apnum.2024.06.019

Anurag Kaur , V. Kanwar , Higinio Ramos

引用次数: 0

Abstract

Investigation of the solutions of the coupled viscous Burgers system is crucial for realizing and understanding some physical phenomena in applied sciences. Particularly, Burgers equations are used in the modeling of fluid mechanics and nonlinear acoustics. In the present study, a modified meshless quadrature method based on radial basis functions is used to discretize the partial derivatives in the spatial variable. A technique to find the best value of the shape parameter is introduced. A high-resolution optimized hybrid block method is then used to solve the problem in the temporal variable. To validate the proposed method, several test problems are considered and the simulated results are compared with exact solutions and previous works. Moreover, a sensitivity analysis for parameter c is conducted, and the unconditional stability of the proposed algorithm has been validated.

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耦合布尔格斯方程数值解的优化算法

研究耦合粘性布尔格斯系统的解对于实现和理解应用科学中的某些物理现象至关重要。特别是在流体力学和非线性声学建模中，布尔格斯方程被广泛应用。本研究采用基于径向基函数的修正无网格正交法来离散空间变量中的偏导数。研究还引入了一种寻找形状参数最佳值的技术。然后使用高分辨率优化混合分块法解决时间变量中的问题。为了验证所提出的方法，我们考虑了几个测试问题，并将模拟结果与精确解法和以前的工作进行了比较。此外，还对参数 c 进行了敏感性分析，并验证了所提算法的无条件稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.