Comparative Analysis of Obstacle Approximation Strategies for the Steady Incompressible Navier–Stokes Equations

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-02-03 DOI:10.1007/s00245-024-10105-w

Piotr Krzyżanowski, Sadokat Malikova, Piotr Bogusław Mucha, Tomasz Piasecki

引用次数: 0

Abstract

This paper aims to compare and evaluate various obstacle approximation techniques employed in the context of the steady incompressible Navier–Stokes equations. Specifically, we investigate the effectiveness of a standard volume penalization approximation and an approximation method utilizing high viscosity inside the obstacle region, as well as their composition. Analytical results concerning the convergence rate of these approaches are provided, and extensive numerical experiments are conducted to validate their performance.

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稳定不可压缩纳维-斯托克斯方程的障碍逼近策略比较分析

本文旨在比较和评估在稳定不可压缩纳维-斯托克斯方程中采用的各种障碍近似技术。具体来说，我们研究了标准体积惩罚近似和利用障碍区域内高粘性的近似方法的有效性，以及它们的组成。我们提供了有关这些方法收敛速度的分析结果，并进行了大量数值实验来验证它们的性能。

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 Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.