Scholarlink

Abstract <p>Often the proceeding of physical and chemical processes (fluid flows in nozzles, channels and shock tubes, external flow around various objects, heat and mass transfer in porous bodies, etc.) has a preferentially spatial direction. Recently 1D models have been proposed for the mathematical description of such processes, but now more detailed 3D&#xa0;models are developed. The modeling complexity increases impressively with the transfer to 3D modeling. The article represents a computational approach based on the artificial extraction “1D terms” in the solution to reduce the amount of computational work in multidimensional modeling. Based on the Dirichlet boundary value problem for Poisson equation in a unit cube, the efficiency of proposed approach associated with solving <i>d</i> = 2.3 auxiliary 1D problems is demonstrated. The article represents results of the convergence analysis of the iterative methods with proposed solution decomposition for the discrete (initial-)boundary value problems. Previously, the efficiency of&#xa0;this approach was demonstrated for the numerical solution of saddle problems (the discrete Navier–Stokes equations).</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Mathematical Modeling of Anisotropic Physical and Chemical Processes

  • 期刊论文

  • 发表日期：

    2025年10月21日

查看全文
  • S. I. Martynenko

摘要

Abstract

Often the proceeding of physical and chemical processes (fluid flows in nozzles, channels and shock tubes, external flow around various objects, heat and mass transfer in porous bodies, etc.) has a preferentially spatial direction. Recently 1D models have been proposed for the mathematical description of such processes, but now more detailed 3D models are developed. The modeling complexity increases impressively with the transfer to 3D modeling. The article represents a computational approach based on the artificial extraction “1D terms” in the solution to reduce the amount of computational work in multidimensional modeling. Based on the Dirichlet boundary value problem for Poisson equation in a unit cube, the efficiency of proposed approach associated with solving d = 2.3 auxiliary 1D problems is demonstrated. The article represents results of the convergence analysis of the iterative methods with proposed solution decomposition for the discrete (initial-)boundary value problems. Previously, the efficiency of this approach was demonstrated for the numerical solution of saddle problems (the discrete Navier–Stokes equations).