{"title":"A high-order pure streamfunction method in general curvilinear coordinates for unsteady incompressible viscous flow with complex geometry","authors":"Bo Wang, Peixiang Yu, Xin Tong, Hua Ouyang","doi":"10.1002/fld.5331","DOIUrl":null,"url":null,"abstract":"<p>In this paper, a high-order compact finite difference method in general curvilinear coordinates is proposed for solving unsteady incompressible Navier-Stokes equations. By constructing the fourth-order spatial discretization schemes for all partial derivative terms of the pure streamfunction formulation in general curvilinear coordinates, especially for the fourth-order mixed derivative terms, and applying a Crank-Nicolson scheme for the second-order temporal discretization, we extend the unsteady high-order pure streamfunction algorithm to flow problems with more general non-conformal grids. Furthermore, the stability of the newly proposed method for the linear model is validated by von-Neumann linear stability analysis. Five numerical experiments are conducted to verify the accuracy and robustness of the proposed method. The results show that our method not only effectively solves problems with non-conformal grids, but also allows grid generation and local refinement using commercial software. The solutions are in good agreement with the established numerical and experimental results.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal for Numerical Methods in Fluids","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/fld.5331","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, a high-order compact finite difference method in general curvilinear coordinates is proposed for solving unsteady incompressible Navier-Stokes equations. By constructing the fourth-order spatial discretization schemes for all partial derivative terms of the pure streamfunction formulation in general curvilinear coordinates, especially for the fourth-order mixed derivative terms, and applying a Crank-Nicolson scheme for the second-order temporal discretization, we extend the unsteady high-order pure streamfunction algorithm to flow problems with more general non-conformal grids. Furthermore, the stability of the newly proposed method for the linear model is validated by von-Neumann linear stability analysis. Five numerical experiments are conducted to verify the accuracy and robustness of the proposed method. The results show that our method not only effectively solves problems with non-conformal grids, but also allows grid generation and local refinement using commercial software. The solutions are in good agreement with the established numerical and experimental results.
期刊介绍:
The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction.
Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review.
The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.