{"title":"用于求解圆形几何体上不可压缩流动的新型无变换非均匀高阶紧凑有限差分方案","authors":"Swapan K. Pandit, Pradip Das","doi":"10.1016/j.euromechflu.2024.10.004","DOIUrl":null,"url":null,"abstract":"<div><div>This paper presents a newly developed higher order compact scheme that is designed on a polar grid by using an implicit form of first order derivatives on nonuniform grids. These derivatives are formulated compactly and implicitly with a relationship of the coefficients in terms of the unknown variables. The proposed scheme is free from transformation technique and third order accurate in space. The objective is to solve Stokes equations and Navier–Stokes equations on curvilinear grids using the polar nature of the coordinate system. Our newly developed scheme is used to solve several problems namely, a problem having an analytical solution, Stokes flow with different orientations of the lids for the half filled annular and wedge cavity, the lid driven polar cavity flow and flow past an impulsively started circular cylinder. Our newly developed scheme is used to analyze the flow structures for the flow governed by different physical control parameters: the cavity radius ratio, the cavity angle and the ratio of the upper and lower lid speeds with rotating coaxial cylinders and Reynolds number for the impulsively started circular cylinder. The Stokes equations and the Navier–Stokes equations are efficiently solved with Dirichlet as well as Neumann boundary conditions. The efficacy and robustness of our proposed scheme are shown through its applicability in all the complex fluid flow problems.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"109 ","pages":"Pages 225-242"},"PeriodicalIF":2.5000,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A novel transformation free nonuniform higher order compact finite difference scheme for solving incompressible flows on circular geometries\",\"authors\":\"Swapan K. Pandit, Pradip Das\",\"doi\":\"10.1016/j.euromechflu.2024.10.004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This paper presents a newly developed higher order compact scheme that is designed on a polar grid by using an implicit form of first order derivatives on nonuniform grids. These derivatives are formulated compactly and implicitly with a relationship of the coefficients in terms of the unknown variables. The proposed scheme is free from transformation technique and third order accurate in space. The objective is to solve Stokes equations and Navier–Stokes equations on curvilinear grids using the polar nature of the coordinate system. Our newly developed scheme is used to solve several problems namely, a problem having an analytical solution, Stokes flow with different orientations of the lids for the half filled annular and wedge cavity, the lid driven polar cavity flow and flow past an impulsively started circular cylinder. Our newly developed scheme is used to analyze the flow structures for the flow governed by different physical control parameters: the cavity radius ratio, the cavity angle and the ratio of the upper and lower lid speeds with rotating coaxial cylinders and Reynolds number for the impulsively started circular cylinder. The Stokes equations and the Navier–Stokes equations are efficiently solved with Dirichlet as well as Neumann boundary conditions. The efficacy and robustness of our proposed scheme are shown through its applicability in all the complex fluid flow problems.</div></div>\",\"PeriodicalId\":11985,\"journal\":{\"name\":\"European Journal of Mechanics B-fluids\",\"volume\":\"109 \",\"pages\":\"Pages 225-242\"},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2024-10-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Mechanics B-fluids\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0997754624001420\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Mechanics B-fluids","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0997754624001420","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
A novel transformation free nonuniform higher order compact finite difference scheme for solving incompressible flows on circular geometries
This paper presents a newly developed higher order compact scheme that is designed on a polar grid by using an implicit form of first order derivatives on nonuniform grids. These derivatives are formulated compactly and implicitly with a relationship of the coefficients in terms of the unknown variables. The proposed scheme is free from transformation technique and third order accurate in space. The objective is to solve Stokes equations and Navier–Stokes equations on curvilinear grids using the polar nature of the coordinate system. Our newly developed scheme is used to solve several problems namely, a problem having an analytical solution, Stokes flow with different orientations of the lids for the half filled annular and wedge cavity, the lid driven polar cavity flow and flow past an impulsively started circular cylinder. Our newly developed scheme is used to analyze the flow structures for the flow governed by different physical control parameters: the cavity radius ratio, the cavity angle and the ratio of the upper and lower lid speeds with rotating coaxial cylinders and Reynolds number for the impulsively started circular cylinder. The Stokes equations and the Navier–Stokes equations are efficiently solved with Dirichlet as well as Neumann boundary conditions. The efficacy and robustness of our proposed scheme are shown through its applicability in all the complex fluid flow problems.
期刊介绍:
The European Journal of Mechanics - B/Fluids publishes papers in all fields of fluid mechanics. Although investigations in well-established areas are within the scope of the journal, recent developments and innovative ideas are particularly welcome. Theoretical, computational and experimental papers are equally welcome. Mathematical methods, be they deterministic or stochastic, analytical or numerical, will be accepted provided they serve to clarify some identifiable problems in fluid mechanics, and provided the significance of results is explained. Similarly, experimental papers must add physical insight in to the understanding of fluid mechanics.