{"title":"二维笛卡尔和圆柱坐标可压缩流的高阶任意拉格朗日-欧勒非连续伽勒金方法","authors":"","doi":"10.1016/j.camwa.2024.06.021","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, a high-order direct arbitrary Lagrangian-Eulerian (ALE) discontinuous Galerkin (DG) scheme is developed for compressible fluid flows in two-dimensional (2D) Cartesian and cylindrical coordinates. The scheme in 2D cylindrical coordinates is based on the control volume approach and it can preserve the conservation property for all the conserved variables including mass, momentum and total energy. In this hydrodynamic scheme, a kind of high-order Taylor expansion basis function on the general element is used to construct the interpolation polynomials of the physical variables for the DG discretization. The terms including the material derivatives of the test functions are omitted, which simplifies the scheme significantly. Furthermore, the mesh velocity in the direct ALE framework is obtained by implementing an adaptive mesh movement method with a kind of dimensional-splitting type monitor function. This type of mesh movement method can automatically concentrate the mesh nodes near the regions with large gradients of the variables, which can greatly improve the resolutions of numerical solutions near the specified regions. For removing the numerical oscillations in the simulations, a Hermite Weighted Essential Non-oscillatory (HWENO) reconstruction is employed as a slope limiter. Finally, some test cases are displayed to verify the accuracy and the good performance of our scheme.</p></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A high-order arbitrary Lagrangian-Eulerian discontinuous Galerkin method for compressible flows in two-dimensional Cartesian and cylindrical coordinates\",\"authors\":\"\",\"doi\":\"10.1016/j.camwa.2024.06.021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, a high-order direct arbitrary Lagrangian-Eulerian (ALE) discontinuous Galerkin (DG) scheme is developed for compressible fluid flows in two-dimensional (2D) Cartesian and cylindrical coordinates. The scheme in 2D cylindrical coordinates is based on the control volume approach and it can preserve the conservation property for all the conserved variables including mass, momentum and total energy. In this hydrodynamic scheme, a kind of high-order Taylor expansion basis function on the general element is used to construct the interpolation polynomials of the physical variables for the DG discretization. The terms including the material derivatives of the test functions are omitted, which simplifies the scheme significantly. Furthermore, the mesh velocity in the direct ALE framework is obtained by implementing an adaptive mesh movement method with a kind of dimensional-splitting type monitor function. This type of mesh movement method can automatically concentrate the mesh nodes near the regions with large gradients of the variables, which can greatly improve the resolutions of numerical solutions near the specified regions. For removing the numerical oscillations in the simulations, a Hermite Weighted Essential Non-oscillatory (HWENO) reconstruction is employed as a slope limiter. Finally, some test cases are displayed to verify the accuracy and the good performance of our scheme.</p></div>\",\"PeriodicalId\":55218,\"journal\":{\"name\":\"Computers & Mathematics with Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-07-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computers & Mathematics with Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S089812212400289X\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computers & Mathematics with Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S089812212400289X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
本文针对二维(2D)笛卡尔坐标和圆柱坐标下的可压缩流体流动,开发了一种高阶直接任意拉格朗日-欧勒(ALE)非连续伽勒金(DG)方案。二维圆柱坐标方案以控制体积法为基础,可以保持包括质量、动量和总能量在内的所有守恒变量的守恒特性。在该流体动力学方案中,使用了一种通用元素上的高阶泰勒扩展基函数来构建用于 DG 离散化的物理变量插值多项式。包括测试函数的材料导数在内的项被省略,从而大大简化了方案。此外,直接 ALE 框架中的网格速度是通过使用一种尺寸分割类型的监控函数实施自适应网格移动方法获得的。这种网格移动方法可以自动将网格节点集中在变量梯度较大的区域附近,从而大大提高指定区域附近数值解的分辨率。为了消除模拟中的数值振荡,采用了赫米特加权基本非振荡(HWENO)重构作为斜率限制器。最后,展示了一些测试案例,以验证我们方案的准确性和良好性能。
A high-order arbitrary Lagrangian-Eulerian discontinuous Galerkin method for compressible flows in two-dimensional Cartesian and cylindrical coordinates
In this paper, a high-order direct arbitrary Lagrangian-Eulerian (ALE) discontinuous Galerkin (DG) scheme is developed for compressible fluid flows in two-dimensional (2D) Cartesian and cylindrical coordinates. The scheme in 2D cylindrical coordinates is based on the control volume approach and it can preserve the conservation property for all the conserved variables including mass, momentum and total energy. In this hydrodynamic scheme, a kind of high-order Taylor expansion basis function on the general element is used to construct the interpolation polynomials of the physical variables for the DG discretization. The terms including the material derivatives of the test functions are omitted, which simplifies the scheme significantly. Furthermore, the mesh velocity in the direct ALE framework is obtained by implementing an adaptive mesh movement method with a kind of dimensional-splitting type monitor function. This type of mesh movement method can automatically concentrate the mesh nodes near the regions with large gradients of the variables, which can greatly improve the resolutions of numerical solutions near the specified regions. For removing the numerical oscillations in the simulations, a Hermite Weighted Essential Non-oscillatory (HWENO) reconstruction is employed as a slope limiter. Finally, some test cases are displayed to verify the accuracy and the good performance of our scheme.
期刊介绍:
Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).