有限元-体积空间离散化方法的描述及收敛阶分析

IF 1.8 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Maria Adela Puscas, Pierre-Emmanuel Angeli, Nathalie Nouaime, Erell Jamelot
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引用次数: 0

摘要

本文综述了TrioCFD代码中实现的四面体网格有限元-体积空间离散化方法。TrioCFD是一款计算流体动力学软件,专为模拟湍流和传热而设计,主要用于核工程应用。它的多功能性也延伸到广泛的工程应用。本文介绍了有限元-体积离散的基本原理,并对其性质和收敛阶进行了分析。时间格式可以是显式或半隐式的,速度和压力根据投影校正格式更新。离散化保证了局部质量守恒,速度二阶收敛,压力一阶收敛。此外,当源项为梯度项时,该方法在二维上实现了超收敛。数值方法的准确性和收敛速度在各种二维和三维测试用例中进行了严格的评估,包括稳定Stokes和具有制造解的Navier-Stokes问题。本文还讨论了经典的盖驱动空腔流动,并将本文数值方法的解与参考文献的结果进行了比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Description and Convergence Order Analysis of the Finite Element-Volume Spatial Discretization Method

Description and Convergence Order Analysis of the Finite Element-Volume Spatial Discretization Method

This article reviews the Finite Element-Volume spatial discretization method on tetrahedral meshes implemented in the TrioCFD code. TrioCFD is a computational fluid dynamics software specifically designed for simulating turbulent flows and heat transfer, with a primary focus on nuclear engineering applications. Its versatility also extends to a wide range of engineering applications. This article presents the principles of Finite Element-Volume discretization and conducts an analysis of its properties and convergence orders. The time scheme can be explicit or semi-implicit, and the velocity and pressure are updated based on a projection-correction scheme. The discretization ensures local mass conservation, second-order convergence for velocity, and first-order convergence for pressure. Moreover, a super-convergence is achieved in two-dimension when the source term is a gradient. The accuracy and convergence rate of the numerical method is rigorously assessed in a variety of two- and three-dimensional test cases, including steady Stokes and Navier–Stokes problems with manufactured solutions. The classical lid-driven cavity flow is also addressed, and the results of comparisons between the solutions from the present numerical method and the results of reference literature are provided.

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来源期刊
International Journal for Numerical Methods in Fluids
International Journal for Numerical Methods in Fluids 物理-计算机:跨学科应用
CiteScore
3.70
自引率
5.60%
发文量
111
审稿时长
8 months
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.
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