Maria Adela Puscas, Pierre-Emmanuel Angeli, Nathalie Nouaime, Erell Jamelot
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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.
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.