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Cell-Centered Finite Volume Methods

Part of the Atmosphere, Earth, Ocean & Space book series (AEONS)

Abstract

This chapter is devoted to the description of finite volume method (FVM). FVM is a discretization technique for partial differential equations, especially those that arise from physical conservation laws. FVM uses a volume integral formulation of the problem with a finite partitioning set of volumes to discretize the equations. Currently, FVM is a common practice for discretizing computational fluid/MHD dynamics equations. Here we devote our attention to the cell-centered FVM in three-dimensional computational domain. We begin with a general introduction to the first order finite volume methods, followed by a description of high-resolution formulations for conservative laws. It is mentioned that all the formulations are aimed to be applicable at least to the hexahedral cell, particularly quadrilaterally-faced hexahedron (cuboid) with 6 faces, 12 edges, and 8 vertices.

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Feng, X. (2020). Cell-Centered Finite Volume Methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere. Atmosphere, Earth, Ocean & Space. Springer, Singapore. https://doi.org/10.1007/978-981-13-9081-4_2

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