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Finite Volume Method

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Multiphysics in Porous Materials

Abstract

One major difference between the finite difference method (FDM) and the finite volume method (FVM) is that the FVM is based on the integral form of the governing equations instead of the differential form. In the FVM, this discretization is conducted over each control volume, which endows FVM with advantages of mass conservation and unstructured meshes. In this chapter, we will first introduce the integral form of the governing equation and show how to formulate this equation into the form for the discretization in the FVM. Then we will discuss the discretization process using a 2D example by including the boundary and initial conditions. Extensions from 2D to multidimensional problems will be made to allow for structured 3D and even more complicated meshes. In the practice problem section, the problem solved in the FDM chapter will be solved again with the FVM.

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  1. Michigan Technological University, Houghton, MI, USA

    Zhen (Leo) Liu

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  1. Zhen (Leo) Liu
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Liu, Z.(. (2018). Finite Volume Method. In: Multiphysics in Porous Materials. Springer, Cham. https://doi.org/10.1007/978-3-319-93028-2_29

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