Finite Volume Methods

Abstract : This chapter focuses on finite volume methods. The finite volume method is a discretization method that is well suited for the numerical simulation of various types (for instance, elliptic, parabolic, or hyperbolic) of conservation laws; it has been extensively used in several engineering fields, such as fluid mechanics, heat and mass transfer, or petroleum engineering. Some of the important features of the finite volume method are similar to those of the finite element method: it may be used on arbitrary geometries, using structured or unstructured meshes, and it leads to robust schemes. The finite volume method is locally conservative because it is based on a “balance" approach: a local balance is written on each discretization cell that is often called “control volume;” by the divergence formula, an integral formulation of the fluxes over the boundary of the control volume is then obtained. The fluxes on the boundary are discretized with respect to the discrete unknowns.
Document type :
Book sections
Complete list of metadatas

Cited literature [164 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02100732
Contributor : Raphaele Herbin <>
Submitted on : Monday, August 12, 2019 - 1:52:18 PM
Last modification on : Tuesday, August 13, 2019 - 1:15:47 AM

File

bookevol.pdf
Files produced by the author(s)

Identifiers

Citation

Robert Eymard, Thierry Gallouët, Raphaèle Herbin. Finite Volume Methods. J. L. Lions; Philippe Ciarlet. Solution of Equation in ℝn (Part 3), Techniques of Scientific Computing (Part 3), 7, Elsevier, pp.713-1020, 2000, Handbook of Numerical Analysis, 9780444503503. ⟨10.1016/S1570-8659(00)07005-8⟩. ⟨hal-02100732v2⟩

Share

Metrics

Record views

50

Files downloads

24