Overview
FrançaisABSTRACT
The finite volume method is used to solve the NavierStokes equations. The paper is divided into two distinct parts. The first part presents the discretization method for solving the diffusion and convectiondiffusion problems 1D, 2D and 3D on structured and unstructured grids as well as the semidiscretization in time to solve the heat equation to then lead to explicit and implicit schemes. The second part presents the solution of the target equations by the finite volume method. In fact, this is equivalent to solve diffusion equations coupled to convectiondiffusion equations; using the results of the first part, various algorithms are presented and compared between them.
Read this article from a comprehensive knowledge base, updated and supplemented with articles reviewed by scientific committees.
Read the articleAUTHOR

Pierre SPITERI: Professor Emeritus  University of Toulouse, INP – ENSEEIHT  IRIT, Toulouse, France
INTRODUCTION
In this series of articles devoted to the numerical solution of NavierStokes equations, we present several methods of resolution based on different types of discretization methods for partial differential equations. We have already presented :
on the one hand, the finitedifference method, where derivatives are replaced by differential quotients
; this method corresponds to the expression of a balance of the quantities represented by the physical model at each point of the mesh;[AF 1 404] on the other hand, the finite element method
where, after having given an equivalent formulation of the problem via Green's formula in an appropriate space of test functions, which corresponds roughly to an extension of the generalized integration by parts formula (or, more generally, to the use of derivation in the sense of distributions) and leads to the application of the principle of virtual work, the solution is decomposed into a finite basis that is well adapted numerically; this is equivalent to projecting the exact solution of an infinitedimensional space onto a finitedimensional space[AF 1 407] [AF 503] [AF 504] ; this finiteelement method has the advantage of being able to solve the NavierStokes equation on unstructured meshes, and is also well suited when the domain Ω is of any shape with a curved boundary ∂Ω ;[AF 505] there are other discretization methods, such as the variational finitedifference...
Exclusive to subscribers. 97% yet to be discovered!
You do not have access to this resource.
Click here to request your free trial access!
Already subscribed? Log in!
The Ultimate Scientific and Technical Reference
KEYWORDS
behavior of a fluid  formulation velocitypressure  staggered grids  structured grids  heat equation
This article is included in
Mathematics
This offer includes:
Knowledge Base
Updated and enriched with articles validated by our scientific committees
Services
A set of exclusive tools to complement the resources
Practical Path
Operational and didactic, to guarantee the acquisition of transversal skills
Doc & Quiz
Interactive articles with quizzes, for constructive reading
Numerical solution of the NavierStokes equations using the finite volume method
Bibliography
Exclusive to subscribers. 97% yet to be discovered!
You do not have access to this resource.
Click here to request your free trial access!
Already subscribed? Log in!
The Ultimate Scientific and Technical Reference