Introduction to Computational Fluid Dynamics

2

Finite Difference and Finite Volume Discretisations

2.1 INTRODUCTION

Partial differential equations occur in almost every branch of science and engineering. Exact analytical solutions may be obtained only for very few simple cases among them. In most cases one has to adopt some numerical method to solve them. Among the numerical methods, the finite difference, finite volume and finite element methods are the most popular. They are applicable to linear as well as nonlinear partial differential equations and the methods can produce results of arbitrarily high accuracy, by refining the grid sizes. In this sense the results delivered are said to be numerically exact. Further, the methods are applicable to higher dimensions also.

Computational ...