Microfluidics: Modeling, Mechanics and Mathematics

Chapter 31

Finite Volume Method

31.1 Introduction

The next method we will discuss is the finite volume method (FVM). Just as with the Galerkin method, FVM can be used on all differential equations, which can be written in the divergence form. This effectively writes the equation using divergence operators (see section 7.1.3.3). The equation is then integrated over the volume. We can then apply Gauss’s theorem (see section 7.2.1) converting the volume integral over the divergence into a surface integral across the boundaries. The integral is therefore turned from integrating the differential of the dependent variable inside of the cells into surface integrals of the fluxes of the dependent variable across the boundary of the cells. These integrals ...