Microfluidics: Modeling, Mechanics and Mathematics

Chapter 34

Numerical Solutions to Three-Dimensional Flow Problems

34.1 Introduction

In section 33 we have studied numerous two-dimensional parallel flows where we only had to consider one velocity component, i.e., v_x. All of these flow problems were based on very simple geometries in the form of straight channels without changes in diameter, width, or height. Obviously, not all fluid mechanics problems are so simple and cases where only one velocity component must be considered are rare.

In this section, we will extend the numerical solvers we have written so far such that we are able to solve three–dimensional fluid mechanical problems. As we will see, the changes we need to implement are not significant, and we have studied all the mathematics ...