Linear Convection-Dominated Problems

Abstract

For most flow problems the motion of the fluid is an important determining factor of the overall flow behaviour. In the equations governing fluid dynamics (Chap. 11) the fluid motion is characterised by the velocity components u, V, W in the x, y, z (Cartesian coordinates) directions. In the one-dimensional x-momentum equation

$$\varrho( \frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x})+\frac{\partial p}{\partial x}=\mu\frac{\partial^2 u}{\partial x^2}$$

the velocity component u appears in the inertia term (∂u/∂t + u∂u/∂y)and the viscous diffusion term µ(∂ ²u/∂x²). The other terms are density (ϱ), pressure (p)and (constant) viscosity (µ).