Gradient Computation

Abstract

As was shown in the previous chapter, the discretization of the gradients of $\phi$ at cell centroids and faces is fundamental to constructing the discretized sets of diffusion equations and, as will be revealed in later chapters, of equations involving the convection term. In addition, the evaluation of gradients is needed for the evaluation of various operators. For example, pressure derivatives are directly needed in the discretized momentum equations, while velocity gradients are required to compute the production term in turbulence models, and the strain rate in non-Newtonian viscosity models. This chapter describes several techniques for evaluating gradients on a general mesh topology. The chapter starts with a description of the techniques for computing the gradient on cartesian structured grids and proceeds with gradient evaluation on unstructured grids. The presented methods follow either the Green-Gauss or the least square approach. Methods to interpolate the gradient to element faces are also presented.