Chapter 1: Mathematical and Fluid Mechanical Introduction


The first chapter of the book is mostly concerned with background definitions and setting out notation from fluid mechanics. Background material for numerical computation is not considered in the book. In this part I am including some elementary numerical computation notes which can be viewed as web pages: Numerical Computation Notes or are available to be downloaded as a postscript file: notes.ps but there are many good texts on numerical techniques which can guide anyone just starting out in numerical computation.

The most time consuming part of two-dimensional streamfunction - vorticity calculations is solving the Poisson equation for the streamfunction given the vorticity. The old fashioned method to solve this was by relaxation combined with Gauss-Seidel or Jacobi iteration. This is nowadays not recommended: either multigrid (for stuctured meshes) or conjugate gradient (for unstructured meshes) are much faster. Both methods are extremeley easy to impliment. An example implimentation of conjugate gradient is available in cg.c . An example two-level multigrid program is in mg2.c . An example three level multigrid program is in mg3.c .


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