Numerical Computation of Natural Convection with the Preconditioning Iterative Method

Hiroyuki Hirano, Hideki Tamaya, Hiroshi Niki and Naotaka Okamoto

Numerical Computation, Preconditioning, Gauss-Seidel Method, Natural Convection
This paper is on the application of the preconditioning Gauss-Seidel iterative method to solve a linear system encountered in the numerical computation of heat transfer and/or fluid flow. Three kinds of preconditioners (matrices) are considered, and these consist of the only matrix elements of a linear system. 
After the validity of preconditioning is illustrated by a simple numerical example, 
this method is applied to the computation of the thermal conduction problem. Further this method is adapted to calculate the natural convection problem. The following conclusions are obtained. The preconditioning is useful especially for the strongly diagonally dominant matrix, and the number of iterations decreases up to almost the half of that without preconditioning.
the 4th JSME-KSME Thermal Engineering Conference

Proceedings of the 4th JSME-KSME Thermal Engineering Conference, Vol.2, pp.233-238