A Multiple Step Random Walk Monte Carlo Method for Heat Conduction Involving Distributed Heat Sources

A multiple step fixed random walk Monte Carlo method for solving heat conduction in solids with distributed internal heat sources is developed. In this method, the probability that a walker reaches a point a few steps away is calculated analytically and is stored in the computer. Instead of moving to the immediate neighboring point the walker is allowed to jump several steps further. The present multiple step random walk technique can be applied to both conventional Monte Carlo and the Exodus methods. Numerical results indicate that the present method compares well with finite difference solutions while the computation speed is much faster than that of single step Exodus and conventional Monte Carlo methods