Solving Phase-Field Models with Finite Difference Algorithms

Abstract

Finite difference algorithms offer a more direct approach to the numerical solution of partial differential equations than any other method. Finite difference algorithms are based on the replacement of each derivative by a difference quotient. Finite difference algorithms are simple to code, economic to compute, and easy to parallelize for the distributed computing environments. However, they also have disadvantages in terms of accuracy and imposing complex boundary conditions. For better understanding of the method, the solution of one-dimensional transient heat conduction is given as an example together with the source code in this section.