A COMPARATIVE STUDY OF NUMERICAL METHODS AND COMPUTATIONAL TOOLS FOR PHASE FIELD EQUATIONS OF SOLIDIFICATION

A Partial Differential Equation (PDE) or coupled PDEs need to be solved in phase field microstructural modelling. Finite difference discretization in space is commonly used to solve such equations numerically. Spectral methods can also solve PDEs to a high accuracy on a simple domain. However, those two methods should be treated with care when the domain of interest is irregular. In such cases, the finite volume method or finite element method is a natural alternative. A numerical algorithm implemented in a basic computer language such as C is a computationally efficient method. However, some high-level computing environments or software packages provide the advantages of easy implementation and flexibilities in visualization. This paper provides a comparative study of different numerical methods and computational tools to solve coupled phase field equations of solidification. The methodologies presented in this paper can be equally applied to other PDEs in phase field modelling.