Numerical simulation of coupled fluid flow and heat transfer with phase change using the Finite Pointset Method

The purpose of this work is to carry out a meshfree implementation for the numerical simulation of two-dimensional transient incompressible flows coupled with heat transfer where phase change is present. The Finite Pointset Method is applied in order to solve the involved partial differential equations where the corresponding classical or strong formulation is directly used instead of the corresponding weak form as needed for some other meshfree approaches. The incorporation of the boundary conditions is done in a direct and simple manner. The simplicity and efficiency of this numerical method are demonstrated on several two-dimensional benchmark problems where solidification and melting processes occurs.