Extended particle difference method for moving boundary problems

In this paper, we present an extended particle difference method for moving boundary (or interface) problems. The particle derivative approximation is further developed to approximate the Taylor polynomial with the moving least squares method through completely node-wise computations. The discontinuity (or singularity) in the derivative field and the kinetic relation of the interfacial physics are effectively immersed into the particle derivative approximation. The segmented points that discretize the moving interface are consecutively updated in an explicit manner to track the evolution of the moving interface topology. Discretized difference equations for the governing equations are directly constructed at the nodes and the segmented points of the computational domain and the moving interface, respectively. Assemblage of the discretized difference equations yields a linear algebraic system of equations that provides efficient and stable solution procedure for a strong formulation. Numerical examples demonstrate that this method achieves excellent accuracy and efficiency for moving boundary problems.