A consistent Moving Particle System Simulation method: Applications to parabolic/hyperbolic heat conduction type problems

In this paper, a consistent MPS (Moving Particle System Semi-implicit/Moving Particle System Simulation) method is established emanating from Taylor Expansion and Gauss's Theorem. The proposed MPS method preserves the consistency between the Gradient and Laplacian approximations, and also has the ability to recover the conventional MPS method which lacks consistency. In addition, the proposed method preserves the first order accuracy in space whereas the traditional MPS method loses the accuracy in the case with arbitrary and non-uniform particle discretization. The applicability of the proposed method for the analysis of first- and second-order transient hyperbolic and parabolic systems is illustrated via a recently developed C-F model (Cattaneo-Fourier model) of heat conduction that has been proven to govern thermal transport in different scales, and also capture the various heat conduction physical phenomena. The approaches of imposing different boundary conditions in the heat conduction problems are investigated comprehensively as well. In addition, a unified GS4 i-Integration framework is exploited in the numerical simulations involving first- and second-order systems in time.