Abstract
Moving Particle Semi-Implicit method (MPS) is applied to the analysis of one and two dimensional scalar wave equations. The author and his coworkers are going to analyze the non-linear characteristics of waves and the physical non-linear phenomena caused by waves. Particle methods, e.g. MPS or Smoothed Particle Hydrodynamics method (SPH), are mesh free numerical methods and well suited to analyze the large non-linear dynamics. But wave analyses by MPS are minimal; therefore we will address linear waves and investigate the wave characteristics of the analysis using MPS. First, we inquired into the stability conditions and the dispersion characteristics of MPS wave analysis. In the process of the analysis, we found if the particles are positioned regularly and re=2Δh in one-dimensional and re≤√2Δh in two-dimensional, the formulation by the MPS is as same as the central difference scheme of a finite difference method. Here, Δh and re is a distance between neighboring particles and a radius of weight function, respectively. Related to the stability conditions, an interesting phenomenon was found that in spite of the Courant number α>1, stable cases existed when re was large. Second, we investigated the dispersion properties vs. parameters α, θ and re in detail. Here, θ shows a propagating direction. Consequentially, in order to achieve the phase velocity error ε[%]<1, a wavelength has to be discretized about over 20Δh, under conditions of α<1, re≤4Δh in one dimensionin case, and α≤1 ⁄ √2, re≤3Δh in two dimensionalin occasion. Last, the results of sound wave propagation analyzed by MPS were good agreed to the analytical predictions.
