A Numerical Analysis of Smoothed Particle Hydrodynamics

摘要: Abstract : This dissertation studies the numerical method of Smoothed Particle Hydrodynamics (SPH) as a technique for solving systems conservation equations. The research starts with detailed consistency analysis method. Higher dimensions and non-smooth functions are considered in addition to smooth one dimensional case. A stability is then performed. Using linear technique, an instability found. Solutions proposed resolve instability. Also total variation performed leading monotone form SPH. concepts used convergence proof. proof uses lemmas derived from Lax-Wendroff theorem finite differences. concluded study SPH kernel function. Measures merit kernels these show bell-shaped be superior over other shaped kernels. Three second-order time schemes applied provide full discretization problem; Lax-Wendroff, central, Shu schemes. In lower-order Lax-Friedrichs type developed. proposing use flux-limited hybrid methods shocks.