Error of Relaxation Equations for SPH Method(Fluids Engineering)

Abstract

The relaxation equations for smoothed particle hydrodynamics (SPH) are able to suppress the numerical disorder around the interface of different fluids. It makes it possible to treat inviscid multi phase flow without separating it in each fluid, but the error of them is not small enough. In this paper, the error of relaxation equations is discussed for the case of same size particles and the case of different size particles composed of different fluids. Formulas to suppress the numerical error around the interface of multi phase flow are proposed, and methods to determine the smoothing length are discussed. Numerical simulations are carried out for air-water 2-phase flow to know the effects of these equations and methods. Results show that the method to determine the smoothing length is the most important to suppress the numerical disorder around the interface of multi phase flow.