Comparison and Development of Equation of State Laws in Smoothed Particle Hydrodynamics

Abstract

In this paper we present a brief comparison of existing equation of state laws used inSmoothed Particle Hydrodynamics (SPH) and introduce some new expressions for the equation ofstate for pressure, as well as to calculate temperature. In SPH literature practical examples of heatconduction and energy are scarce when compared with fluid flow formulations that determine pressuresimply from density and an artificial speed of sound. Such simplifications may be appropriate forisothermal flow problems; however, a more thermodynamically rigorous formulation is necessary forcomplex and thermally driven problems, particularly in geophysics. This work discusses conventionalequations of state, as well as presenting some new relations. This includes having pressure depend onthe energy of the system, and applying these relations to a number of proof of concept examplesdemonstrating natural convection and examining the parameters of the new equation of state. Thesedevelopments facilitate future work towards modelling more complex physical phenomena such asheat driven convective flow.