Peacock, Patrick, and Holmes, David (2014) Comparison and development of equation of state laws in smoothed particle hydrodynamics. Applied Mechanics and Materials, 553. pp. 144-149.

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Abstract

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

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