Peacock, Patrick H., and Holmes, David W. (2013) Development and verification of a particle number density variant of sph to robustly incorporate energy and heat transfer. In: Proceedings of the Third International Conference on Particle-Based Methods: fundamentals and applications. pp. 1-12. From: Particles 2013: Third International Conference on Particle-Based Methods: fundamentals and applications, 18-20 September 2013, Stuttgart, Germany.

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Abstract

In this paper we present a particle number density variation on the standard smooth particle hydrodynamics (SPH) form of the heat conduction equation and show progress towards a the development of a robust equation of state to incorporate particle energy. Including energy terms into the SPH governing equations and the equation of state will allow for more complex physical phenomena in to be modelled such as natural convection and eventually processes such as change of state. A brief derivation of a particle number density heat conduction equation is presented along with a 2D heat conduction validation problem as well as an introduction to current progress towards developing an equation of state for pressure that incorporates energy (as a function of temperature only at this stage) and a simple proof of concept example demonstrating natural convection in an enclosed square.

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