Conduction Modelling Using Smoothed Particle Hydrodynamics

Abstract

Heat transfer is very important in many industrial and geophysical problems. Because these problems often have complicated fluid dynamics, there are advantages in solving them using Lagrangian methods like smoothed particle hydrodynamics (SPH). Since SPH particles become disordered, the second derivative terms may be estimated poorly, especially when materials with different properties are adjacent. In this paper we show how a simple alteration to the standard SPH formulation ensures continuity of heat flux across discontinuities in material properties. A set of rules is formulated for the construction of isothermal boundaries leading to accurate conduction solutions. A method for accurate prediction of heat fluxes through isothermal boundaries is also given. The accuracy of the SPH conduction solutions is demonstrated through a sequence of test problems of increasing complexity.