The solution of the thermal conduction term in the energy equation
presents special problems in an SPH formulation. An SPH equation can be
formulated using the standard procedures for single derivatives. First, by
solving for the heat flux and then using this solution in the energy equation.
This procedure is found to be very sensitive to particle disorder.
An alternative SPH form is presented, based on a Taylor
series expansion. Tests
demonstrate the robustness of the alternate form. Limitations and
disadvantages of the alternate form are also discussed.
