On the modelling of Shocks and Solitons in ideal and adiabatic gases and plasma with a symmetry analysis
In numerical simulations involving fluid equations various thermodynamic assumptions are employed in the closure of the set model equations. For instance these may or may not involve the energy equation and may not involve gas laws. What effect does such a choice have on the form, propagation and stability of solitons, shocks and related nonlinear wave structures. This has not been explored to any great extent by means of time evolutionary integrations of the fluid equations. Here we examine various one-dimensional models with initial conditions which give rise to soliton and shock formation and examine the effects of thermodynamic assumptions used in each case on the structures. The physical situations considered range from gas dynamics to electrical plasma fluid dynamics. The numerical integration schemes are derived from recent classes of high resolution schemes for hyperbolic systems which have been successfully deployed in shock propagation computations. Furthermore we use the Lie group analysis to determine invariant solutions.
Joint work with Richard Naidoo (Durban Institute of Technology, South Africa).