Peter Enders

DISCRETE MODELS OF HEAT FLOW IN LAYERED MATERIALS USING SIMPLE AND CORRELATED RANDOM WALKS

The paper reviews some discrete probabilistic numerical techniques with particular emphasis on heat flow in inhomogeneous materials. The effects of different nodal configurations on the development of suitable algorithms are outlined and we suggest a new and consistent description for the discrete apparent effusivity. Our approach is then discussed in the context of TLM, and analogues are presented for flux relaxation time and effusivity.

IMPEDANCE TRANSFORMATIONS AND MESH COARSENING IN TLM HEAT FLOW MODELING

Numerical models of multimaterial systems are often constrained by stiffness factors, which impede numerical efficiency. Thus, heat flow simulations in problems involving widely different thermal time constants can require excessively fine meshes, extremely small iteration time steps, or both. The transmission line matrix method is an unconditionally stable technique that uses a network of impedances and resistances to model thermal diffusion, This paper outlines a method by which these parameters can be transformed as a means of improving computational efficiency while maintaining compatibility with microscopic models.

CAN THE TRANSMISSION LINE MATRIX METHOD YIELD STATIONARY SOLUTIONS OF THE TIME‐DEPENDENT SCHRÖDINGER EQUATION?

By virtue of the success of the transmission line matrix method (TLM) in solving heat and matter diffusion problems, it should also be applicable to the time-dependent Schrodinger equation. The occurrence of complex-valued circuit elements does notdestroy the unconditional stability of the routine. But it seems to be impossible to obtain stationary (eigen)solutions to this equation as well as separable solutions to the diffusion equation. It is suggested that this is due to the non-dissipativity of the TLM routine.