Simulation of non-linearheat conduction by means of thermodynamics-based algorithm

Describes an extension of cellular automata to simulate heat conduction process. The offered algorithms is rather the tool for the direct simulation of a process than for the solution of partial differential equations. Its essential feature is the absence of any partial differential equations used widely for the description of heat conduction. Moreover, Fourier's law (or any of its generalizations) is not even used. Instead, the equations of state for a medium are applied immediately together with a rule of updating of cell's states which follows from thermodynamic laws applied to interacting systems. The interaction is described in terms of Gibbsian state space. One-dimensional heat conduction in a stationary layer is considered as an example. Shows that steady-state temperature distributions are linear in the case of solids in full correspondence with the classical theory. At the same time, these distributions are significantly non-linear in water, especially under sufficiently large gravitational force or in regions of phase transitions.