PRACTICAL CONDITIONS TO PROVIDE STABILITY OF HEAT WAVE SIMULATIONS IN IMPLICIT DIFFERENCE SCHEMES
Yu. A. Bondarenko, A. A. Gorbunov
VANT. Ser.: Mat. Mod. Fiz. Proc 2008. Вып.4. С. 3-12.
Implicit difference schemes with an explicit time-dependent heat conductivity factor, as well as two-stage implicit difference schemes with single refinement of the explicit heat conductivity factor are considered as applied to the quasi-linear diffusion equation. Conditions to provide stability of such difference schemes have been obtained. For implicit difference schemes with an implicit heat conductivity factor, conditions to provide convergence of simple iterations with respect to the heat conductivity factor have been obtained that have minor differences as against the stability conditions for the two-stage difference schemes with the refined explicit heat conductivity factor. Results of 2D heat wave simulations on irregular grids show that apart from being commensurately accurate, the use of the explicit (with single refinement) heat conductivity factor with automatic time step selection is more efficient than simple iterations with respect to the non-linearity of implicit heat conductivity factor. At the same time, simulations without time step constraint may lead to considerable uncertainties.
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