PRACTICAL STABILITY CONDITIONS FOR A DIFFERENCE SCHEME FOR SOLVING THE HEAT TRANSFER EQUATION WITH DOUBLE THERMAL CONDUCTIVITY REMAPPING
Yu. A. Bondarenko, A. A. Gorbunov, B. P. Tikhomirov
VANT. Ser.: Mat. Mod. Fiz. Proc 2016. Вып.4. С. 20-25.
In some codes, the nonlinear heat transfer equation is solved numerically using implicit conditionally stable difference schemes with a fixed maximum permissible number of iterations with respect to the nonlinearity of thermal conductivity having the value of 1, 2 or 3. In this paper, the von Neumann-Fourier method is combined with the Newton numerical method for initial data stability analysis of a scheme with double remapping of the field of thermal conductivities. From the stability condition we derived a time step constraint suitable for practical simulations. It is shown that the dependence of the time step on the mesh spacing is not quadratic. Keywords: radiant heat transfer, implicit difference scheme, thermal conductivity, initial data stability, von Neumann-Fourier method, iterative Newton method, time step, test simulations.
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