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RUSSIAN FEDERAL NUCLEAR CENTER -
ALL-RUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS
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APPLICATION OF THE TVD-APPROACH TO SOLVE THE THERMAL RADIATION TRANSPORT EQUATION WITH QUASIDIFFUSION METHOD
A. D. Gadzhiev, S. A. Grabovenskaya, V. V. Zavyalov, A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc 2010. Вып.3. С. 3-14.
A nonlinear TVD-type scheme of the second order of approximation used to solve the thermal radiation transport equation with the quasi-diffusion method is described. The numerical simulation results for some test problems are also given.Keywords: TVD-scheme, quasi-diffusion method.
DIAGONAL ELEMENT SINGLING-OUT SCHEMES USED TO SPEED UP ITERATIONS DURING THE THERMAL RADIATION TRANSPORT EQUATION SOLUTION IN DIFFUSION APPROXIMATIONS
A. D. Gadzhiev, A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc 2010. Вып.3. С. 15-27.
The paper describes the numerical schemes of singling out a diagonal element used to speed up iterations during the thermal radiation transport equation solution in diffusion approximations. The principal idea of such methods can be implemented in three stages:
For each computational grid cell, the energy equation is solved first and then the diagonal element singling-out schemes are used to find the temperature value via the density of radiation.
The temperature value is used to calculate the Planck function value.
The new values of density and radiation flux are found with the sweep method using the known right-hand part of equation.Keywords: acceleration of iterations, thermal radiation transport.
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