NUMERICAL SOLUTION OF THE 2D RADIATIVE HEAT TRANSFER EQUATION USING SPH METHOD
A. A. Lazarev, S. N. Polischuk, B. P. Tikhomirov
VANT. Ser.: Mat. Mod. Fiz. Proc 2018. Вып.2. С. 15-24.
The numerical solution of the 2D radiative heat transfer equation using smoothed-particle hydrodynamics (SPH) is considered. The difference approximation to the equation is given for the planar and axially symmetric problems. The equation discretization is performed using an implicit difference scheme with further linearization of the equation according to Newton. For problems with axial symmetry, the paper offers the method of calculations in the vicinity of rotation axis, which is based on the use of a planar interpolation kernel and auxiliary (fictitious) particles. A simple algorithm of simulating boundary conditions is given. Simulation results are presented for some test problems having known exact solutions. Keywords: radiative heat transfer equation, smoothed-particle hydrodynamics (SPH), implicit difference scheme, uniform and chaotic arrangement of particles, test simulations.
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