NUMERICAL SOLUTION OF 1D RADIATIVE HEAT TRANSFER PROBLEMS WITH PHASE TRANSFORMATIONS IN A ONCE-THROUGH RUN WITH THE "ROMB" SCHEME
A. M. Mustafin, N. N. Pashentseva, S. N. Lebedev
VANT. Ser.: Mat. Mod. Fiz. Proc 2022. Вып.4. С. 19-32.
The paper considers the numerical solution of 1D Stephan´s problem in a once-through run with the "Romb" scheme and studies the efficiency of the mesh adaptation to the problem. The algorithm of building an adaptive difference mesh for a three-phase heat transfer problem is given. The difference scheme "Romb" was derived on the adaptively refined mesh, it allows approximating the heat transfer equation within one cell and operating with boundary conditions of different forms. The numerical solutions were obtained for three Stephan´s problems: for two planar three-phase problems and for the application spherical two-phase melting problem for a microparticle of iron. It is shown that the solutions found agree with the results obtained by the other authors. The advantages of the difference mesh adaptation against the use of conventional meshes are clearly demonstrated for the solution of Stephan´s problems.Keywords: Stephan´s problem, the "Romb" difference scheme, adaptive difference mesh, hybrid data structure, binary tree, double-linked list.
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