Oral Presentation
3D operator numerical method. Application to neutron stars anisotropic heat transfer simulations.
Presenter: Ilia Kondratev (Space Reseach Institute; National Research nuclear University MEPhI, Moscow, Russia)
Support operator method (Samarskii's method, operator-difference method) has proven itself well in 2D numerical simulations of different astrophysical problems. The idea of operator approach consists of inclusion the boundary conditions into difference form of the solving problem and its formulation as one operator equation. The finite difference operators are constructed in the way to fulfill corresponding relations between continuous operators (for example, div(rot)=0, div is conjugated to -grad so div(grad) is self-conjugated etc.). Such approach allows to obtain completely conservative implicit finite difference schemes. Efficient iterative methods, can be used to find the solution because constructed matrixes have good properties, symmetry and positive definitness. The method was extended for three dimensional case. 3D grid analogues for continuous differential operators using a cell-node approximation on thetrahedral grid were constructed. The 3D code was tested on the calculation of Newtonian gravitational potential and solution of the stationary heat transfer equation.
The anisotropic heat transfer in neutron stars in the presence of the strong magnetic field was studied. Tensorial heat conductivity coefficient for our simulations was taken from the paper by G. S. Bisnovatyi-kogan and M. V. Glushikhina (Plasma Physics Reports, 2018, Vol. 44, No. 4, pp. 405-423). Results of simulations are discussed.
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