Численные методы решения задач теплопроводности для изучения температурного состояния керамического ядерного топлива

Abstract

Рассматриваются численные методы решения задач теплопроводности: классический метод сеток и метод полудискретизации с сеточной дискретизацией в пространственной области исследования температурного состояния керамического ядерного топлива. Показано, что применение метода полудискретизации, приводящего к системе обыкновенных дифференциальных уравнений с начальными условиями относительно узловых значений искомых величин, имеет ряд преимуществ перед классическим методом сеток из-за более широких возможностей выбора схемы интегрирования по времени.

The purpose of this research was to study the opportunities of numerical methods used for the solution of heat conductivity problems to study the temperature state of ceramic nuclear fuel the specific feature of which is its low heat conductivity. Therefore, this scientific paper gives consideration to the two options of the grid method used to solve the problem of nonstationary heat conductivity of the rod made of uranium dioxide and the solutions were compared to what was obtained using the method of separation of variables by an accurate analytical solution. The computation data show that a classic option of the grid method allows for the derivation of sufficiently accurate solutions, though the application of it requires a priori substantiation of the choice of the pitch relation for time and 3D grids; in general it is a very complicated mathematical problem. The computations showed that it is convenient to use the method of semi-descritization for the solution of heat conductivity problems to study the temperature state of ceramic nuclear fuel. This method allows us to derive ordinary differential equations with initial conditions for node temperature values on the 3D grid that can be solved using highly-efficient numerical methods of stepwise integration with the self-selection of the pitch. The investigation data show that it is advisable to use the method of semi-descritization with 3D grids and numerical time integration using the Merson method to solve heat conductivity problems when studying the temperature state of ceramic nuclear fuel in the future.