Numerical modeling of a one-dimensional quasilinear heat conduction process

Abstract

The object of research in this article is the applicability of some conservative difference schemes and methods for calculating the values of the thermal conductivity coefficient at the nodes of the difference grid for the numerical modeling of a one-dimensional quasilinear heat conduction process, in which the coefficient of thermal conductivity is a power-law function of temperature. As a result of solving the differential problem, it is necessary to obtain the most accurate numerical solution of the problem posed. Therefore, choosing a difference scheme for the numerical solution of the differential equation in the mathematical model of the problem and method for calculating the values of the thermal conductivity coefficient is relevant.The study is performed by the method of carrying out computational experiments on a computer and comparing the numerical solutions with the known analytical solution of the form of a traveling wave. A group of methods for calculating the thermal conductivity coefficient values at the nodes of the difference mesh, which are advisable to use in the numerical simulation of the nonlinear heat conduction process, is identified. The results of computational experiments on a computer show that using these methods using both an explicit difference scheme with a central difference, and an implicit difference scheme without iterations, and an implicit difference scheme with iterations, it is possible to obtain numerical solutions of a one-dimensional quasilinear heat conduction problem which are close enough to the analytical solution.Consequently, the listed above conservative difference schemes can be used for numerical modeling of a one-dimensional quasilinear heat conduction process.