Analysis of Methods for Calculating the Value of the Thermal Conductivity Coefficient in Numerical Modeling
Novel Research Aspects in Mathematical and Computer Science Vol. 3,
14 May 2022
The effect of the method for calculating the values of the thermal conductivity coefficient at the nodes of the difference grid on the numerical solutions of a one-dimensional nonlinear problem of heat conduction according to explicit and implicit conservative difference schemes is investigated in this article using the method of computational experiments on a computer. The thermal conductivity is a power-law function of temperature. It is shown that the accuracy of numerical solutions obtained by both the explicit difference scheme and the implicit difference scheme depends on the method for calculating the values of the thermal conductivity coefficient at the nodes of the difference grid. A method is indicated that makes it possible to obtain a numerical solution that is sufficiently close to the analytical solution, including in the zone of the temperature front.
- Nonlinear processes
- nonlinear differential equation
- finite difference method
- conservative difference scheme Taylor series