A NUMERICAL METHOD FOR SOLVING NONLINEAR HEAT CONDUCTION EQUATION ON A PARALLELOGRAM POINT MESH

A. V. Zabrodin, A. V. Pekarchuk
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1982. Вып.2. С. 14-22.

      A nonlinear heat conduction equation integration algorithm for the case of two space variables is presented. Time step calculation is divided into two stages. The first, or intermediate stage, solves a linearized equation using an implicit scheme and finds the temperature distribution for t + ατ (0,5 ≤ α ≤ 1). The operator conversion is made by means of an iteration loop, containing four-directional runs with iteratin parameters selection. The second stage defines a final temperature distribution for t + τ using the conservation law. Heat flux values are computed from the temperature distribution in the first stage. Examples illustrating numerical calculations are given.