Simple algorithms for calculation of the axial‐symmetric heat transport problem in a cylinder

Abstract

The approximation of axial‐symmetric heat transport problem in a cylinder is based on the finite volume method. In the classical formulation of the finite volume method it is assumed that the flux terms in the control volume are approximated with the finite difference expressions. Then in the 1‐D case the corresponding finite difference scheme for the given source function is not exact. There we propose the exact difference scheme. In 2‐D case the corresponding integrals are approximated using different quadrature formulae. This procedure allows one to reduce the heat transport problem described by a partial differential equation to an initial‐value problem for a system of two ordinary differential equations of the order depending on the quadrature formulae used. Numerical solutions of the corresponding algorithms are obtained using MAPLE routines for stiff system of ordinary differential equations.

Naudojantis baigtiniu tūriu metodu sudaryta tiksli schema, susiejanti sprendinio reikšmes srities krašte ir simetrijos taške. Gautoji lygčiu sistema aproksimuojama skaitinio integravimo formulemis ir sprendžiamas pradinis dvieju diferencialiniu lygčiu sistemos uždavinys. Pateikti skaitinio eksperimento rezultatai.