Numerical solution of a transformed parabolic equation

摘要

A numerical analysis of a parabolic partial differential equation (PDE) which originates from the governing equations of transient fluid flow and heat transfer is presented. The parabolic PDE is transformed by introducing an exponential function to eliminate the convection terms in the equation. A fourth-order central differencing scheme and a second-order central differencing scheme are used to solve the transformed parabolic PDE numerically. The analytical solutions of this equation are also given. Comparisons against the analytical solutions are made for the numerical results using the present schemes and those using the four classical differencing schemes, namely, the first-order upwind scheme, hybrid scheme, power-law scheme, and exponential scheme.