A widely used numerical technique for the solution of nonlinear parabolic problems, such as nonlinear transient heat transfer, makes use of a two-fold discretization procedure. In the first stage, a set of first-order nonlinear differential equations is obtained. The time integration of these equations is accomplished during the second stage. The present investigation is concerned with the methods employed for the time integration of the system of equations. Two-level integration schemes are considered, taking into account linear one-step methods and higher-order one-step schemes. Attention is also given to three-level integration schemes, and an application of the proposed schemes to a homogeneous model equation. The fully implicit three-level scheme is found to be the best scheme for long-time responses. It is also quite adequate for short-time response in the case of small time steps.
Numerical Methods in Heat Transfer
- Pub Date:
- Conductive Heat Transfer;
- Nonlinear Equations;
- Numerical Integration;
- Finite Element Method;
- Fluid Mechanics and Heat Transfer