A new finite-difference scheme for parabolic differential equations
Abstract
Finite-difference methods for unsteady heat conduction are considered. It is shown that the Crank-Nicolson scheme, although unconditionally stable in the mathematical sense, produces physically unrealistic solutions when the time step is large. The fully implicit scheme shows more satisfactory behavior, but is less accurate for small time steps. A new scheme is presented that is satisfactory for the entire range of time steps. It is also shown how the scheme can be applied to boundary-layer situations. The performance of the new scheme is demonstrated by its application to a heat conduction problem and a boundary-layer problem.
- Publication:
-
Numerical Heat Transfer
- Pub Date:
- March 1978
- Bibcode:
- 1978NumHT...1...27P
- Keywords:
-
- Conductive Heat Transfer;
- Finite Difference Theory;
- Parabolic Differential Equations;
- Thermal Boundary Layer;
- Couette Flow;
- Laminar Flow;
- Numerical Stability;
- Temperature Distribution;
- Wall Flow;
- Fluid Mechanics and Heat Transfer