Super-time-stepping schemes for parabolic equations with boundary conditions
- Merton College, Oxford (United Kingdom)
- Univ. of Notre Dame, IN (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
In this work, we present a super-time-stepping scheme for numerically solving parabolic partial differential equations with Dirichlet boundary conditions (BC). Using the general Forward Euler scheme, one can show that by taking varying step sizes there is the potential of propagating the solution forward in time by a greater amount than with uniform step sizes, while maintaining the same order of accuracy. As shown in previous works, if one further requires that the scheme have the Convex Monotone Property (CMP), then there exists a scheme which results in linear, monotone stability of the solution. This monotone stability is highly desirable in many physical situations, such as thermal diffusion, where the physical system will not oscillate, but will behave monotonically. However, the schemes devised in previous works do not include situations that have a boundary condition, and the inclusion of boundary conditions will henceforth be our focus. It is shown that a particular Runge-Kutta-Gegenbauer class of schemes [5] will maintain the CMP even in the presence of Dirichlet BC.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- 89233218CNA000001
- OSTI ID:
- 1671091
- Alternate ID(s):
- OSTI ID: 1775919
OSTI ID: 23203569
- Report Number(s):
- LA-UR--20-20465
- Journal Information:
- Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 425; ISSN 0021-9991
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Similar Records
Analysis of the Spectral Stability of the Generalized Runge–Kutta Methods Applied to Initial-Boundary-Value Problems for Equations of the Parabolic Type. I. Explicit Methods
A stabilized Runge–Kutta–Legendre method for explicit super-time-stepping of parabolic and mixed equations