A new approach to enforcing discrete maximum principles in continuous Galerkin methods for convection-dominated transport equations
- Dortmund Univ. of Technology (Germany)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States)
This work introduces a set of design principles and new algorithmic tools for enforcing maximum principles and/or positivity preservation in continuous finite element approximations to convection-dominated transport problems. Enabling a linear first-order advection equation as a model problem, we address the design of first-order artificial diffusion operators and their higherorder counterparts at the element matrix level. The proposed methodology leads to a nonlinear high-resolution scheme capable of resolving moving fronts and internal/boundary layers as sharp localized nonoscillatory features. The amount of numerical dissipation depends on the difference between the solution value at a given node and a local maximum or minimum. The shockcapturing numerical diffusion coefficient is designed to vanish as the nodal values approach a mass-weighted or linearity-preserving average. The universal applicability and simplicity of the element-based limiting procedure makes it an attractive alternative to edge-based algebraic flux correction.
- Research Organization:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 1512882
- Report Number(s):
- SAND-2015-9790J; 666885
- Journal Information:
- Journal of Computational Science, Journal Name: Journal of Computational Science
- Country of Publication:
- United States
- Language:
- English
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