A new approach to enforcing discrete maximum principles in continuous Galerkin methods for convection-dominated transport equations

Journal Article · Sun Nov 01 04:00:00 EST 2015 · Journal of Computational Science

OSTI ID:1512882

Kuzmin, D. ^[1]; Shadid, John N. ^[2]

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1. Dortmund Univ. of Technology (Germany)
2. 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 Laboratories (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