Journal
COMPUTERS & FLUIDS
Volume 200, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.compfluid.2020.104451
Keywords
Advection problems; High-order finite elements; Bernstein polynomials; Matrix-free methods; Discrete maximum principles; Residual distribution; Limiters
Funding
- U.S. Department of Energy [DE-AC52-07NA27344, LLNLJRNL-796580]
- German Research Association (DFG) [KU 1530/23-1]
- U.S. Department of Energy, Office of Science, Office of Applied Scientific Computing Research
- U.S. Department of Energy's National Nuclear Security Administration [DE-NA0003525]
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This paper is focused on the aspects of limiting in residual distribution (RD) schemes for high-order finite element approximations to advection problems. Both continuous and discontinuous Galerkin methods are considered in this work. Discrete maximum principles are enforced using algebraic manipulations of element contributions to the global nonlinear system. The required modifications can be carried out without calculating the element matrices and assembling their global counterparts. The components of element vectors associated with the standard Galerkin discretization are manipulated directly using localized subcell weights to achieve optimal accuracy. Low-order nonlinear RD schemes of this kind were originally developed to calculate local extremum diminishing predictors for flux-corrected transport (FCT) algorithms. In the present paper, we incorporate limiters directly into the residual distribution procedure, which makes it applicable to stationary problems and leads to well-posed nonlinear discrete problems. To circumvent the second-order accuracy barrier, the correction factors of monolithic limiting approaches and FCT schemes are adjusted using smoothness sensors based on second derivatives. The convergence behavior of presented methods is illustrated by numerical studies for two-dimensional test problems. (C) 2020 Elsevier Ltd. All rights reserved.
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