Matrix-free subcell residual distribution for Bernstein finite elements: Monolithic limiting

Hajduk, Hennes; Kuzmin, Dmitri; Kolev, Tzanio; Tomov, Vladimir; Tomas, Ignacio; Shadid, John N.

doi:10.1016/j.compfluid.2020.104451

Matrix-free subcell residual distribution for Bernstein finite elements: Monolithic limiting

Journal Article · Tue Jan 21 23:00:00 EST 2020 · Computers and Fluids

DOI:https://doi.org/10.1016/j.compfluid.2020.104451· OSTI ID:1769913

^[1]; Kuzmin, Dmitri ^[1]; Kolev, Tzanio ^[2]; Tomov, Vladimir ^[2]; Tomas, Ignacio ^[3]; Shadid, John N. ^[4]

Technische Univ. of Dortmund (Germany). Inst. of Applied Mathematics (LS III)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States)

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. Finally, the convergence behavior of presented methods is illustrated by numerical studies for two-dimensional test problems.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); German Research Foundation (DFG)

Grant/Contract Number:: AC04-94AL85000; AC52-07NA27344; NA0003525

OSTI ID:: 1769913

Alternate ID(s):: OSTI ID: 1776663
OSTI ID: 1595530

Report Number(s):: SAND--2021-2058J; 693984

Journal Information:: Computers and Fluids, Journal Name: Computers and Fluids Vol. 200; ISSN 0045-7930

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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