Vol. 12, No. 1, 2017

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
A single-stage flux-corrected transport algorithm for high-order finite-volume methods

Christopher Chaplin and Phillip Colella

Vol. 12 (2017), No. 1, 1–24
Abstract

We present a new limiter method for solving the advection equation using a high-order, finite-volume discretization. The limiter is based on the flux-corrected transport algorithm. We modify the classical algorithm by introducing a new computation for solution bounds at smooth extrema, as well as improving the preconstraint on the high-order fluxes. We compute the high-order fluxes via a method-of-lines approach with fourth-order Runge–Kutta as the time integrator. For computing low-order fluxes, we select the corner-transport upwind method due to its improved stability over donor-cell upwind. Several spatial differencing schemes are investigated for the high-order flux computation, including centered-difference and upwind schemes. We show that the upwind schemes perform well on account of the dissipation of high-wavenumber components. The new limiter method retains high-order accuracy for smooth solutions and accurately captures fronts in discontinuous solutions. Further, we need only apply the limiter once per complete time step.

Keywords
finite-volume method, high order, advection, limiter
Mathematical Subject Classification 2010
Primary: 65M08
Milestones
Received: 4 May 2015
Revised: 13 January 2017
Accepted: 18 January 2017
Published: 8 May 2017
Authors
Christopher Chaplin
Applied Numerical Algorithms Group, Computational Research Division
Lawrence Berkeley National Laboratory
1 Cyclotron Road
MS 50A-3111
Berkeley, CA 94720
United States
Phillip Colella
Applied Numerical Algorithms Group, Computational Research Division
Lawrence Berkeley National Laboratory
1 Cyclotron Road
MS 50A-3111
Berkeley, CA 94720
United States