A single-stage flux-corrected transport algorithm for high-order finite-volume methods

Chaplin, Christopher; Colella, Phillip

doi:10.2140/camcos.2017.12.1

A single-stage flux-corrected transport algorithm for high-order finite-volume methods

Journal Article · Mon May 08 00:00:00 EDT 2017 · Communications in Applied Mathematics and Computational Science

DOI:https://doi.org/10.2140/camcos.2017.12.1· OSTI ID:1420104

Chaplin, Christopher ^[1]; Colella, Phillip ^[1]

Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Applied Numerical Algorithms Group, Computational Research Division

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. Here, 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.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1420104

Journal Information:: Communications in Applied Mathematics and Computational Science, Journal Name: Communications in Applied Mathematics and Computational Science Journal Issue: 1 Vol. 12; ISSN 1559-3940

Publisher:: Mathematical Sciences PublishersCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
advection
finite-volume method
high order
limiter

A single-stage flux-corrected transport algorithm for high-order finite-volume methods

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