An Eulerian–Lagrangian Weighted Essentially Nonoscillatory scheme for nonlinear conservation laws

Huang, Chieh‐sen; Arbogast, Todd

doi:10.1002/num.22091

An Eulerian–Lagrangian Weighted Essentially Nonoscillatory scheme for nonlinear conservation laws

Journal Article · Wed Sep 28 00:00:00 EDT 2016 · Numerical Methods for Partial Differential Equations

DOI:https://doi.org/10.1002/num.22091· OSTI ID:1533200

Huang, Chieh‐sen ^[1]; Arbogast, Todd ^[2]

National Sun Yat‐sen Univ., Kaohsiung, Taiwan (China); DOE/OSTI
Univ. of Texas, Austin, TX (United States)

Here, we develop a formally high order Eulerian–Lagrangian Weighted Essentially Nonoscillatory (EL-WENO) finite volume scheme for nonlinear scalar conservation laws that combines ideas of Lagrangian traceline methods with WENO reconstructions. The particles within a grid element are transported in the manner of a standard Eulerian–Lagrangian (or semi-Lagrangian) scheme using a fixed velocity v. A flux correction computation accounts for particles that cross the v-traceline during the time step. If v = 0, the scheme reduces to an almost standard WENO5 scheme. The CFL condition is relaxed when v is chosen to approximate either the characteristic or particle velocity. Excellent numerical results are obtained using relatively long time steps. The v-traceback points can fall arbitrarily within the computational grid, and linear WENO weights may not exist for the point. A general WENO technique is described to reconstruct to any order the integral of a smooth function using averages defined over a general, nonuniform computational grid. Moreover, to high accuracy, local averages can also be reconstructed. By re-averaging the function to a uniform reconstruction grid that includes a point of interest, one can apply a standard WENO reconstruction to obtain a high order point value of the function.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF); Taiwan National Science Council

Grant/Contract Number:: SC0001114

OSTI ID:: 1533200

Alternate ID(s):: OSTI ID: 1786567

Journal Information:: Numerical Methods for Partial Differential Equations, Journal Name: Numerical Methods for Partial Differential Equations Journal Issue: 3 Vol. 33; ISSN 0749-159X

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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An Eulerian–Lagrangian Weighted Essentially Nonoscillatory scheme for nonlinear conservation laws

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