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]

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1. National Sun Yat‐sen Univ., Kaohsiung, Taiwan (China)
2. Univ. of Texas, Austin, TX (United States)

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. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 651–680, 2017

• 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; DMS-0835745; DMS-1418752; 99-2115-M-110-006-MY3; 102-2115-M-110-010-MY3
• OSTI ID: 1533200
• Alternate ID(s): OSTI ID: 1786567
• Journal Information: Numerical Methods for Partial Differential Equations, Vol. 33, Issue 3; ISSN 0749-159X
• Publisher: Wiley
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
mathematics
characteristics
finite volume
hyperbolic transport
locally conservative
re-average
semi-Lagrangian
traceline
WENO