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AN EULERIAN-LAGRANGIAN WENO FINITE VOLUME SCHEME FOR ADVECTION PROBLEMS
 

Summary: AN EULERIAN-LAGRANGIAN WENO
FINITE VOLUME SCHEME FOR ADVECTION PROBLEMS
CHIEH-SEN HUANG, TODD ARBOGAST, AND JIANXIAN QIU
Abstract. We develop a locally conservative Eulerian-Lagrangian finite volume scheme with the
weighted essentially non-oscillatory property (EL-WENO) in one-space dimension. This method has
the advantages of both WENO and Eulerian-Lagrangian schemes. It is formally high-order accurate
in space (we present the fifth order version) and essentially non-oscillatory. Moreover, it is free of a
CFL time step stability restriction and has small time truncation error. The scheme requires a new
integral-based WENO reconstruction to handle trace-back integration. A Strang splitting algorithm
is presented for higher-dimensional problems, using both the new integral-based and pointwise-based
WENO reconstructions. We show formally that it maintains the fifth order accuracy. It is also locally
mass conservative. Numerical results are provided to illustrate the performance of the scheme and
verify its formal accuracy.
Key words. Eulerian-Lagrangian, semi-Lagrangian, WENO reconstruction, finite volume, lo-
cally mass conservative, characteristics, hyperbolic, Strang splitting
1. Introduction. Given a(x, t), consider the one (and later, two) space dimen-
sional initial value problem for a hyperbolic advection equation
u
t
+

  

Source: Arbogast, Todd - Center for Subsurface Modeling & Department of Mathematics, University of Texas at Austin

 

Collections: Mathematics; Geosciences