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A wave propagation method for three-dimensional hyperbolic conservation laws

Langseth, Jan Olav; LeVeque, Randall J., 1955- (Elsevier, 2000-11-20)

A class of wave propagation algorithms for three-dimensional conservation laws and other hyperbolic systems is developed. These unsplit finite-volume methods are based on solving one-dimensional Riemann problems at the ...
A class of approximate Riemann Solvers and their relation to relaxation schemes

LeVeque, Randall J., 1955-; Pelanti, Marica (Elsevier/Academic Press, 2001-09-30)

We show that a simple relaxation scheme of the type proposed by Jin and Xin [Comm. Pure Appl. Math.48, 235 (1995)] can be reinterpreted as defining a particular approximate Riemann solver for the original system of m ...
A Wave Propagation Method for Conservation Laws and Balance Laws with Spatially Varying Flux Functions

LeVeque, Randall J., 1955-; Bale, Derek S.; Mitran, Sorin; Rossmanith, James A. (Society for Industrial and Applied Mathematics, 2002)

We study a general approach to solving conservation laws of the form qt+f(q,x)x=0, where the flux function f(q,x) has explicit spatial variation. Finite-volume methods are used in which the flux is discretized spatially, ...
A wave propagation algorithm for hyperbolic systems on curved manifolds

Rossmanith, James A.; Bale, Derek S.; LeVeque, Randall J., 1955- (Elsevier, 2004-09-20)

An extension of the wave propagation algorithm first introduced by LeVeque [J. Comput. Phys. 131 (1997) 327] is developed for hyperbolic systems on a general curved manifold. This extension is important in a variety of ...
High-resolution rotated grid method for conservation laws with embedded geometries

Helzel, Christiane, 1971-; Berger, Marsha J.; LeVeque, Randall J., 1955- (2005)

We develop a second-order rotated grid method for the approximation of time dependent solutions of conservation laws in complex geometry using an underlying Cartesian grid. Stability for time steps adequate for the ...
High-resolution finite volume methods for dusty gas jets and plumes

Pelanti, Marcia; LeVeque, Randall J., 1955- (2006)

We consider a model for dusty gas flow that consists of the compressible Euler equations for the gas coupled to a similar (but pressureless) system of equations for the mass, momentum, and energy of the dust. These sets ...
Finite volume methods and adaptive refinement for global tsunami propagation and local inundation

George, David L.; LeVeque, Randall J., 1955- (2006)

The shallow water equations are a commonly accepted approximation governing tsunami propagation. Numerically capturing certain features of local tsunami inundation requires solving these equations in their physically ...
CORRECTION TO THE ARTICLE A COMPARISON OF THE EXTENDED FINITE ELEMENT METHOD WITH THE IMMERSED INTERFACE METHOD FOR ELLIPTIC EQUATIONS WITH DISCONTINUOUS COEFFICIENTS AND SINGULAR SOURCES BY VAUGHAN ET AL.

Beale, J. T. (John Thomas), 1947-; Chopp, David L.; LeVeque, Randall J., 1955-; Li, Zhilin, 1956- (2008)

A recent paper by Vaughan, Smith, and Chopp [Comm. App. Math. &and Comp. Sci. 1 (2006), 207–228] reported numerical results for three examples using the immersed interface method (IIM) and the extended finite element method ...
Probabilistic Tsunami Hazard Assessment (PTHA) for Crescent City, CA. Final Report for Phase I

Gonzalez, Frank I.; LeVeque, Randall J., 1955-; Adams, Loyce M. (University of Washington Department of Applied Mathmatics, 2013-02-02)

This demonstration Probabilistic Tsunami Hazard Assessment (PTHA) study of Crescent City, California was funded by BakerAECOM and motivated by FEMA's desire to explore methods to improve products of the FEMA Risk Mapping, ...

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