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Wave Propagation Algorithms for Multidimensional Hyperbolic Systems
 JOURNAL OF COMPUTATIONAL PHYSICS
, 1997
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Finite volume evolution galerkin methods for nonlinear hyperbolic systems
 J. Comput. Phys
"... Abstract. We present a new Finite Volume Evolution Galerkin (FVEG) scheme for the solution of the shallow water equations (SWE) with the bottom topography as a source term. Our new scheme will be based on the FVEG methods presented in (Lukáčová, Noelle and Kraft, J. Comp. Phys. 221, 2007), but adds ..."
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Cited by 33 (9 self)
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Abstract. We present a new Finite Volume Evolution Galerkin (FVEG) scheme for the solution of the shallow water equations (SWE) with the bottom topography as a source term. Our new scheme will be based on the FVEG methods presented in (Lukáčová, Noelle and Kraft, J. Comp. Phys. 221, 2007), but adds the possibility to handle dry boundaries. The most important aspect is to preserve the positivity of the water height. We present a general approach to ensure this for arbitrary finite volume schemes. The scheme is also wellbalanced and a new entropy fix improves the reproduction of sonic rarefaction waves.
A Wave Propagation Method for Three Dimensional Hyperbolic Problems
, 1996
"... A class of wave propagation algorithms for threedimensional conservation laws is developed. This unsplit nite volume method is based on solving onedimensional Riemann problems at the cell interfaces and applying fluxlimiter functions to suppress oscillations arising from second derivative terms. ..."
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Cited by 29 (6 self)
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A class of wave propagation algorithms for threedimensional conservation laws is developed. This unsplit nite volume method is based on solving onedimensional Riemann problems at the cell interfaces and applying fluxlimiter functions to suppress oscillations arising from second derivative terms. Waves emanating from the Riemann problem are further split by solving Riemann problems in the transverse direction to model crossderivative terms. Due to proper upwinding, the method is stable for Courant numbers up to one. Several examples using the Euler equations are included.
Capturing Shock Reflections: An improved flux formula
 J. Comput. Phys
, 1996
"... Godunov type schemes, based on exact or approximate solutions to the Riemann problem, have proven to be an excellent tool to compute approximate solutions to hyperbolic systems of conservation laws. However, there are many instances in which a particular scheme produces inappropriate results. In thi ..."
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Cited by 28 (8 self)
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Godunov type schemes, based on exact or approximate solutions to the Riemann problem, have proven to be an excellent tool to compute approximate solutions to hyperbolic systems of conservation laws. However, there are many instances in which a particular scheme produces inappropriate results. In this paper we consider several situations in which Roe's scheme gives incorrect results (or blows up all together) and propose an alternative flux formula that produces numerical approximations in which the pathological behavior is either eliminated or reduced to computationally acceptable levels. Key Words. Nonlinear Systems of Conservation Laws, Shock Capturing schemes, Shock Reflections. AMSMOS Classification: Primary 65M05, Secondary 65M10 1 Introduction Shock capturing techniques for the computation of discontinuous solutions to hyperbolic conservation laws are based on an old (by now) theorem of Lax and Wendroff establishing that the limit solutions of a consistent scheme in conservat...
The MoTICE: A new highresolution wavepropagation algorithm based on Fey’s Method of Transport
, 2000
"... Fey’s Method of Transport (MoT) is a multidimensional fluxvectorsplitting scheme for systems of conservation laws. Similarly to its onedimensional forerunner, the Steger–Warming scheme, and several other upwind finitedifference schemes, the MoT suffers from an inconsistency at sonic points when ..."
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Cited by 14 (3 self)
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Fey’s Method of Transport (MoT) is a multidimensional fluxvectorsplitting scheme for systems of conservation laws. Similarly to its onedimensional forerunner, the Steger–Warming scheme, and several other upwind finitedifference schemes, the MoT suffers from an inconsistency at sonic points when used with piecewiseconstant reconstructions. This inconsistency is due to a cellcentered evolution scheme, which we call MoTCCE, that is used to propagate the waves resulting from the fluxvectorsplitting step. Here we derive new firstorder and secondorderconsistent characteristic schemes based on interfacecentered evolution, which we call MoTICE. We prove consistency at all points, including the sonic points. Moreover, we simplify Fey’s wave decomposition by distinguishing clearly between a linearization and a decomposition step. Numerical experiments confirm the stability and accuracy of the new schemes. Owing to the simplicity of the two new ingredients of the MoTICE, its secondorder version is several times faster than that of the
for the Shallow Water Equations with Dry Beds
"... Well–balanced schemes, dry boundaries, shallow water equations, evolution Galerkin schemes, source terms. ..."
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Well–balanced schemes, dry boundaries, shallow water equations, evolution Galerkin schemes, source terms.
A Nonlinear Flux Split Method for Hyperbolic Conservation Laws
, 2001
"... Note: 1..eps and.tif are preferred file formats. 2. Preferred resolution for line art is 600 dpi and that for Halftones is 300 dpi. 3. Art in the following formats is not supported:.jpeg,.gif,.ppt,.opj,.cdr,.bmp,.xls,.wmf and pdf. 4. Line weight should not be less than.27 pt. ..."
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Note: 1..eps and.tif are preferred file formats. 2. Preferred resolution for line art is 600 dpi and that for Halftones is 300 dpi. 3. Art in the following formats is not supported:.jpeg,.gif,.ppt,.opj,.cdr,.bmp,.xls,.wmf and pdf. 4. Line weight should not be less than.27 pt.