Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations

By Randall J. LeVeque. 2002

4,812 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c75ae911808d12c78dc9097371be8ec812fde13b

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

A weighted surface-depth gradient method for the numerical integration of the 2D shallow water equations with topography (2008, methodology): “In the fractional step method [31,20] the complete equations are split into a homogeneous problem and an ODE system.”
Structure-preserving discretization of incompressible fluids (2009, methodology): “We also wish to investigate the use of an ‘‘upwind’’ version of the discrete velocity A, possessing only positive fluxes as often used in the discretization of hyperbolic partial differential equations [29].”
A Discontinuous Galerkin Global Shallow Water Model (2005, methodology): “Then the flux Ja- cobian in x1 direction is defined to be F 1(q) (for details, see Leveque 2002).”
Numerical methods for Hamiltonian PDEs (2006, background): “The issues of discretization are therefore very different from the theory for hyperbolic conservation laws (see Leveque [87] for example), where the equations themselves are in conservation law form.”
A “Vertically Lagrangian” Finite-Volume Dynamical Core for Global Models (2004, background): “There exists a rich body of literature on high-performance finite-volume schemes designed for other disciplines (e.g., Roe 1981; Colella and Woodward 1984; Woodward and Colella 1984; Shu and Osher 1988; Harten 1989; Huynh 1996; Leveque 2002 ).”
Multiphase Porous Electrode Theory (2017, methodology): “These oscillations could be eliminated by using a flux limiter, commonly used in higher order discretization schemes and especially for hyperbolic problems [166].”
Solutal-convection regimes in a two-dimensional porous medium (2014, background): “This is a substantial approximation and, more significantly, it is not clear how to correctly introduce the shock because the ‘true’ conservation form of (4.5) is unknown (see, for example, LeVeque 2002).”
Edge Functions for Spectral Element Methods (2011, background): “The metric-free form, (15), resembles a finite volume discretization, see for instance [11, 16–18] of the sample problem.”
A continuum of physics-based lithium-ion battery models reviewed (2022, methodology): “Different techniques can be employed to discretise the spatial operators in the governing PDEs, examples being: finite volume methods [72], control volume methods [144], and finite element methods (FEMs) [54, 64].”