Journal ArticleDOI
Quasilinear hyperbolic systems
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In this article, the authors construct global solutions for quasilinear hyperbolic systems and study their asymptotic behaviors, including models of gas flows in a variable area duct and flows with a moving source.Abstract:
We construct global solutions for quasilinear hyperbolic systems and study their asymptotic behaviors. The systems include models of gas flows in a variable area duct and flows with a moving source. Our analysis is based on a numerical scheme which generalizes the Glimm scheme for hyperbolic conservation laws.read more
Citations
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Journal ArticleDOI
The Riemann problem for fluid flow of real materials
Ralph Menikoff,Bradley J. Plohr +1 more
TL;DR: In this article, the properties of the isentropes and the shock Hugoniot loci that follow from conditions imposed on the equation of state are reviewed systematically, and additional questions related to shock stability and nonuniqueness of the solution of the Riemann problem are discussed.
Journal ArticleDOI
Improved Treatment of Source Terms in Upwind Schemes for the Shallow Water Equations in Channels with Irregular Geometry
TL;DR: A stationary solution that emphasizes the source terms considered is obtained and is used to test the proposed extensions of theQ-scheme of van Leer and Roe in terms of a “conservation” property.
Journal ArticleDOI
On the Relation Between the Upwind-Differencing Schemes of Godunov, Engquist–Osher and Roe
TL;DR: In this article, the upwind-differencing first-order schemes of Godunov, Engquist-Osher and Roe are discussed on the basis of the inviscid Burgers equations.
Journal ArticleDOI
Numerical Schemes for Hyperbolic Conservation Laws with Stiff Relaxation Terms
Shi Jin,C. David Levermore +1 more
TL;DR: This article introduces a modification of higher order Godunov methods that possesses the correct asymptotic behavior, allowing the use of coarse grids (large cell Peclet numbers) and builds into the numerical scheme the asymPTotic balances that lead to this behavior.
Journal ArticleDOI
A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms☆
TL;DR: A way to construct robust numerical schemes for the computations of numerical solutions of one- and two-dimensional hyperbolic systems of balance laws by reforming the source terms as nonconservative products and treating them directly in the definition of the numerical fluxes.
References
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Book
Linear and Nonlinear Waves
TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.
Book
Methods of Mathematical Physics
Richard Courant,David Hilbert +1 more
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Book
Supersonic flow and shock waves
Richard Courant,Kurt Friedrichs +1 more
TL;DR: In this article, the authors proposed a method to compressible ecoulement for compressible compressible and supersonique and onde de choc Reference Record created on 2005-11-18, modified on 2016-08-08