Entropy Weak Solutions to Nonlinear Hyperbolic Systems in Nonconservation Form

1989 ◽  
pp. 362-373 ◽  
Author(s):  
Philippe Floch
Keyword(s):  
Weak Solutions ◽  
Hyperbolic Systems ◽  
Nonlinear Hyperbolic Systems

scholarly journals Schemes with Well-Controlled Dissipation. Hyperbolic Systems in Nonconservative Form

2017 ◽  
Vol 21 (4) ◽  
pp. 913-946 ◽  
Author(s):  
Abdelaziz Beljadid ◽  
Philippe G. LeFloch ◽  
Siddhartha Mishra ◽  
Carlos Parés
Keyword(s):  
Fluid Dynamics ◽  
Numerical Method ◽  
Linear Stability ◽  
Weak Solutions ◽  
Hyperbolic Systems ◽  
Small Scale ◽  
Numerical Schemes ◽  
Nonconservative System ◽  
Complex Fluid ◽  
Nonlinear Hyperbolic Systems

AbstractWe propose here a class of numerical schemes for the approximation of weak solutions to nonlinear hyperbolic systems in nonconservative form—the notion of solution being understood in the sense of Dal Maso, LeFloch, and Murat (DLM). The proposed numerical method falls within LeFloch-Mishra's framework of schemes with well-controlled dissipation (WCD), recently introduced for dealing with small-scale dependent shocks. We design WCD schemes which are consistent with a given nonconservative system at arbitrarily high-order and then analyze their linear stability. We then investigate several nonconservative hyperbolic models arising in complex fluid dynamics, and we numerically demonstrate the convergence of our schemes toward physically meaningful weak solutions.

On the Convergence Rate of Vanishing Viscosity Approximations for Nonlinear Hyperbolic Systems

2012 ◽  
Vol 44 (5) ◽  
pp. 3537-3563 ◽  
Author(s):  
Alberto Bressan ◽  
Feimin Huang ◽  
Yong Wang ◽  
Tong Yang
Keyword(s):  
Convergence Rate ◽  
Hyperbolic Systems ◽  
Vanishing Viscosity ◽  
Nonlinear Hyperbolic Systems

scholarly journals Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems

2010 ◽  
Vol 229 (18) ◽  
pp. 6485-6511 ◽  
Author(s):  
J. Tryoen ◽  
O. Le Maître ◽  
M. Ndjinga ◽  
A. Ern
Keyword(s):  
Hyperbolic Systems ◽  
Galerkin Methods ◽  
Nonlinear Hyperbolic Systems
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