Weak Convergence of Nonlinear Finite Volume Schemes for Linear Hyperbolic Systems

2014 ◽  
pp. 411-419
Author(s):  
Michaël Ndjinga
Keyword(s):  
Weak Convergence ◽  
Finite Volume ◽  
Hyperbolic Systems ◽  
Finite Volume Schemes

Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems

2007 ◽  
Vol 226 (1) ◽  
pp. 204-243 ◽  
Author(s):  
Michael Dumbser ◽  
Martin Käser ◽  
Vladimir A. Titarev ◽  
Eleuterio F. Toro
Keyword(s):  
Finite Volume ◽  
Hyperbolic Systems ◽  
Unstructured Meshes ◽  
Finite Volume Schemes ◽  
Nonlinear Hyperbolic Systems

scholarly journals Well-balanced finite volume schemes for 2D non-homogeneous hyperbolic systems. Application to the dam break of Aznalcóllar

2008 ◽  
Vol 197 (45-48) ◽  
pp. 3932-3950 ◽  
Author(s):  
M.J. Castro Díaz ◽  
T. Chacón Rebollo ◽  
E.D. Fernández-Nieto ◽  
J.M. González Vida ◽  
C. Parés
Keyword(s):  
Finite Volume ◽  
Hyperbolic Systems ◽  
Dam Break ◽  
Finite Volume Schemes

scholarly journals Finite-volume schemes for shallow-water equations

Acta Numerica ◽  
2018 ◽  
Vol 27 ◽  
pp. 289-351 ◽  
Author(s):  
Alexander Kurganov
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Hyperbolic Systems ◽  
Bottom Topography ◽  
Water System ◽  
Problem Solver ◽  
Finite Volume Schemes ◽  
Upwind Schemes ◽  
Central Schemes

Shallow-water equations are widely used to model water flow in rivers, lakes, reservoirs, coastal areas, and other situations in which the water depth is much smaller than the horizontal length scale of motion. The classical shallow-water equations, the Saint-Venant system, were originally proposed about 150 years ago and still are used in a variety of applications. For many practical purposes, it is extremely important to have an accurate, efficient and robust numerical solver for the Saint-Venant system and related models. As their solutions are typically non-smooth and even discontinuous, finite-volume schemes are among the most popular tools. In this paper, we review such schemes and focus on one of the simplest (yet highly accurate and robust) methods: central-upwind schemes. These schemes belong to the family of Godunov-type Riemann-problem-solver-free central schemes, but incorporate some upwinding information about the local speeds of propagation, which helps to reduce an excessive amount of numerical diffusion typically present in classical (staggered) non-oscillatory central schemes. Besides the classical one- and two-dimensional Saint-Venant systems, we will consider the shallow-water equations with friction terms, models with moving bottom topography, the two-layer shallow-water system as well as general non-conservative hyperbolic systems.

scholarly journals Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics

2006 ◽  
Vol 51 (3) ◽  
pp. 205-228 ◽  
Author(s):  
Mária Lukáčová-Medviďová ◽  
Jitka Saibertová-Zatočilová
Keyword(s):  
Finite Volume ◽  
Hyperbolic Systems ◽  
Finite Volume Schemes
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