scholarly journals Numerical Scheme for a Viscous Shallow Water System Including New Friction Laws of Second Order: Validation and Application

2015 ◽  
pp. 227-239
Author(s):  
Olivier Delestre ◽  
Ulrich Razafison
Keyword(s):  
Shallow Water ◽  
Numerical Scheme ◽  
Water System ◽  
Second Order ◽  
Friction Laws ◽  
Shallow Water System

scholarly journals A simple well-balanced and positive numerical scheme for the shallow-water system

2015 ◽  
Vol 13 (5) ◽  
pp. 1317-1332 ◽  
Author(s):  
Emmanuel Audusse ◽  
Christophe Chalons ◽  
Philippe Ung
Keyword(s):  
Shallow Water ◽  
Numerical Scheme ◽  
Water System ◽  
Shallow Water System

WELL-BALANCED NUMERICAL SCHEMES BASED ON A GENERALIZED HYDROSTATIC RECONSTRUCTION TECHNIQUE

2007 ◽  
Vol 17 (12) ◽  
pp. 2055-2113 ◽  
Author(s):  
MANUEL J. CASTRO ◽  
ALBERTO PARDO MILANÉS ◽  
CARLOS PARÉS
Keyword(s):  
Shallow Water ◽  
Numerical Scheme ◽  
Source Term ◽  
Hyperbolic Systems ◽  
Water System ◽  
The Other ◽  
Reconstruction Technique ◽  
Numerical Schemes ◽  
Shallow Water System ◽  
The One

The goal of this paper is to generalize the hydrostatic reconstruction technique introduced in Ref. 2 for the shallow water system to more general hyperbolic systems with source term. The key idea is to interpret the numerical scheme obtained with this technique as a path-conservative method, as defined in Ref. 35. This generalization allows us, on the one hand, to construct well-balanced numerical schemes for new problems, as the two-layer shallow water system. On the other hand, we construct numerical schemes for the shallow water system with better well-balanced properties. In particular we obtain a Roe method which solves exactly every stationary solution, and not only those corresponding to water at rest.

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