A well-balanced path conservative SPH scheme for nonconservative hyperbolic systems with applications to shallow water and multi-phase flows

2017 ◽  
Vol 154 ◽  
pp. 102-122 ◽  
Author(s):  
Giulia Rossi ◽  
Michael Dumbser ◽  
Aronne Armanini
Keyword(s):  
Shallow Water ◽  
Hyperbolic Systems ◽  
Multi Phase ◽  
Nonconservative Hyperbolic Systems

Central Schemes for Nonconservative Hyperbolic Systems

2012 ◽  
Vol 34 (5) ◽  
pp. B523-B558 ◽  
Author(s):  
M. J. Castro ◽  
Carlos Parés ◽  
Gabriella Puppo ◽  
Giovanni Russo
Keyword(s):  
Hyperbolic Systems ◽  
Central Schemes ◽  
Nonconservative Hyperbolic Systems

scholarly journals Nonconservative hyperbolic systems in fluid mechanics

2018 ◽  
Vol 64 ◽  
pp. 1-16
Author(s):  
Denise Aregba-Driollet ◽  
Stéphane Brull ◽  
Xavier Lhébrard
Keyword(s):  
Kinetic Model ◽  
Magnetic Fields ◽  
Fluid Mechanics ◽  
Numerical Approximation ◽  
Hyperbolic Systems ◽  
Euler System ◽  
Kinetic Approach ◽  
Nonconservative Hyperbolic Systems

This paper is devoted to the numerical approximation of nonconservative hyperbolic systems. More precisely, we consider the bitemperature Euler system and we propose two methods of discretization. The first one is a kinetic approach based on an underlying kinetic model. The second one deals with a Suliciu approach when magnetic fields are taken into account.

Path-conservative central-upwind schemes for nonconservative hyperbolic systems

2019 ◽  
Vol 53 (3) ◽  
pp. 959-985 ◽  
Author(s):  
Manuel Jesús Castro Díaz ◽  
Alexander Kurganov ◽  
Tomás Morales de Luna
Keyword(s):  
Hyperbolic Systems ◽  
Bottom Topography ◽  
Nonlinear Partial Differential Equations ◽  
Water System ◽  
Upwind Scheme ◽  
One Dimensional ◽  
Upwind Schemes ◽  
Shallow Water System ◽  
Nonconservative Hyperbolic Systems ◽  
Very High

We develop path-conservative central-upwind schemes for nonconservative one-dimensional hyperbolic systems of nonlinear partial differential equations. Such systems arise in a variety of applications and the most challenging part of their numerical discretization is a robust treatment of nonconservative product terms. Godunov-type central-upwind schemes were developed as an efficient, highly accurate and robust ``black-box’’ solver for hyperbolic systems of conservation and balance laws. They were successfully applied to a large number of hyperbolic systems including several nonconservative ones. To overcome the difficulties related to the presence of nonconservative product terms, several special techniques were proposed. However, none of these techniques was sufficiently robust and thus the applicability of the original central-upwind schemes was rather limited. In this paper, we rewrite the central-upwind schemes in the form of path-conservative schemes. This helps us (i) to show that the main drawback of the original central-upwind approach was the fact that the jump of the nonconservative product terms across cell interfaces has never been taken into account and (ii) to understand how the nonconservative products should be discretized so that their influence on the numerical solution is accurately taken into account. The resulting path-conservative central-upwind scheme is a new robust tool for both conservative and nonconservative hyperbolic systems. We apply the new scheme to the Saint-Venant system with discontinuous bottom topography and two-layer shallow water system. Our numerical results illustrate the good performance of the new path-conservative central-upwind scheme, its robustness and ability to achieve very high resolution.

Two-Dimensional Compact Third-Order Polynomial Reconstructions. Solving Nonconservative Hyperbolic Systems Using GPUs

2011 ◽  
Vol 48 (1-3) ◽  
pp. 141-163 ◽  
Author(s):  
José M. Gallardo ◽  
Sergio Ortega ◽  
Marc de la Asunción ◽  
José Miguel Mantas
Keyword(s):  
Hyperbolic Systems ◽  
Two Dimensional ◽  
Third Order ◽  
Order Polynomial ◽  
Nonconservative Hyperbolic Systems

scholarly journals High Order Extensions of Roe Schemes for Two-Dimensional Nonconservative Hyperbolic Systems

2008 ◽  
Vol 39 (1) ◽  
pp. 67-114 ◽  
Author(s):  
M. J. Castro ◽  
E. D. Fernández-Nieto ◽  
A. M. Ferreiro ◽  
J. A. García-Rodríguez ◽  
C. Parés
Keyword(s):  
Hyperbolic Systems ◽  
High Order ◽  
Two Dimensional ◽  
Nonconservative Hyperbolic Systems
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