scholarly journals Flux difference splitting for hyperbolic systems of conservation laws with source terms

1993 ◽  
Vol 26 (7) ◽  
pp. 79-96 ◽  
Author(s):  
P. Glaister
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Systems ◽  
Source Terms ◽  
Systems Of Conservation Laws ◽  
Flux Difference

A WELL-BALANCED SCHEME USING NON-CONSERVATIVE PRODUCTS DESIGNED FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS WITH SOURCE TERMS

2001 ◽  
Vol 11 (02) ◽  
pp. 339-365 ◽  
Author(s):  
LAURENT GOSSE
Keyword(s):  
Asymptotic Behavior ◽  
Conservation Laws ◽  
Euler Equations ◽  
Hyperbolic Systems ◽  
Zero Order ◽  
Inhomogeneous System ◽  
Source Terms ◽  
First Order ◽  
Systems Of Conservation Laws ◽  
The Right

The aim of this paper is to present a new kind of numerical processing for hyperbolic systems of conservation laws with source terms. This is achieved by means of a non-conservative reformulation of the zero-order terms of the right-hand side of the equations. In this context, we decided to use the results of Dal Maso, Le Floch and Murat about non-conservative products, and the generalized Roe matrices introduced by Toumi to derive a first-order linearized well-balanced scheme in the sense of Greenberg and Le Roux. As a main feature, this approach is able to preserve the right asymptotic behavior of the original inhomogeneous system, which is not an obvious property. Numerical results for the Euler equations are shown to handle correctly these equilibria in various situations.

scholarly journals On the uniqueness of solutions to hyperbolic systems of conservation laws

2021 ◽  
Vol 291 ◽  
pp. 110-153
Author(s):  
Shyam Sundar Ghoshal ◽  
Animesh Jana ◽  
Konstantinos Koumatos
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Systems ◽  
Uniqueness Of Solutions ◽  
Systems Of Conservation Laws

High-order relaxation approaches for adjoint-based optimal control problems governed by nonlinear hyperbolic systems of conservation laws

2016 ◽  
Vol 24 (1) ◽  
Author(s):  
Elimboto M. Yohana ◽  
Mapundi K. Banda
Keyword(s):  
Optimal Control ◽  
Conservation Laws ◽  
Optimal Control Problems ◽  
Initial Conditions ◽  
Hyperbolic Systems ◽  
Control Problems ◽  
Computational Investigation ◽  
Backward Problem ◽  
Systems Of Conservation Laws ◽  
The Cost

AbstractA computational investigation of optimal control problems which are constrained by hyperbolic systems of conservation laws is presented. The general framework is to employ the adjoint-based optimization to minimize the cost functional of matching-type between the optimal and the target solution. Extension of the numerical schemes to second-order accuracy for systems for the forward and backward problem are applied. In addition a comparative study of two relaxation approaches as solvers for hyperbolic systems is undertaken. In particular optimal control of the 1-D Riemann problem of Euler equations of gas dynamics is studied. The initial values are used as control parameters. The numerical flow obtained by optimal initial conditions matches accurately with observations.

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