scholarly journals On the wave-front tracking algorithm for 2×2 hyperbolic systems of conservation laws

2013 ◽  
Vol 397 (1) ◽  
pp. 172-181 ◽  
Author(s):  
Hiroki Ohwa
Keyword(s):  
Conservation Laws ◽  
Wave Front ◽  
Hyperbolic Systems ◽  
Front Tracking ◽  
Tracking Algorithm ◽  
Systems Of Conservation Laws ◽  
Wave Front Tracking

Local exact boundary controllability of entropy solutions to linearly degenerate quasilinear hyperbolic systems of conservation laws

2018 ◽  
Vol 24 (2) ◽  
pp. 793-810
Author(s):  
Tatsien Li ◽  
Lei Yu
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Systems ◽  
Front Tracking ◽  
Entropy Solutions ◽  
Exact Boundary Controllability ◽  
Boundary Controllability ◽  
Quasilinear Hyperbolic Systems ◽  
Exact Boundary ◽  
Systems Of Conservation Laws ◽  
Linearly Degenerate

In this paper, we study the local exact boundary controllability of entropy solutions to linearly degenerate quasilinear hyperbolic systems of conservation laws with characteristics of constant multiplicity. We prove the two-sided boundary controllability, the one-sided boundary controllability and the two-sided boundary controllability with fewer controls, by applying the strategy used in [T. Li and L. Yu, J. Math. Pures et Appl. 107 (2017) 1–40; L. Yu, Chinese Ann. Math., Ser. B (To appear)]. Our constructive method is based on the well-posedness of semi-global solutions constructed by the limit of ε-approximate front tracking solutions to the mixed initial-boundary value problem with general nonlinear boundary conditions, and on some further properties of both ε-approximate front tracking solutions and limit solutions.

BASIC ESTIMATES FOR A FRONT TRACKING ALGORITHM FOR GENERAL 2×2 CONSERVATION LAWS

2002 ◽  
Vol 12 (02) ◽  
pp. 155-182 ◽  
Author(s):  
F. ANCONA ◽  
A. MARSON
Keyword(s):  
Conservation Laws ◽  
Approximate Solutions ◽  
Front Tracking ◽  
Tracking Algorithm ◽  
Nonlinear Characteristic ◽  
Riemann Solvers ◽  
Systems Of Conservation Laws ◽  
Approximate Riemann Solvers

We analyze a front tracking algorithm for 2×2 systems of conservation laws with non-genuinely nonlinear characteristic fields. The convergence of the corresponding approximate Riemann solvers is established and the basic interaction estimates for the front tracking approximate solutions are provided.

Numerical Investigation of the Wave-Front Tracking Algorithm for the Full Ultra-Relativistic Euler Equations

2018 ◽  
Vol 19 (2) ◽  
pp. 223-229 ◽  
Author(s):  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Wave Front ◽  
Euler Equations ◽  
Numerical Test ◽  
Front Tracking ◽  
Euler System ◽  
Tracking Algorithm ◽  
Test Case ◽  
Test Cases ◽  
Relativistic Euler Equations ◽  
Wave Front Tracking

AbstractWe introduce a generalized version of the front tracking algorithm for the full ultra-relativistic Euler system. The construction and analysis of this algorithm are somewhat simpler than other algorithms. Moreover, this scheme leads to a more robust and efficient result. The scheme also satisfies positivity. This scheme is compared with other two schemes by two numerical test cases. Furthermore we give another application of this scheme, namely we check the explicit formula of interaction of two generalized shocks, by further numerical test case.

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
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