[PDF] Top 20 Numerical Methods for the solution of Hyperbolic Conservation Laws

... words. Hyperbolic Conservation Laws, Riemann problem, Godunov’s method, van Leer’s method, limiter, Burgers’ equation 1 Introduction The mathematical description of many practical ... Voir le document complet

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... estimates for non-local scalar conservation laws Felisia Angela Chiarello 1 Paola Goatin 1 Elena Rossi 1 Abstract We prove the stability of entropy weak solutions of a class ... Voir le document complet

... weak solution of (1.1) is called an entropy satisfying solution if and only if the entropy inequality ...holds for any pair entropy-entropy flux (η, G). Integrating in space the ... Voir le document complet

... claim of uniqueness of the solution of ...(1.4). The initial-boundary value problem for hyperbolic systems of conservation laws is a very ... Voir le document complet

... applications of Galerkin projection to conservation laws include [13, 14, ...that the Galerkin pro- jection leads to a system of conservation laws governing the ... Voir le document complet

... order numerical approximations of the solutions of non- local conservation laws in one space dimension motivated by application to traffic flow and sedimentation ...evaluate ... Voir le document complet

... The C compatibility conditions at the point (t, x) = (0, L) are ...Review of the Literature and Open Problems Exact Boundary Controllability There are many publications concerning the ... Voir le document complet

... and the current adjoint weighted-ones, η adj κ , ...how the final mesh is refined along both discontinuites, giving a very good resolution for the both corresponding jumps, see figure ... Voir le document complet

... adapted numerical schemes to compute approximate solutions to such kind of ...evaluation of the conserved variables through a convolution product. First of all, we prove the ... Voir le document complet

... highlight the key aspects of the software implementation of wave front ...Go of Ram. The code was fully programmed in collaboration with Guillaume ...on the computa- tion ... Voir le document complet

... Abstract: The system of Maxwell equations describes the evolution of the interaction of an electromagnetic field with a propagation ...medium. The different properties ... Voir le document complet

... exact solution In this section we compare the calculated and exact solutions of two Riemann ...consider the following functions f (s, c) = s(4 − s)/(1 + c), a(c) = ...0 for all c and ... Voir le document complet

... is the numerical computation of γ ∈ Γ, µ > 0 and of a diagonal positive definite matrix Q such that Assumption 1 ...holds. The problem is bilinear in Q, γ and e −µ and the ... Voir le document complet

... equations of this type naturally appear in the kinetic formulation of hyperbolic systems of conservation laws: see for instance ...in the context of ... Voir le document complet

... Over the last decades, traffic congestion, car accidents and pollution became daily ...movement of traffic and minimal traffic ...to conservation laws, which are hyperbolic partial ... Voir le document complet

... The passage to the limit in this constraint is only possible in an indirect way, ...using the Green-Gauss formula (see ( 7 ) below). The situation is far more delicate if only weak ... Voir le document complet

... In the present section, we construct solutions of the conservation law ...via the vanishing diffusion method. We establish the existence of smooth solutions to a ... Voir le document complet

... is the nonuniqueness of weak ...from the way one fills the empty region by a ...at the underlying physical phenomena a concept of an ”Entropy” cri- terion is introduced which ... Voir le document complet

... method for the discretization of nonlinear hy- perbolic conservation laws posed on the two-dimensional ...sphere. The semi-discrete version of the proposed ... Voir le document complet