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Keywords: Entropy viscosity Conservation laws Euler equations Finite elements Spectral elements Fourier method Godunov schemes Central schemes a b s t r a c t A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of(More)
A new class of Godunov-type numerical methods for solving nonlinear scalar conservation laws in one space dimension is introduced. This new class of methods , called weakly non-oscillatory (WNO), is a generalization of the classical non-oscillatory schemes. Under certain conditions, convergence and error estimates for the methods are proved. Examples of(More)
The T2K experiment has observed electron neutrino appearance in a muon neutrino beam produced 295 km from the Super-Kamiokande detector with a peak energy of 0.6 GeV. A total of 28 electron neutrino events were detected with an energy distribution consistent with an appearance signal, corresponding to a significance of 7.3σ when compared to 4.92±0.55(More)
We discover that the choice of a piecewise polynomial reconstruction is crucial in computing solutions of nonconvex hyperbolic (systems of) conservation laws. Using semi-discrete central-upwind schemes we illustrate that the obtained numerical approximations may fail to converge to the unique entropy solution or the convergence may be so slow that achieving(More)
The T2K experiment observes indications of ν(μ) → ν(e) appearance in data accumulated with 1.43×10(20) protons on target. Six events pass all selection criteria at the far detector. In a three-flavor neutrino oscillation scenario with |Δm(23)(2)| = 2.4×10(-3)  eV(2), sin(2)2θ(23) = 1 and sin(2)2θ(13) = 0, the expected number of such events is 1.5±0.3(syst).(More)
We discuss an extension of the Jiang–Tadmor and Kurganov–Tadmor fully-discrete non-oscillatory central schemes for hyperbolic systems of conservation laws to unstructured triangular meshes. In doing so, we propose a new, ''genuinely multidimensional, " non-oscillatory reconstruction—the minimum-angle plane reconstruction (MAPR). The MAPR is based on the(More)
This paper focuses on the notion of suitable weak solutions for the three-dimensional incompressible Navier–Stokes equations and discusses the relevance of this notion to Computational Fluid Dynamics. The purpose of the paper is twofold (i) to recall basic mathematical properties of the three-dimensional in-compressible Navier-Stokes equations and to show(More)
This paper proposes an explicit, (at least) second-order, maximum principle satisfying , Lagrange finite element method for solving nonlinear scalar conservation equations. The technique is based on a new viscous bilinear form introduced in Guermond and Nazarov [Com-put. a high-order entropy viscosity method, and the Boris–Book–Zalesak flux correction(More)