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Many of the recently developed high-resolution schemes for hyperbolic conservation laws are based on upwind diierencing. The building block of these schemes is the averaging of an approximate Godunov solver; its time consuming part involves the eld-by-eld decomposition which is required in order to identify the \direction of the wind." Instead, we propose(More)
Central schemes may serve as universal finite-difference methods for solving non-linear convection–diffusion equations in the sense that they are not tied to the specific eigenstructure of the problem, and hence can be implemented in a straightforward manner as black-box solvers for general conservation laws and related equations governing the spontaneous(More)
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We study the entropy stability of difference approximations to nonlinear hy-perbolic conservation laws, and related time-dependent problems governed by additional dissipative and dispersive forcing terms. We employ a comparison principle as the main tool for entropy stability analysis, comparing the entropy production of a given scheme against properly(More)
Let u(x; t) be the possibly discontinuous entropy solution of a nonlinear scalar conservation law with smooth initial data. Suppose u"(x; t) is the solution of an approximate viscosity regularization, where " > 0 is the small viscosity amplitude. We show that by post-processing the small viscosity approximation u", we can recover pointwise values of u and(More)
We consider the 2 x 2 hyperbolic system of isentropic gas dynamics, in both Eulerian or Lagrangian variables (also called the p-system). We show that they can be reformulated as a kinetic equation, using an additional kinetic variable. Such a formulation was first obtained by the authors in the case of multidimensional scalar conservation laws. A new(More)
The central scheme of Nessyahu and Tadmor [J. 408–463] solves hyperbolic conservation laws on a staggered mesh and avoids solving Riemann problems across cell boundaries. To overcome the difficulty of excessive numerical dissipation for small time steps, the recent work of Kurganov and Tadmor [J. employs a variable control volume, which in turn yields a(More)
ROSENAO [R] has recently proposed a regularized version of the Chapman-Enskog expansion of hydrodynamics. This regularized expansion resembles the usual Navier-Stokes viscosity terms at low wave numbers, but unlike the latter, it has the advantage of being a bounded macroscopic approximation to the linearized collision operator. In this paper we study the(More)
We construct, analyze, and implement a new nonoscillatory high-resolution scheme for two-dimensional hyperbolic conservation laws. The scheme is a predictor-corrector method which consists of two steps: starting with given cell averages, we first predict pointvalues which are based on nonoscillatory piecewise-linear reconstructions from the given cell(More)