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In this paper we review and further develop a class of strong stability-preserving (SSP) high-order time discretizations for semidiscrete method of lines approximations of partial differential equations. Previously termed TVD (total variation diminishing) time discretizations, these high-order time discretization methods preserve the strong stability(More)
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)
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)
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)
Contents 1. Introduction and motivations 2 2. The hierarchical (BV, L 2) decomposition 3 2.1. The hierarchical decomposition 4 2.2. Convergence of the (BV, L 2) expansion 5 2.3. Initialization 8 2.4. A dual (BV, L 2) expansion 9 3. Examples of (BV, L 2) expansions 10 3.1. Hierarchical decomposition over IR 2 10 3.2. Hierarchical decomposition over bounded(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)
In this paper, we construct second-order central schemes for multidimensional Hamilton–Jacobi equations and we show that they are nonoscillatory in the sense of satisfying the maximum principle. Thus, these schemes provide the first examples of nonoscillatory second-order Godunov-type schemes based on global projection operators. Numerical experiments are(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)
The computations reported in this paper demonstrate the remarkable versatility of central schemes as black-box, Jacobian-free solvers for ideal magnetohydrodynamics (MHD) equations. Here we utilize a family of high-resolution, non-oscillatory central schemes for the approximate solution of the one-and two-dimensional MHD equations. We present simulations(More)
We discuss a general framework for recovering edges in piecewise smooth functions with finitely many jump discontinuities, where [f ](x) := f (x+) − f (x−) = 0. Our approach is based on two main aspects—localization using appropriate concentration kernels and separation of scales by nonlinear enhancement. To detect such edges, one employs concentration(More)