The entropy condition and the total variation boundedness of weak solutions of convex scalar conservation laws are enforced by Lip+-stability which the physical solutions satisfy. The first order Godunov and LaxFriedrichs schemes, and the second order Maxmod scheme are consistent with this Lip+-stability and are, therefore, entropy convergent. In this paper, a uniformly third order accurate sch...

Staggered grid finite volume methods (also called central schemes) were introduced in one dimension by Nessyahu and Tadmor in 1990 in order to avoid the necessity of having information on solutions of Riemann problems for the evaluation of numerical fluxes. We consider the general case in multidimensions and on general staggered grids which have to satisfy only an overlap assumption. We interpr...

We study theL1-stability and error estimates of general approximate solutions for the Cauchy problem associated with multidimensional Hamilton-Jacobi (H-J) equations. For strictly convex Hamiltonians, we obtain a priori error estimates in terms of the truncation errors and the initial perturbation errors. We then demonstrate this general theory for two types of approximations: approximate solut...

We discuss the reconstruction of piecewise smooth data from its (pseudo-) spectral information. Spectral projections enjoy superior resolution provided the data is globally smooth, while the presence of jump discontinuities is responsible for spurious O(1) Gibbs oscillations in the neighborhood of edges and an overall deterioration to the unacceptable rst-order convergence rate. The purpose is ...

We are concerned with central differencing schemes for solving scalar hyperbolic conservation laws arising in the simulation of multiphase flows in heterogeneous porous media. We compare the Kurganov-Tadmor (KT) [3] semi-discrete central scheme with the NessyahuTadmor (NT) [27] central scheme. The KT scheme uses more precise information about the local speeds of propagation together with integr...

Multiscale image registration techniques are presented for the registration of medical images using deformable registration models. The techniques are particularly effective for registration problems in which one or both of the images to be registered contains significant levels of noise. A brief overview of existing deformable registration techniques is presented, and experiments using B-splin...

For Runge–Kutta methods and linear multistep methods, much attention has been paid, in the literature, to special nonlinear stability properties indicated by the terms total-variationdiminishing (TVD), strong-stability-preserving (SSP), and monotonicity. Stepsize conditions, guaranteeing these properties, were studied, e.g., by Shu and Osher [J. Comput. Phys., 77 (1988), pp. 439–471], Gottlieb,...

Submitted for the DFD15 Meeting of The American Physical Society Proper Orthogonal Decomposition of Flow-Field in NonStationary Geometry VICTOR TROSHIN, School of Mechanical Engineering, faculty of Engineering, Tel Aviv University, AVRAHAM SEIFERT, TAU, DAVID SIDILKOVER, SOREQ NRC, GILEAD TADMOR, Northeastern — This work presents a proper orthogonal decomposition (POD) methodology for a flow fi...

A traction-displacement relationship that may be embedded into a cohesive zone model for microscale problems of intergranular fracture is extracted from atomistic molecular-dynamics simulations. A molecular-dynamics model for crack propagation under steady-state conditions is developed to analyze intergranular fracture along a flat Σ99 [1 1 0] symmetric tilt grain boundary in aluminum. Under hy...

The aim of this work is to solve hyperbolic conservation laws by means of a finite volume method for both spatial and time discretization. We extend the ideas developed in [X.-D. Liu and S. Osher, SIAM J. Numer. Anal., 33 (1996), pp. 760–779; X.-D. Liu and E. Tadmor, Numer. Math., 79 (1998), pp. 397–425] to fourth-order upwind and central schemes. In order to do this, once we know the cell-aver...