Second-order accurate upwind and centered schemes are presented in a framework that facilitates their analysis and comparison. The upwind scheme employed consists of a reconstruction step (Van Leer 1977) followed by an upwind step (Roe 1981). The two centered schemes are of Lax-Friedrichs (L-F) type. They are the nonstaggered versions of the N-T scheme (called ORD in Nessyahu-Tadmor 1990) and t...

The nonlinear shallow water equations (SWEs) are widely used to model the unsteady flows in rivers and coastal areas. In this work, we present a novel class of locally conservative, entropy stable well-balanced discontinuous Galerkin (DG) methods for equation with non-flat bottom topography. major novelty our work is use velocity field as an independent solution unknown DG scheme, which closely...

and we allow general boundary conditions. Solving PDEs of this generality is not routine and the success of our software is not assured. On the other hand, it is very easy to use and has performed well on a wide variety of problems. Explicit central finite difference methods are quite attractive for hyperbolic PDEs of this generality. We have implemented four: A two-step variant of the Lax-Frie...

During the recent decades there was an enormous amount of activity related to the construction and analysis of modern algorithms for the approximate solution of nonlinear hyperbolic conservation laws and related problems. To present some aspects of this successful activity, we discuss the analytical tools which are used in the development of convergence theories for these algorithms. These incl...

3-D kinematical conservation laws (KCL) are equations of evolution of a propagating surface Ωt in three space dimensions and were first derived in 1995 by Giles, Prasad and Ravindran [15] assuming the motion of the surface to be isotropic. We start with a brief introduction to 3-D KCL and mention some properties relevant to this paper. The 3-D KCL, a system of 6 conservation laws, is an under-d...

We give a brief account of the numerical radius of a linear bounded operator on a Hilbert space and some of its better-known properties. Both finiteand infinitedimensional aspects are discussed, as well as applications to stability theory of finite-difference approximations for hyperbolic initial-value problems. 1. DEFINITION, BOUNDS, AND EVALUATION Let H be a Hilbert space over the complex fie...

– The (21̄1̄)〈111〉 twinning energy landscape of BCC Mo is determined using the density functional theory for embryos containing 2 to 7 layers. The 2-layer embryo is metastable, whereas the 3and 4-layer ones are unstable. Layer-by-layer growth starts at 5 layers. The twin boundary formation and migration energies are found to be 607mJ/m and 40mJ/m, respectively, indicating that twin partial disloc...

Several models in mathematical physics are described by quasilin ear hyperbolic systems with source term which in several cases may become sti Here a suitable central numerical scheme for such problems is developed and application to shallow water equations Broadwell model and Extended Thermodynamics are mentioned The numerical methods are a generalization of the Nessyahu Tadmor scheme to the n...

The psychophysical task of discriminating changes in the slopes of the amplitude spectra of complex images has been used in the past to test whether the human visual system might be optimised for coding the spatial structure in natural images (e.g. Knill et al., 1990; Tadmor & Tolhurst, 1994). We have reported that the dependency of these discrimination thresholds on the reference slope has the...

We present a preliminary study of a new phenomena associated with the Euler-Poisson equations — the so called critical threshold phenomena, where the answer to questions of global smoothness vs. finite time breakdown depends on whether the initial configuration crosses an intrinsic, O(1) critical threshold. We investigate a class of Euler-Poisson equations, ranging from one-dimensional problems...