There is widespread recognition of the growing importance of universities in a knowledge society and a competitive economy, and of their required role in stimulating growth through University-Industry-Government interaction. As Tadmor (2003, p.22) put it "[universities] can show the way, offer the solutions and produce the hardware to resolve the most crucial problems". While the education and ...

In this paper, we consider several high order schemes in one space dimension. In particular, we compare the second order relaxation (<<1) or "relaxed" (=0) schemes of Jin-Xin 4], with the second order Lax-Friedrichs scheme of Nessyahu-Tadmor 6], and with higher order ENO and WENO schemes. This comparison is rst made on Sod shock tube, and then on a very pathological example of a p-system constr...

We show the discrete lip+-stability for a relaxation scheme proposed by Jin and Xin [Comm. Pure Appl. Math., 48 (1995), pp. 235–277] to approximate convex conservation laws. Equipped with the lip+-stability we obtain global error estimates in the spaces W s,p for −1 ≤ s ≤ 1/p, 1 ≤ p ≤ ∞ and pointwise error estimates for the approximate solution obtained by the relaxation scheme. The proof uses ...

We study the stability of Runge-Kutta methods for the time integration of semidiscrete systems associated with time dependent PDEs. These semidiscrete systems amount to large systems of ODEs with the possibility that the matrices involved are far from being normal. The stability question of their Runge-Kutta methods, therefore, cannot be addressed by the familiar scalar arguments of eigenvalues...

Fluid-structure interaction (FSI) occurs when the dynamic water hammer forces; cause vibrations in the pipe wall. FSI in pipe systems due to Poisson and junction coupling has been the center of attention in recent years. It causes fluctuations in pressure heads and vibrations in the pipe wall. The governing equations of this phenomenon include a system of first order hyperbolic partial differen...

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...

We present three-dimensional central finite volume methods for solving systems of hyperbolic equations. Based on the Lax–Friedrichs and Nessyahu–Tadmor one-dimensional central finite difference schemes, the numerical methods we propose involve an original and a staggered grid in order to avoid the resolution of the Riemann problems at the cell interfaces. The cells of the original grid are Cart...

In this thesis, the following type Tikhonov regularization problem will be systematically studied: (ut, vt) := argmin u+v=f {‖v‖X + t‖u‖Y }, where Y is a smooth space such as a BV space or a Sobolev space and X is the space in which we measure distortion. Examples of the above problem occur in denoising in image processing, in numerically treating inverse problems, and in the sparse recovery pr...