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) (Kurganov and Tadmor, 2000) semi-discrete central scheme with the Nessyahu-Tadmor (NT) (Nessyahu and Tadmor, 1990) central scheme. The KT scheme uses more precise information about the ...

Professor Eitan Tadmor turned 50 earlier this year. He is one of the most active and influential mathematicians in the area of numerical analysis, general theory of applied PDEs, and scientific computing. He has influenced the field of applied mathematics in many ways: through his deep and broad mathematical research, his strong efforts in advising, training, and mentoring young scientists, and...

1 Department of Mathematics, Institute for Physical Science & Technology and Center for Scientific Computation And Mathematical Modeling (CSCAMM), University of Maryland College Park, MD 20742-3289 [email protected] 2 Department of Mathematics University of California Davis, CA 95616 [email protected] “Hyperbolic Problems: Theory, Numerics, Applications”, Proceedings of the 9th Inter...

A prototype modular single screw extruder fitted with a screw extracting device is used to monitor melting of an immiscible polymer blend (PP/PA6, with different weight ratios) in this popular type of processing equipment. As anticipated, the observed phenomena are much more complex than those involved in extruding PP or PA6, when the well known Maddock/Tadmor mechanism is valid. Consequently a...

Kurganov and Tadmor have developed a numerical scheme for solving the initial value problem for hyperbolic systems of conservation laws. They showed that in the scalar case their scheme satisfies a local maximum–minimum principle i.e., the solution at future is bounded above and below by the solution at current locally. In this paper we show that this scheme is positive in the sense of Friedric...

We study the behavior of oscillatory solutions to convection-diffusion problems, subject to initial and forcing data with modulated oscillations. We quantify the weak convergence in W−1,∞ to the ’expected’ averages and obtain a sharp W−1,∞-convergence rate of order O(ε) – the small scale of the modulated oscillations. Moreover, in case the solution operator of the equation is compact, this weak...

Abstract. Among the efficient numerical methods based on atomistic models, the quasicontinuum (QC) method, introduced by Tadmor, Ortiz, and Phillips (1996), has attracted growing interest in recent years. Originally, the QC method was developed for materials with simple crystalline lattice (simple crystals) and later was extended to complex lattice (Tadmor et al, 1999). In the present paper we ...