Four explicit finite difference schemes, including Lax-Friedrichs, Nessyahu-Tadmor, Lax-Wendroff and Lax-Wendroff with a nonlinear filter are applied to solve water hammer equations. The schemes solve the equations in a reservoir-pipe-valve with an instantaneous and gradual closure of the valve boundary. The computational results are compared with those of the method of characteristics (MOC), a...

Abstract This paper is devoted to the numerical analysis of non-smooth ensemble optimal control problems governed by Liouville (continuity) equation that have been originally proposed R.W. Brockett with purpose determining an efficient and robust strategy for dynamical systems. A methodology solving these presented based on a Lagrange optimization framework where controls are characterized as s...

The high-order accuracy of Fourier method makes it the method of choice in many large scale simulations. We discuss here the stability of Fourier method for nonlinear evolution problems, focusing on the two prototypical cases of the inviscid Burgers’ equation and the multi-dimensional incompressible Euler equations. The Fourier method for such problems with quadratic nonlinearities comes in two...

We present VAH, a (3+1)-dimensional simulation that evolves the far-from-equilibrium quark-gluon plasma produced in ultrarelativistic heavy-ion collisions with anisotropic fluid dynamics. solve hydrodynamic equations on an Eulerian grid using Kurganov-Tadmor algorithm combination new adaptive Runge-Kutta method. Our numerical scheme allows us to start soon after nuclear collision, largely avoid...

We are concerned with central differencing schemes for solving scalar hyperbolic conservation laws. We compare the Kurganov-Tadmor (KT) two-dimensional (Kurganov and Tadmor, 2000) second order semi-discrete central scheme in dimension by dimension formulation with a new two-dimensional approach introduced here and applied in numerical simulations for two-phase, two-dimensional flows in heteroge...

A spectral vanishing viscosity technique (SVV) is presented for the simulation of 3D turbulent incompressible flows within a rotor–stator cavity. One characteristic of this technique is that the SVV is active only for the short length scales, a feature which is reminiscent of Large Eddy Simulation models. The Spectral Vanishing Viscosity, first introduced by E. Tadmor for the inviscid Burgers e...

The aim of this paper is to present a streamlined and fully three-dimensional version of the quasicontinuum (QC) theory of Tadmor et al. [18, 19] and to analyze its accuracy and convergence characteristics. Specifically, we assess the effect of the summation rules on accuracy; we determine the rate of convergence of the method in the presence of strong singularities, such as point loads; and we...

The hydrodynamic limit of a kinetic Cucker-Smale flocking model is investigated. The starting point is the model considered in [17], which in addition to free-transport of individuals and a standard Cucker-Smale alignment operator, includes Brownian noise and strong local alignment. The latter was derived in [18] as the singular limit of an alignment operator first introduced by Motsch and Tadm...

We design efficient numerical schemes for approximating the MHD equations in multidimensions. Numerical approximations must be able to deal with the complex wave structure of the MHD equations and the divergence constraint. We propose schemes based on the genuinely multidimensional (GMD) framework of [S. Mishra and E. Tadmor, Commun. Comput. Phys. 9 (2010) 688–710; S. Mishra and E. Tadmor, SIAM...

Here, we indicate how to integrate the set of conservation equations for mass, momentum and energy for a two-fluid plasma coupled to Maxwell’s equations for the electromagnetic field, written in a composite conservative form, by means of a recently modified non-staggered version of the staggered second order central difference scheme of Nessyahu and Tadmor [H. Nessyahu, E. Tadmor, Non-oscillato...