A hybrid approach to the problem of predicting the dispersion of contaminants (e.g. suspended solids or heated water) in coastal areas is presented. A neutral random walk particle tracking method is adopted in the vicinity of the source point, where steep concentration gradients occur. In the case of heat dispersion particles are assigned with buoyancy, which leads to additive horizontal diffus...

The accurate simulation of the dynamics of polydisperse evaporating sprays in unsteady gaseous flows with large-scale vortical structures is both a crucial issue for industrial applications and a challenge for modeling and scientific computing. The difficulties encountered by the usual Lagrangian approaches make the use of Eulerian models attractive, aiming at a lower cost and an easier couplin...

A poset P is called k-Eulerian if every interval of rank k is Eulerian. The class of k-Eulerian posets interpolates between graded posets and Eulerian posets. It is a straightforward observation that a 2k-Eulerian poset is also (2k+1)-Eulerian. We prove that the ab-index of a (2k+1)Eulerian poset can be expressed in terms of c = a + b, d = ab + ba and e2k+1 = (a − b)2k+1. The proof relies upon ...

Abstract In this paper, we explore the interrelationship between Eulerian numbers and B splines. Specifically, using B splines, we give the explicit formulas of the refined Eulerian numbers, and descents polynomials. Moreover, we prove that the coefficients of descent polynomials D d (t) are logconcave. This paper also provides a new approach to study Eulerian numbers and descent polynomials.

The transport of fluid, heat ,and particles (bubbles and solid inclusions) in flowing molten steel is investigated in steel refining ladles, the continuous casting tundish, continuous casting mold and strand, and steel ingot casting processes. The two-equation k-ε model is used to simulate the turbulence. Multiphase fluid flow is numerically simulated with a Lagrangian-Eulerian approach, an Eul...

The linear Schrödinger equation with periodic potentials is an important model in solid state physics. The most efficient direct simulation using a Bloch decomposition based time-splitting spectral method [18] requires the mesh size to be O(ε) where ε is the scaled semiclassical parameter. In this paper, we generalize the Gaussian beam method introduced in [23] to solve this problem asymptotica...

An Eulerian multi-fluid model is validated by comparison with experimental measurements in the test case of laminar spray counterflow diffusion flames. Special attention is devoted, both from the modelling and experimental point of view, to the treatment of the droplet distribution tail, characterized by the rare occurrence of relatively large droplets carrying a non-negligible amount of mass. ...

In this paper we present further studies of recurrent configurations of Chip-firing games on Eulerian directed graphs (simple digraphs), a class on the way from undirected graphs to general directed graphs. A computational problem that arises naturally from this model is to find the minimum number of chips of a recurrent configuration, which we call the minimum recurrent configuration (MINREC) ...

Solid rocket motor flows depend strongly on alumina granulometry, which spreads up with coalescence. Solving droplet sizes in unsteady flows is a modeling and numerical challenge, specially when high loadings generate retrocoupling. As an alternative to Lagrangian approaches, the Eulerian Multi-Fluid model describes polydispersity with size-sorted droplet fluids called sections. A two size mome...