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ACMS Abstracts: Fall 2016

Nicolas Seguin (Universite Nantes)

Non-hydrostatic extension of classical shallow-water models

When modeling incompressible flows with a free surface, many situations are compatible with the so-called shallow-water assumption: the length of the domain is much larger than the average depth. Starting from the Navier-Stokes equations or the Euler equations for water flows with free surface, average processing or asymptotic analysis may lead to the Saint-Venant equations, which is a classical hyperbolic system of conservation laws. The goal of this talk is to go one step further, accounting for vertical effects. This leads to dispersive equations, such as the well-known Green–Naghdi model. Despite the change of nature of the equations, we will see that many properties are shared by the Saint-Venant equations and the Green–Naghdi equations.

Rich Kerswell (Bristol University)

Using optimization to reveal scaling laws in turbulent flows

In many fluid flow situations there is an a priori unknown global quantity, such as heat flux in convection or mass flux in pressure-driven flow, which is of overriding physical interest. Understanding how this quantity scales with the non-dimensional parameters describing the flow situation as one or more of these parameters become large (so that the flow is turbulent) is then a fundamental problem. In this talk, I will briefly review one particular approach to tackling this issue based upon optimization and then discuss how a variety of new developments augur well for future progress.

Yalchin Efendiev (TAMU)

A generalized multiscale model reduction technique for heterogeneous problems

In this talk, I will discuss multiscale model reduction techniques for problems in heterogeneous media. I will describe a framework for constructing local (space-time) reduced order models for problems with multiple scales and high contrast. I will focus on a recently proposed method, Generalized Multiscale Finite Element Method, that systematically constructs local multiscale finite element basis functions on a coarse grid, which is much larger than the underlying resolved fine grid. The multiscale basis functions take into account the fine-scale information of the resolved solution space via careful choices of local snapshot spaces and local spectral decompositions. I will discuss the issues related to the construction of multiscale basis functions, main ingredients of the method, and a number of applications. These methods are intended for multiscale problems without scale separation and high contrast.