# Applied/ACMS/absF16

## Contents

# 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.

### Michael Ferris (Madison)

*Fish, cows, fields of fuel and optimization*

We describe several applications of optimization modeling to address environmental constraints. At the core of these models are complex interacting physical, biological, social and economic systems. We show how spatial visualizations of the underlying decision spaces can expose critical features of the problem to the domain experts in ways that facilitate greater understanding of optimization tradeoffs. We will detail specific optimization models underlying three applications, including a nutrient managagement system (Anmods), a fish barrier removal project (Fishwerks), and a bio-energy game (Fields of fuel).

### Nick Moore (FSU)

*How bodies erode and dissolve in fluid flows*

A variety of landscapes are formed by the action of flowing fluids, either air or water. In these settings, the development of morphology is a reciprocal process: as a structure is carved by a fluid, its changing shape can alter the local flow. In the laboratory we can examine this coevolution of shape and flow by immersing erodible or soluble bodies in fast-flowing water. I will discuss a simplified Prandtl-based model that accounts for the vanishing rates and emergent shapes observed in the experiments. In particular, determining the terminal shape can be posed as a singular Riemann-Hilbert problem, and this analysis links the different processes of erosion, dissolution, and melting.