## Numerical Analysis Seminar

Date: December 6, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Chris Kees, Coastal and Hydraulics Laboratory, US Army ERDC

Title: A two-scale computational framework for air-water-sediment dynamics

Abstract: A better understanding of sediment erosion and deposition processes is critical to the mission of the US Army Corps of Engineers. Long-term engineering of the Mississippi river, beach nourishment projects for coastal communities, and design of levees, breakwaters, and dunes for flood and storm protection all turn on the interaction of fluids with granular materials. Hunter Rouse, the father of modern hydraulics'' wrote in 1939 that, neither mathematical tools nor physical understanding of their use can be considered sufficiently far advanced to cope with so intricate a problem at the present time''. Today, the state of practice in computational modeling of sediment dynamics still relies heavily on empirical relationships. In recent decades, however, much progress has been made on the development of numerical methods capable of obtaining qualitatively correct solutions of fluid-grain dynamics at the microscale and on thermodynamically correct averaging methods to obtain practical computational models at the macroscale. This presentation will describe a combination of level set and immersed boundary methods for simulating microscale air-water-solid dynamics, averaging methods for deriving a 3D air-water-sediment model, and an incremental projection scheme for the three-phase Navier-Stokes system that arises at the macroscale.