Inflow/outflows are an important class of problems in fluid dynamics and are widely encountered in computational science and engineering. They are typically associated with physically unbounded flow domains. In order to numerically simulate such problems it is necessary to truncate the domain to a finite size. Consequently, part of domain boundary will be open, in the sense that the fluids can freely leave (or even enter) the domain through such boundaries, and appropriate boundary conditions will be required on the open portions of the domain boundary. Backflow instability is a well-known issue associated with open boundaries at moderate and high Reynolds numbers.

This talk focuses on the open-boundary problem with multiphase flows containing two or more immiscible incompressible fluids in the system. We are particularly interested in situations where the fluid interfaces may pass through the open boundary. The design of effective techniques for treating such problems is quite challenging. One is confronted with several issues. Apart from the backflow instability, the presence of fluid interfaces on the open boundary and the density/viscosity contrasts between the fluids pose additional significant difficulties. In the case of three or more fluid components, the reduction consistency issue pose other constraints on the open boundary conditions. We will look into some of these issues. In particular I will present a set of energy-stable open boundary conditions, which turn out to be very effective in overcoming these challenges for simulating the dynamics of two-/multi-phase flows involving outflows or open boundaries. They are devised based on the energy stability property, in the sense that the contributions of these boundary conditions to the energy balance will not cause the total energy to increase over time, at least on the continuum level. We discuss the development of these boundary conditions and look into their numerical treatments. A number of numerical simulations with two-phase and three-phase flows involving inflow/outflow boundaries will be presented to demonstrate the performance of the method.

Suchuan Dong is a professor in the center for computational and applied mathematics, department of mathematics at Purdue University. He received his Bachelor's degree from the National University of Defense Technology, his Master's degree from Zhejiang University, and his PhD degree from the State University of New York at Buffalo. He did a post-doc at Brown University. He joined Purdue University in 2006 as an Assistant Professor, and then an Associate Professor (2011) and a Full Professor (2016). His research is in the broad area of computational fluid dynamics, in particular in the development of physically consistent models, high-order numerical methods and efficient algorithms, as well as their applications. In the past few years, his research interest has been in the modeling and computations of two-phase and multiphase problems, where the interactions among multiple fluid components and the fluid interfaces can play critical roles in the system dynamics.