About Me

I am a PhD candidate in applied mathematics. I am working with professor Neil Balmforth. My research interest is fluid mechanics, including multiphase fluid dynamics, asymptotic analysis, numerical algorithms and analysis. I am also interested in solving problems by mathematical tool, such as graphical modeling.

My hobbies include coding and reading. I swim a lot in summer, while in winter I would do skating instead. I am willing to help people feel the beauty of math.

Teaching

Below are some of my past TA duties

2017: Mech 2 Computer Lab

2016W2: Math 215/255(Ordinary Differential Equations) Lab

2016W1: Math 184(Differential Calculus) Workshop

2015W2: Math 340(Linear Programming), Math 401(Green's Functions and Variational Methods)

2015W1: Math 340(Linear Programming), Math 405(Numerical Methods for Differential Equations)

Research

Non-Newtonian Fluid Mechanics

Most fluids have linear relations between its viscous stress and strain rate, which is called Newtonian fluid. Water, air, milk alcohol, thin motor oils are all examples of this. However, there are quite a number of fluids, such as ketchup, toothpaste, paint, blood, in which the relations are complicated. We call them Non-Newtonian fluid.

Collapse of Viscoplastic Fluid under Gravity

Viscoplastic fluid is a particular kind of Non-Newtonian fluid. The typical model of this kind of fluid is the Herschel-Bulkley model.

\tau = \tau_c+K\gamma^n

where \tau,\gamma,K are the stress, strain rate, and consistency, respectively. n is a scalar. \tau_c is called the yield stress. If the stress is less than \tau_c, there is no local deformation, thus the fluid would behave like solid. Therefore, the collapse of viscoplastic fluid will form some special final shape. We simplify this problem in a 2D geometry, and conduct both theoretical analysis and numerical simulations to solve this problem. Below is an example of the comparison.

Liu, Y., Balmforth, N.J., Hormozi, S. and Hewitt, D.R., Two–dimensional viscoplastic dambreaks, Journal of Non-Newtonian Fluid Mechanics, 2016 238(65–79)

Slump of Viscoplastic Fluid

We are also interested in viscoplastic collapse in an axisymmetrical geometry. The application of our numerical simulation is known as "slump test", used as a measurement of the rheology of fresh concrete.

Liu, Y., Balmforth, N.J. and Hormozi, S., Axisymmetric viscoplastic dambreaks and the slump test , Journal of Non-Newtonian Fluid Mechanics, 2018 258(45–57)

Steady Flow Regime on a Moving Slope

Flowing on an inclined conveyor belt, the fluid would approach an equilibrium state, under some circumstances. We are interested in its dynamics.

Computation Tools

Pelicans software platform is the major tool we are using to implement the algorithms for the numerical simulations. It is written in C++. A description of the code can be found here. We also use Gerris as a validation of our algorithms.

Contact Me

1984 Mathematic Rd,
Vancouver, V6T1Z2
778-919-7882
yliu0218@math.ubc.ca
My Github

Links

Department of Mathematics, UBC
Institute of Applied Mathematics, UBC
Fluid Lab, UBC