PhD, Applied and Computational Math, Florida State University

I am interested in the applied analysis of partial differential equations arising from fluid dynamics, as well as related numerical analysis and scientific computation. In particular, I am working on:

• Modeling, analysis, and, numerical simulations of multiphase flow by phase field approach and hybridizable discontinuous Galerkin methods;
• Mathematical analysis of Prandtl boundary layer theory; 
• Flow instability and dynamical transitions.

A unique feature of my research is the combination of rigorous mathematics with genuine physical applications. 

• Gang Chen, Daozhi Han, John Singler, Yangwen Zhang. On the superconvergence of a  hybridizable discontinuous Galerkin method for the Cahn-Hilliard equation, SIAM Journal on Numerical Analysis 61(2023) 83-109.
• Yali Gao,  Daozhi Han, Xiaoming He, Ulrich Rude. Unconditionally stable numerical methods for Cahn-Hilliard-Navier-Stokes-Darcy system with different densities and viscosities, Journal of Computational Physics 454 (2022),  110968.
• Guosheng Fu, Daozhi Han. A linear second-order in time unconditionally energy stable finite element scheme for a Cahn-Hilliard phase-field model for two-phase incompressible flow of variable densities, Comput. Methods Appl. Mech. Engrg. 387(2021), 114186.
• Jia Zhao, Daozhi Han. Second-order decoupled energy-stable schemes for Cahn-Hilliard-Navier-Stokes equations, Journal of Computational Physics 443(2021), Paper No. 110536.
• Daozhi Han, Marco Hernandez, Quan Wang. Dynamic transitions and bifurcations for a class of axisymmetric geophysical fluid flow, SIAM Applied Dynamical System 20(2021), 38–64.
• Makram Hamouda, Daozhi Han, Chang-Yeol Jung, Krutika Tawri, Roger Temam.  Boundary layers for  the 3D primitive equations in a cube: subcritical modes, Journal of Differential Equations 267(2019), 61-96.
• Wenbin Chen, Daozhi Han, Xiaoming Wang. Uniquely solvable and energy stable decoupled numerical schemes for the Cahn-Hilliard-Stokes-Darcy system for two-phase flows in karstic geometry, Numerische Mathematik 137(2017), 229-255.
• Daozhi Han, Xiaoming Wang. A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn-Hilliard-Navier-Stokes equation, J. Comput. Phys. 290(2015),139-156.
• Daozhi Han, Xiaoming Wang. Initial-boundary layer associated with the nonlinear Darcy-Brinkman system, Journal of Differential Equations 256(2014), 609-639.
  
• Daozhi Han, Anna L. Mazzucato, Dongjuan Niu, Xiaoming Wang. Boundary layer for a class of nonlinear pipe flow,  Journal of Differential Equations 252(2012), 6387-6413.