Daozhi Han

PhD

Daozhi Han.

Daozhi Han

PhD

Daozhi Han

PhD

Assistant Professor

Research Interests

Applied mathematics, numerical analysis, PDEs, fluid dynamics

Education

PhD, Applied and Computational Math, Florida State University

Research

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. 

Selected Publications

  • 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.