Research at FAST

98 Department of Applied Mathematics Department of Applied Mathematics Qualification BSc (Zhèngdà) MSc (Zhèngdà) PhD (HKBU) ORCID ID 0000-0002-0553-1404 Representative Publications • SIAM J. Numer. Anal., 57 ( 2019 ), pp. 875-898 • Math. Comp., 87 ( 2018 ), pp. 1859-1885 • J. Sci. Comput., 70 ( 2017 ), pp. 301-341 • SIAM J. Numer. Anal., 54 ( 2016 ), pp. 1653-1681 • SIAM J. Sci. Comput., 36 ( 2014 ), B708-B728 • SIAM J. Sci. Comput., 33 ( 2011 ), 1395-1414 Awards and Achievements • Departmental Best Paper Award, Department of Applied Mathematics, The Hong Kong Polytechnic University, 2019 • Hong Kong Mathematical Society Award for Young Scholars, The Hong Kong Mathematical Society, 2018 • The 2013 - 2014 Early Career Award, the Research Grants Council of Hong Kong Prof. QIAO Zhonghua Professor Research Overview Prof. Qiao’s primary interest is on the numerical investigation of nonlinear mathematical models of phase transition, which have become important and popular in many applications, e.g. multiphase flow problems, material science, biology, etc. Prof. Qiao made a systematical study on the numerical approximation for Cahn-Hilliard type equation, which is a key component of phase-field modeling. He has made remarkable improvement over previous works on the stability analysis of stabilized schemes for Cahn-Hilliard equation, which is the first successful attempt with a clean mathematical justification on numerical stability. He also developed an adaptive time-stepping algorithm based on the energy variation, which can greatly save CPU time without losing accuracy. Prof. Qiao applied his research on energy-stability-preserving numerical methods for numerical simulations of phase field models with a realistic Equation of State for hydrocarbon fluid in the petroleum industry. This work describes quantitative (rather than qualitative) behaviors of two phases with targeted application to petroleum fluids. It is expected that this new framework will have long impact in computational-engineering fields. Recently, Prof. Qiao focuses on developing high order structure preserving numerical schemes for phase field equations. It has been successfully used to solve non-local Allen-Cahn equations, which has important applications in material sciences. Intrinsic properties of these models could be preserved numerically, e.g. maximum bound principle, energy stability, etc. See figures below.