Dr Zhenquan Li's areas of expertise are in the fields of mathematical modelling, computational science and neural networks. His current research interest focuses on the applications of the adaptive mesh refinement methods he proposed based on the qualitative theory of differential equations. The accuracy and reliability of the methods have been verified by some test benchmarks. These methods can be applied to any mathematical models containing continuity equation for steady flow or incompressible fluid. In our daily life, the methods can be used to investigate any water or air flows with speed less than 370km per hour.
External Appointments & Memberships
Member of Society for Industrial and Applied Mathematics (SIAM).
Member of Australian Mathematical Society (Aus MS)
Peer Reviewed Papers
Li, Z., Wood, R., (2017) Accuracy verification of a 2D adaptive mesh refinement method for incompressible or steady flow. Journal of Computational and Applied Mathematics, 318: 259–265.
Li, Z. (2017) Computational complexity of the algorithm for a 2D adaptive mesh refinement method using lid-driven cavity flows. Computational Thermal Sciences, 9: 395-403
Li, Z., Wood, R. (2017) Accuracy verification of a 2D adaptive mesh refinement method for incompressible or steady flow, Journal of Computational and Applied Mathematics. 318: 259–265. http://www.sciencedirect.com/science/article/pii/S0377042716304423
Lal, R., Li, Z., (2015) Sensitivity analysis of a mesh refinement method using the numerical solutions of 2D lid-driven cavity flow. Journal of Mathematical Chemistry, 53, 844-867. DOI: 10.1007/s10910-014-0461-7
Li, Z., Wood, R., (2015) Accuracy analysis of an adaptive mesh refinement method using benchmarks of 2-D steady incompressible lid-driven cavity flows and coarser meshes. Journal of Computational and Applied Mathematics, 275 262–271.
Li, Z., (2014) Accuracy analysis of a mesh refinement method using benchmarks of 2-D lid-driven cavity flows and finer meshes. Journal of Mathematical Chemistry, 52, 1156-1170. DOI: 10.1007/s10910-014-0334-0
Mungkasi, S., Li, Z., Roberts, S., (2014) Weak local residuals as smoothness indicators for the shallow water equations. Applied Mathematics Letters, 30, 51-55.
Li, Z., (2012) A Mass Conservative Streamline Tracking Method using Dual Stream Functions over Tetrahedral Domains. Visualization of Mechanical Process, 4(2), DOI: 10.1615/VisMechProc.2013003332.
Li, Z. (2017) CFD Analysis of 2D Unsteady Flow Past a Square Cylinder at Low Reynolds Numbers. 2017 International Conference Applied Mathematics, Computational Science and Systems Engineering in Athens, Greece, Oct 6-8. http://doi.org/10.1051/itmconf/20181602003
PIT tag data analysis project. Huang, X., Baumgartner, L., and Li, J.(2018-2019) Karltek Pty Ltd., $25,000
Applications of adaptive meshless methods in environmental problems (ongoing)
An implementation of adaptive mesh refinement method in C++ (ongoing)
Expert review of hydraulic models of locks 7,8 and 9 vertical slot fishways, (2016) Li, J. MDBA, $3600
An implementation of a two-dimensional finite volume method for refined meshes in Matlab (2015 - 2016)
A new computational method for fluid flow (2000 – 2015)