Research 

Computational Science and Mathematical Modeling Laboratory (CSMML)


My research has been on modeling and computation of soft matter and complex fluids with applications to complex fluid flows, complex biological systems, materials science and life science. Soft matter and complex fluids are ubiquitous in nature and in synthesized materials. Modeling and simulation of complex fluids has been listed as one of the 21st century mathematical challenges by DARPA. My group has also been conducting research on developing efficient and stable numerical methods for the partial differential equations arisen from modeling the complex systems.

My research focuses on developing the state-of-the-art mathematical and computational models, analysis as well as cutting-edge simulation tools to study the properties of the soft matter and complex fluids to gain deeper understanding of the fascinating phenomena. My research has been partially supported by grants from various state and federal funding agencies in the past 30 years.

Current Projects: 

1.     Numerical methods for thermodynamically consistent partial differential equations

2.     Fluid Dynamics and rheology of complex fluids, especially, flows of active liquid crystals, liquid crystals, phase transition, pattern formation and defect dynamics of liquid crystalline polymers.

3.     Non-equilibrium thermodynamics theories and analyses for polymer blends, multiphase complex fluids and flows.

4.     Multiscale theory, kinetic theory and continuum theory for flows of complex fluids and soft matter.

5.     Modeling and computation of ion transport in microscale channels.

6.     Modeling and computation of complex biological systems, complex biofluids (biofilms, biogels, liquid-liquid phase separation), and cellular dynamics (cell motility, migration, and fusion).

7.     Application of data science and machine learning in materials and life science

Research Laboratory: Computational Science and Mathematical Modeling Laboratory is located in the Sumwalt building on campus (SUM 103).

Computational Facilities: Our research is supported by a state-of-the-art midrange hybrid HPC node in the Hyperion hyper-performance compute cluster maintained by the university Research Computing Institute, which is equipped with state-of-the-art Tesla GPUs. Cuda, C, C++, Fortran, Open ACC compiler are available together with a plethora of software packages ranging from FLUENT, POLYFLOW, COMSOL, GAUSSIAN, Q-CHME, C^2FD (Computational Complex Fluid Dynamics, an in-house software package developed by my group) etc.

Recent Publications (last 5 years):

1.Xiaowen Shen and Qi Wang, Thermodynamically Consistent Algorithms for Models of Block Copolymer Solutions Interacting with Electric and Magnetic Fields, Journal of Scientific Computing, 2020.

2.Di Wang, Yongyong Cai and Qi Wang, Central Vortex Steady States and Dynamics of Bose-Einstein Condensates Interacting with Magnetic Fields. Physica D, in press, 2020.

3.Lin Lu, Qi Wang, Yongzhong Song, Yushun Wang, Local structure-preserving algorithms for the molecular beam epitaxy model with slope selection. Discrete and Continuous Dynamical System-B, in press, 2020.

4.Qi Hong, Jia Zhao and Qi Wang, Structure-preserving Numerical Approximations to Network Generating Partial Differential Equation Models, Computers and Mathematics with Applications, in press, 2020.

5.Qi Hong, Jun Li and Qi Wang, Supplementary Variable Method for Structure-Preserving Approximations to Partial Differential Equations with Deduced Equations. Applied Mathematics Letter, 110 (2020), 106576.

6.Cheng Lei, Yu Wang, Jia Zhao, Kexun Li, Hua Jiang and Qi Wang. A Patient Specific Predicative Model for Human Albumin Based on Deep Neural Networks. Computer Methods and Programs in Biomedicine, 196 (2020), 105555.

7.Shouwen Sun, Jun Li, Jia Zhao, and Qi Wang, Structure-Preserving Numerical Approximations to Thermodynamically Consistent Non-isothermal Models of Binary Viscous Fluid Flows. Journal of Scientific Computing, 83 (2020), 50.

8.Yuezheng Gong, Jia Zhao and Qi Wang. Arbitrarily high-order linear unconditionally energy stable schemes for gradient ow models. Journal of Computational Physics, 419 (2020), 109610.

9.Yuezheng Gong, Jia Zhao, Qi Wang, Arbitrarily high-order unconditionally energy stable SAV schemes for gradient flow models. Computer Physics Communications, 249 (2020), 107033.

10.Xueping Zhao, Tiezheng Qian and Qi Wang, Thermodynamically Consistent Hydrodynamic Models of Multi-component Fluid Flows, Communications in Mathematical Sciences, Vol. 18, No. 5 (2020), 1441-1468.

11.Xiaobo Jing and Qi Wang, Linear Second Order Energy Stable Schemes of Phase Field Models with Nonlocal Constraints for Crystal Growth. Computers & Mathematics with Applications, 79(3) (2020), 764-788.

12.Yuezheng Gong and Qi Wang and Jia Zhao. Arbitrarily High-Order Unconditionally Energy Stable Schemes for Thermodynamically Consistent Gradient Flow Models. Siam Journal on Scientific Computing. 42(1) (2020), B135-B156.

13.Yucan Zhao, Jun Li, Jia Zhao and Qi Wang, A Linear Energy and Entropy-production-rate Preserving Scheme for Thermodynamically Consistent Crystal Growth Models. Applied Mathematics Letters, 98, (2019), pp. 142-147.

14.Xueping Zhao and Qi Wang. A Second Order Fully-discrete Linear Unconditionally Energy Stable Numerical Scheme for Phase Field Models of Binary Compressible Fluid Flows. Journal of Computational Physics, 395 (2019), 382-409.

15.Xiaobo Jing, Jun Li, Xueping Zhao and Qi Wang. Second Order Linear Energy Stable Schemes for Allen-Cahn Equations with Nonlocal Constraints. Journal of Scientific Computing, 80 (1) (2019), 500-537.

16.Jun Li, Jia Zhao and Qi Wang. Structure Preserving Numerical Approximations of Thermodynamically Consistent Crystal Growth Models. Journal of Computational Physics, 382 (2019), pp. 202-220.

17.Xiaobo Jing, Xiangya Huang, Markus Haapasalo, Ya Shen and Qi Wang, Modeling Oral Multispecies Biofilm Recovery after Antibacterial Treatment, Scientific Reports. 9 (2019), pp. 804.

18.Shouwen Sun, Xiaobo Jing and Qi Wang, Error Estimates of Energy Stable Numerical Schemes for Allen-Cahn Equations with Nonlocal Constraints. Journal of Scientific Computing, Volume 79(1) (2019), pp. 593-623.

19.Xiaogang Yang, Jun Li, Yuezheng Gong, Robert S. Eisenberg, Qi Wang, Quasi-compressible Ionic Fluid Models, Journal of Molecular Liquids, 273 (2019), pp. 677-691.

20.Yuezheng gong, Jia Zhao, and Qi Wang, Second Order Fully-Discrete Energy Stable Methods on Staggered Grids for Hydrodynamic Phase Field Models of Binary Viscous Fluids, Siam Journal on Scientific Computing, 40:2, (2018), pp. B528-B553.

21.Jia Zhao, Xiaofeng Yang, Yuezheng Gong, Xueping Zhao, Jun Li, Xiaogang Yang and Qi Wang, A General Strategy for Numerical Approximations of Thermodynamically Consistent Nonequilibrium Models--Part I: Thermodynamical Systems, International Journal of Numerical Analysis and Modeling, 15(16) (2018), pp 884-918.

22.Xiaogang Yang, Yuezheng Gong, Jun Li, Jia Zhao, and Qi Wang, Comparison of Hydrodynamic Phase Field Models for Binary Fluid Mixtures, Theoretical and Computational Fluid Dynamics, 32(5) (2018), pp 537-560.

23.Yuezheng Gong, Jia Zhao, and Qi Wang, Linear Second Order in Time Energy Stable Schemes for Hydrodynamic Models of Binary Mixtures Based on a Spatially Pseudospectral Approximationadvances in Computational Mathematics, 44 (5) (2018), pp.1573-1600.

24.Yuezheng Gong, Jia Zhao, Xiaogang Yang and Qi Wang, Second-order Linear Schemes for Hydrodynamic Phase Field Models of Binary Viscous Fluids with Variable Densities, Siam Journal on Scientific Computing, 40-1 (2018), pp. B138-B167.

25.Jia Zhao and Qi Wang, 3-D Numerical Simulations of Biofilm Dynamics with Quorum Sensing in a Flow Cell, Bulletin of Mathematical Biology, 79(4) (2017), pp. 884-919.

26.Yi Sun and Qi Wang, In-Silico Analysis on 3D Biofabrication using Kinetic Monte Carlo Simulations, Advances in Tissue Engineering and Regenerative Medicine, 2(5) (2017), pp. 00045.

27.E. A. Bulanova, E. V. Koudan, J. Degosserie, C. Heymans, F. D. Pereira, V. A. Parfenov, Yi Sun, Qi Wang, S. A. Akhmedova , N. S. Sergeeva, G. A. Frank, Y. D. Khesuani, C. E. Pierreux, V. A. Mironov. Bioprinting of functional vascularized mouse thyroid gland construct, Biofabrication, 2017, 9(3), 034105.

28.Yuezheng Gong, Jia Zhao, and Qi Wang, An Energy Stable Algorithm for the Quasi-incompressible Hydrodynamic Model of Viscous Fluid Mixtures, Computer Physics Communications, 219 (2017), pp. 20-34.

29.Xiaofeng Yang, Jia Zhao, and Qi Wang, Linear and Unconditionally Energy Stable Schemes for Molecular Beam Epitaxial Growth Model Based on Invariant Energy Quadratization Methods, Journal of Computational Physics, 333 (2017), pp. 104-127.

30.Jia Zhao, Xiaofeng Yang, Yuezheng Gong, and Qi Wang, A Novel Linear Second Order Unconditionally Energy-stable Scheme for a Hydrodynamic Q-tensor Model of Liquid Crystals, Computer Methods in Applied Mechanics and Engineering, 318 (2017), pp. 803-825.

31.Xiaogang Yang and Qi Wang, Structures and basic patterns in cavity flows of active liquid crystals. Computers and Fluids, 155 (2017), pp. 33-49.

32.Xiaofeng Yang, Jia Zhao, Qi Wang, Jie Shen, Numerical Approximations for a three-component Cahn-Hilliard phase-field Model based on the Invariant Energy Quadratization method, Mathematical Models and Methods in Applied Sciences, 27(11) (2017), pp. 1993-2030.

33.Yuezheng Gong, Qi Wang, and Zhu Wang, Structure-Preserving Galerkin POD Reduced-Order Modeling of Hamiltonian Systems, Computer Methods in Applied Mechanics and Engineering, 315 (2017), pp. 780-798.

34.Xiaofeng Yang, Jia Zhao, and Qi Wang, Numerical Approximations for a phase field dendritic Growth Model Based on the Invariant Energy Quadratization Approach, International journal for Numerical Methods in Engineering, 110(3) (2017), pp. 279-300.

35.Jia Zhao, Huiyuan Li, Qi Wang, and Xiaofeng Yang, A Linearly Decoupled Energy Stable Scheme for Phase Field Models of Three-phase Incompressible Viscous Fluid Flows, Journal of Scientific Computing, 70(3) (2017), 1367-1389.

36.Jia Zhao, Tianyu Zhang, and Qi Wang, Treatment of Biofilms by Nanotechnology and Applications to Food Science, NANOTECHNOLOGY IN AGRICULTURE AND FOOD SCIENCES, edited by, Monique A. V. Axelos and Marcel Van de Voorde, Wiley-VCH, 2017.

37.Yuezheng Gong, Qi Wang, Yushun Wang, Jiaxiang Cai, A conservative Fourier pseudospectral method for the nonlinear Schrodinger equation, Journal of Computational Physics, 328 (2017), pp. 354-370.

38.Yuezheng Gong, Xinfeng Liu, and Qi Wang, Fully Discretized Energy Stable Schemes for Hydrodynamic Models of Two-phase Viscous Fluid Flows, Journal of Scientific Computing, 69(3) (2016), 921-945.

39.Norazaliza mohd Jamil and Qi Wang, CFD-PBE Modelling and Simulation of Enzymatic Hydrolysis of Cellulose in a Stirred Tank, Journal of Mathematics and Statistics, 12(4) (2016), pp. 225-237.

40.Jia Zhao, Qi Wang, and Xiaofeng Yang, Numerical Approximations to a New Phase Field Model for Immiscible Mixtures of Nematic Liquid Crystals and Viscous Fluids, Computer Methods in Applied Mechanics and Engineering, 310 (2016), pp. 77-97.

41.Jia Zhao, P. Seeluangsawat , and Qi Wang, A hydrodynamic model for biofilms accounting for persisters and susceptibles, Mathematics of Biosciences, 282 (2016), pp. 1-15.

42.Xiaogang Yang and Qi Wang, Role of Active Viscosity and Self-propelling Speed on Channel Flows of Active Polar Liquid Crystals, Soft Matter, 12 (2016), pp. 1262 - 1278.

43.Jia Zhao, Ya Shen, Markus Haapasalo, Zhejun Wang, and Qi Wang, A 3D Numerical Study of Antimicrobial Persistence in Heterogeneous Multi-species Biofilms, Journal of Theoretical Biology, 392 (2016), pp. 83-98.

44.Jia Zhao and Qi Wang, Semi-Discrete Energy-Stable Schemes for a Tensor-Based Hydrodynamic Model of Nematic Liquid Crystal Flows, Journal of Scientific Computing, 68(3) (2016), pp. 1241-1266.

45.Jia Zhao and Qi Wang, A 3D Hydrodynamic Model for Cytokinesis of Eukaryotic Cells, Communication in Computational Physics, 19(3) (2016), pp. 663-681.

46.Jia Zhao and Qi Wang, Modeling and Simulations of Cytokinesis of Eukaryotic Cells, International Journal for Numerical Methods in Biomedical Engineering, 32 (12) (2016), pp. e2774.

47.Xiaogang Yang, Jun Li, M. G. Forest, and Qi Wang, Hydrodynamic Theories for Flows of Active Liquid Crystals and the Generalized Onsager Principle, Entropy, 18 (2016), pp. 202.

48.Kapustina, M., Tsygankov, J., Zhao, J., Yang, X., Chen, A., Roach, N., Wessler, T., Elston, T.C., Wang, Q., Jacobson, K., Forest, G., Modeling the excess cell surface stored in a complex morphology of bleb-like protrusions. PLOS Computational Biology, 12(3) (2016), pp. e1004841.

49.Jia Zhao, Xiaofeng Yang, Jun Li and Qi Wang, Energy stable numerical schemes for a hydrodynamic model of nematic liquid crystals, Siam J. Sci. Comp., 38(5) (2016), pp. 3264-3290.

50.Ya Shen, Jia Zhao, Cesar de la Fuente-Nunez, Zhejun Wang, Robert E. W. Hancock, Clive R. Roberts, Jingzhi Ma, Jun Li, Markus Haapasalo and Qi Wang, Development and Experimental Validation of a Model for Oral Multispecies Biofilm Recovery after Chlorhexidine Treatment, Scientific Reports, 6 (2016), pp. 27537.

51.Noraza liza Mohd Jamil and Qi Wang, One-Dimensional Simulation of Diffusion and Advection Effects in Enzymatic Hydrolysis of Cellulose, American Journal of Applied Sciences. 13(7) (2016), pp. 870-876.

52.Jia Zhao, Xiaofeng Yang, Jie Shen, Qi Wang, A Decoupled Energy Stable Scheme for a Hydrodynamic Phase-field Model of Mixtures of Nematic Liquid Crystals and Viscous Fluids, Journal of Computational Physics, 305 (2016), pp. 539-556.