## Research interests

**Computational and Applied Mathematics.**- Mathematical Modeling
- Numerical Analysis
- Scientific Computing
- Applications to Soft Matter/Complex Fluids/BioCell Dynamics.

## Grants

**NSF Grant (PI) DMS-2309731, $246,734, Aug. 2023-Jul. 2026.****NSF Grant (PI) DMS-2012490, $135,000, Aug. 2020-Aug. 2024.**- NSF Grant (PI) DMS-1818783, $57,185, Aug. 2018-Aug. 2021.
- NSF Grant (PI) DMS-1720212, $159,996, Aug. 2017-Aug. 2020.
- NSF Grant (PI) DMS-1418898, $100,000, Aug. 2014-Aug. 2017.
- NSF Grant (co-PI) DMS-1200487, $591,213, Aug. 2012-Aug. 2017.
- AFOSR Grant (co-PI) FA9550-12-1-0178, $405,000, Aug. 2012-Aug. 2016.
- ARO Grant (co-PI), W911NF-09-1-0389, $225,000, 2009-2012.
- USC ASPIRE I Fund (PI), $14,905, Jul. 2022-Jul. 2023.
- USC ASPIRE I Fund (PI), $15,000, Jul. 2018-Jul. 2019.
- USC ASPIRE I Track-I Fund (PI), $14,924, Aug. 2012-Aug. 2013.
- SC EPSCOR GEAR-CI (co-PI), $75,000, Aug. 2013-Aug. 2014.
- SC EPSCOR GEAR (co-PI), $50,000, Aug. 2012-Aug. 2013.
- SC EPSCOR GEAR (co-PI), $85,000, Aug. 2011-Aug. 2012.

## Selected Publications List

- Disclaimer: The copyright for these papers belongs to the publisher of the journal. The papers may be downloaded for personal use only. Any other use requires prior permission of the author and the publisher.
**Ranking of World's Top 2% Scientists by Stanford**---**2022,****2021,****2020,****2019****Ranking of World's Top 100,000 Scientists by www.globalauthorid.com****Most Cited Citations by Years of Ph.D. Degree (based on citation data from MathSciNet)****(Scopus);****(ResearchGate);****(Mathscinet)****Google Scholar ------ Full Publication List**- G.-D. Zhang, X. He, and X. Yang. A unified framework of the SAV-ZEC method for a mass-conserved Allen-Cahn type two-phase ferrofluid flow model, SIAM Journal on Scientific Computing (
**SISC**), 46:B77-B106, 2024. - Q. Pan, Y. Huang, T. Rabczuk and X. Yang. The subdivision-based IGA-EIEQ numerical scheme for the Navier-Stokes equations coupled with Cahn-Hilliard phase-field model of two-phase incompressible flow on complex curved surfaces, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 424:116901, 2024. - Q. Pan, Y. Huang, C. Chen, X. Yang, and Y. J. Zhang. The subdivision-based IGA-EIEQ numerical scheme for the Cahn-Hilliard-Darcy system of two-phase Hele-Shaw flow on complex curved surfaces, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 420:116709, 2024. - G. Zou, B. Wang and X. Yang. Efficient Linear, Fully-decoupled and unconditionally energy-stable Discontinuous Galerkin scheme with second-order temporal accuracy for the magneto-hydrodynamic system, Journal of Computational Physics (
**JCP**), 495:112562, 2023. - Q. Pan, C. Chen, T. Rabczuk, J. Zhang and X. Yang, Subdivision-based IGA Coupled EIEQ Method for the Cahn-Hilliard Phase-Field Model of Homopolymer Blends on Complex Surfaces, Computer-Aided Design (
**CAD**), 164:103589, 2023. - S. Zeng, Z. Xie, J. Wang and X. Yang. Fully Discrete, Decoupled And Energy-stable Fourier-Spectral Numerical Scheme For the Nonlocal Cahn-Hilliard Equation Coupled With Navier-Stokes/Darcy Flow Regime of Two-phase Incompressible Flows, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 415:116289, 2023. - G.-D. Zhang and X. Yang. Error estimates with low-order polynomial dependence for the fully-discrete finite element Invariant Energy Quadratization scheme of the Allen-Cahn Equation, Mathematical Models and Methods in Applied Sciences (
**M3AS**), 33:2463-2505, 2023. - G.-D. Zhang, X. He, and X. Yang. Reformulated Weak Formulation and Efficient Fully-Discrete Finite Element Method for a Two-Phase Ferrohydrodynamics Shliomis Model, SIAM Journal on Scientific Computing (
**SISC**), 45:B253-B282, 2023. - Q. Pan, J. Zhang, T. Rabczuk, C. Chen and X. Yang, Numerical Algorithms of Subdivision-based IGA-EIEQ method for the Molecular Beam Epitaxial Growth Models on Complex Surfaces, Computational Mechanics (
**CM**), 72:927-948, 2023. - C. Chen and X. Yang, Efficient fully-decoupled and fully-discrete Explicit-IEQ numerical algorithm for the two-phase incompressible flow-coupled Cahn-Hilliard phase-field model, Science China Mathematics (
**SCM**), http://engine.scichina.com/doi/10.1007/s11425-022-2096-x, 2023. - G. Zou, Z. Li and X. Yang, Fully discrete discontinuous Galerkin numerical scheme with second-order temporal accuracy for the hydrodynamically coupled lipid vesicle model, Journal of Scientific Computing (
**JSC**), 95:5, 2023. - Q. Pan, C. Chen, T. Rabczuk, J. Zhang and X. Yang, The Subdivision-based IGA-EIEQ numerical Scheme for the Binary surfactant Cahn-Hilliard model on Complex curved Surfaces, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 406:115905, 2023. - Q. Pan, C. Chen, Y. Zhang and X. Yang, A novel hybrid IGA-EIEQ numerical method for the Allen-Cahn/Cahn-Hilliard equations on complex curved surfaces, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 404:115767, 2023. - X. Yang. Efficient linear, fully-decoupled and energy stable numerical scheme for a variable density and viscosity, volume-conserved, hydrodynamically coupled phase-field elastic bending energy model of lipid vesicles, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 400:115479, 2022. - C. Chen and X. Yang. Fully-decoupled, energy stable second-order time-accurate and finite element numerical scheme of the binary immiscible Nematic-Newtonian model, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 395:114963, 2022. - X. Yang and X. He. A fully-discrete decoupled finite element method for the conserved Allen-Cahn type phase-field model of three-phase fluid flow system, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 389:114376, 2022. - X. Yang and X. He. Numerical approximations of flow coupled binary phase field crystal system: Fully discrete finite element scheme with second-order temporal accuracy and decoupling structure, Journal of Computational Physics (
**JCP**), 467:111448, 2022. - C. Chen and X. Yang. A Second-order time accurate and fully-decoupled numerical scheme of the Darcy-Newtonian-Nematic model for two-phase complex fluids confined in the Hele-Shaw cell, Journal of Computational Physics (
**JCP**), 456:111026, 2022. - G.-D. Zhang, X. He, and X. Yang. A fully decoupled linearized finite element method with second-order temporal accuracy and unconditional energy stability for incompressible MHD equations, Journal of Computational Physics (
**JCP**), 448:110752, 2022. - G. Zou, B. Wang, and X. Yang, A fully-decoupled discontinuous Galerkin
approximation and optimal error estimate of the Cahn-Hilliard-Brinkman-Ohta-Kawasaki tumor growth model, ESAIM: Mathematical Modelling and Numerical Analysis (
**M2AN**), 56:2141-2180, 2022. - X. Yang. Fully-discrete, decoupled, second-order time-accurate and energy stable finite element numerical scheme of the Cahn-Hilliard binary surfactant model confined in the Hele-Shaw cell, ESAIM: Mathematical Modelling and Numerical Analysis (
**M2AN**), 56:651-678, 2022. - C. Chen and X. Yang. Highly efficient and unconditionally energy stable semi-discrete time-marching numerical scheme for the two-phase incompressible flow phase-field system with variable-density and viscosity, Science China Mathematics (
**SCM**), 65:2631-2656, 2022. - J. Wang, K. Pan and X. Yang. Convergence Analysis of the Fully Discrete Hybridizable
Discontinuous Galerkin Method for the Allen-Cahn Equation
Based on the Invariant Energy Quadratization Approach, Journal of Scientific Computing (
**JSC**), 91:49, 2022. - X. Yang. On a novel fully-decoupled, second-order accurate energy stable numerical scheme for a binary fluid-surfactant phase-field model, SIAM Journal on Scientific Computing (
**SISC**), 43:B479-B507, 2021. - G-D. Zhang, X. He, and X. Yang. Decoupled, linear, and unconditionally energy stable fully-discrete finite element numerical scheme for a two-phase ferrohydrodynamics model, SIAM Journal on Scientific Computing (
**SISC**), 43:B167-B193, 2021. - X. Yang. Efficient and Energy Stable scheme for the hydrodynamically coupled three components Cahn-Hilliard phase-field model using the stabilized-Invariant Energy Quadratization (S-IEQ) Approach,Journal of Computational Physics (
**JCP**), 438:110342, 2021. - X. Yang. A novel fully-decoupled, second-order time-accurate, unconditionally energy stable scheme for a flow-coupled volume-conserved phase-field elastic bending energy model, Journal of Computational Physics (
**JCP**), 432:110015, 2021.

- X. Yang. Efficient, second-order in time, and energy stable scheme for a new hydrodynamically coupled three components volume-conserved Allen-Cahn phase-field model, Mathematical Models and Methods in Applied Sciences (
**M3AS**), 31(4):753-787, 2021. - X. Yang. A novel decoupled second-order time marching scheme for the two-phase incompressible Navier-Stokes/Darcy coupled nonlocal Allen-Cahn model, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 377:113597, 2021. - X. Yang. A new efficient Fully-decoupled and Second-order time-accurate scheme for Cahn-Hilliard phase-field model of three-phase incompressible flow, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 376:13589, 2021.

- X. Yang. Numerical approximations of the Navier-Stokes equation coupled with volume-conserved multi-phase-field vesicles system: fully-decoupled, linear, unconditionally energy stable and second-order time-accurate numerical scheme, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 375:113600, 2021.

- X. Yang. A novel fully-decoupled, second-order and energy stable numerical scheme of the conserved Allen-Cahn type flow-coupled binary surfactant model, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 373:113502, 2021. - X. Yang. On a novel full decoupling, Linear, Second-order accurate, and unconditionally energy stable numerical scheme for the anisotropic phase-field dendritic crystal growth model, International Journal for Numerical Methods in Engineering (
**IJNME**), 122:4129-4153, 2021. - X. Yang. A novel fully-decoupled scheme with second-order time accuracy and unconditional energy stability for the Navier-Stokes equations coupled with mass-conserved Allen-Cahn phase-field model of two-phase incompressible flow, International Journal for Numerical Methods in Engineering (
**IJNME**), 122:1283-1306, 2021. - X. Yang. Fully-discrete spectral-Galerkin scheme with decoupled structure and second-order time accuracy for the anisotropic phase-field dendritic crystal growth model, International journal of Heat and Mass transfer (
**IJHMT**), 180:121750, 2021. - G.-D. Zhang and X. Yang. Efficient and stable schemes for the magnetohydrodynamic potential model, Communication in Computational Physics (
**CICP**), 30:771-798, 2021. - Q. Pan, T. Rabczuk and X. Yang. Subdivision-based Isogeometric Analysis for Second Order Partial Differential Equations on Surfaces, Computational Mechanics (
**CM**), 68:1205-1221, 2021. - C. Chen and X. Yang. Fully-discrete finite element numerical scheme with decoupling structure and energy stability for the Cahn-Hilliard phase-field model of two-phase incompressible flow system with variable density and viscosity, ESAIM: Mathematical Modelling and Numerical Analysis (
**M2AN**), 55:2323, 2021. - X. Yang. On a novel fully-decoupled, linear and Second-order accurate numerical scheme for the Cahn-Hilliard-Darcy System of two-phase Hele-Shaw flow, Computer physics Communication (
**CPC**), 263:107868, 2021. - C. Chen, J. Zhang and X. Yang, Efficient numerical scheme for a new hydrodynamics-coupled conserved Allen-Cahn type Ohta-Kawaski phase-field model for Diblock Copolymer Melt, Computer Physics Communication (
**CPC**), 256:107418, 2020. - Z. Xu, X. Yang, and H. Zhang, Error analysis of a decoupled, linear stabilization scheme for the Cahn-Hilliard model of two-phase incompressible flows, Journal of Scientific Computing (
**JSC**), 83:57, 2020. - X. Yang and G-D. Zhang, Convergence Analysis for the Invariant Energy Quadratization (IEQ) Schemes for Solving the Cahn-Hilliard and Allen-Cahn Equations with General Nonlinear Potential, Journal of Scientific Computing (
**JSC**), 82:55, 2020. - J. Shen and X. Yang, The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems. Contemporary Mathematics (
**CM**), 754:217--245, 2020. - J. Zhang and X. Yang, A fully decoupled, linear and unconditionally energy stable numerical scheme for a melt-convective phase-field dendritic solidification model, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 363:112779, 2020. - J. Zhang and X. Yang, Unconditionally Energy Stable Large time stepping method for the L2-gradient flow based ternary Phase-Field model with precise nonlocal volume conservation, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 361:112743, 2020. - J. Zhang and X. Yang, Efficient and accurate numerical scheme for a magnetic-coupled phase-field-crystal model for ferromagnetic solid materials, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 371:113110, 2020. - J. Zhang, C. Chen, J. Wang and X. Yang, Efficient, Second order accurate, and unconditionally energy stable numerical scheme for a new hydrodynamics coupled binary phase-field surfactant system, Computer Physics Communications (
**CPC**), 251:107122,2020. - J. Zhang and X. Yang, Efficient second order Unconditionally Stable time marching numerical scheme for a modified phase-field crystal model with a strong nonlinear vacancy potential, Computer Physics Communications (
**CPC**), 245:106860, 2019. - J. Zhang and X. Yang, Numerical approximations for a new L2-gradient flow based Phase field crystal model with precise nonlocal mass conservation, Computer Physics Communications, 243:51-67 (
**CPC**), 2019. - Z. Xu, X. Yang, H. Zhang and Z. Xie, Efficent and linear schemes for anisotropic Cahn-Hilliard equations using the stabilized Invariant Energy Quadratization (S-IEQ) approach, Computer Physics Communications (
**CPC**), 238:36-49, 2019. - X. Yang and J. Zhao, Efficient Linear Schemes for the Nonlocal Cahn-Hilliard Equation of Phase Field Models, Computer Physics Communications (
**CPC**), 235:234-245, 2019. - J. Yang, S. Mao, X. He, X. Yang, and Y. He, A diffuse interface model and semi-implicit energy stable finite element method for two-phase magneto-hydrodynamic flows, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 356:435-464, 2019. - X. Yang, Efficient Linear, stabilized, second order time marching schemes for an anisotropic phase field dendritic crystal growth model, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 347:316–339, 2019. - C. Chen, and X. Yang, Fast, provably unconditionally energy stable, and second-order accurate algorithms for the anisotropic Cahn-Hilliard Model, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 351:35-59, 2019. - G-D. Zhang, X. He, and X. Yang, A Decoupled, linear and uncondition- ally energy stable scheme with finite element discretizations for magneto-hydrodynamic equations, Journal of Scientific Computing (
**JSC**), 81:1678-1711, 2019. - C. Chen and X. Yang, Efficient Numerical Scheme for a dendritic Solidification Phase Field model with melt convection, Journal of Computational Physics (
**JCP**), 388:41-62, 2019. - Q. Cheng, J. Shen and X. Yang, Highly efficient and accurate numerical schemes for the epitaxial thin film growth models by using the SAV approach, Journal of Scientific Computing (
**JSC**), 78:1467-1487, 2019. - X. Yang and J. Zhao, On Linear and Unconditionally Energy Stable Algorithms for Variable Mobility Cahn-Hilliard Type Equation with Logarithmic Flory-Huggins Potential, Communications in Computational Physics (
**CICP**), 25:703-728, 2019. - X. Yang, Numerical Approximations for the Cahn-Hilliard phase field model of the binary fluid-surfactant system, 74(3):1533-1553, Journal of Scientific Computing (
**JSC**), 2018. - X. Yang and H. Yu, Efficient Second Order Unconditionally Stable Schemes for a Phase Field Moving Contact Line Model Using an Invariant Energy Quadratization Approach, SIAM. Journal on Scientific Computing (
**SISC**),40(3): B889--B914, 2018. - Y. Gao, X. He, L. Mei and X. Yang, Decoupled, Linear, and Energy Stable Finite Element Method for the Cahn-Hilliard-Navier-Stokes-Darcy Phase Field Model, SIAM. Journal on Scientific Computing (
**SISC**), 40(1): B110–B137, 2018. - Q. Cheng,X. Yang and J. Shen, Efficient and accurate numerical schemes for a
hydro-dynamically coupled phase field diblock copolymer
model, Journal of Computational Physics (
**JCP**), 341:44–60, 2017. - H. Yu and X. Yang, Numerical approximations for a phase-field moving contact line model with variable densities and viscosities, Journal of Computational Physics (
**JCP**), 334: 665-686, 2017. - X. Yang, J. Zhao and Q. Wang, Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method, Journal of Computational Physics (
**JCP**), 333:104-127, 2017. - X. Yang and D. Han, Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model, Journal of Computational Physics (
**JCP**), 330:1116-1134, 2017. - J. Zhao, X. Yang, Y. Gong and Q. 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 (
**CMAME**), 318:803-825, 2017. - X. Yang and L. Ju, Linear and Unconditionally Energy Stable Schemes for the binary Fluid-Surfactant Phase field Model, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 318:1005-1029, 2017. - X. Yang and L. Ju, Efficient linear schemes with unconditional energy stability for the phase field elastic bending energy model, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 315:691--712, 2017. - R. Chen, X. Yang and H. Zhang, Second Order, Linear, and Unconditionally Energy Stable Schemes for a Hydrodynamic Model of Smectic-A Liquid Crystals, SIAM. Journal on Scientific Computing (
**SISC**), 39(6): A2808-A2833, 2017. - D. Han, A. Brylev, X. Yang and Z. Tan, Numerical Analysis of Second Order, Fully Discrete Energy Stable Schemes for Phase Field Models of Two-Phase Incompressible Flows, Journal of Scientific Computing (
**JSC**), 70(3):965-989, 2017. - J. Zhao, H. Li, Q. Wang and X. Yang, Decoupled Energy Stable Schemes for a Phase Field Model of Three-Phase Incompressible Viscous Fluid Flow, Journal of Scientific Computing (
**JSC**), 70(3): 1367-1389, 2017. - J. Zhao, Q. Wang and X. Yang, Numerical approximations for a phase field dendritic crystal growth model based on the invariant energy quadratization approach, International Journal for Numerical Methods in Engineering (
**IJNME**), 110(3): 279-300, 2017. - X. Yang, J. Zhao, Q. Wang and J. 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 (
**M3AS**), 27(11), 1993-2030, 2017. - L. Ma, R. Chen, X. Yang and H. Zhang, Numerical Approximations for Allen-Cahn type Phase field model of two-phase incompressible fluids with Moving Contact Lines, Communications in Computational Physics (
**CICP**), 21(3): 867-889, 2017. - J. Zhao, X. Yang, J. Li, and Q. Wang, Energy Stable Numerical Schemes for a Hydrodynamic Model of Nematic Liquid Crystals, SIAM. Journal on Scientific Computing (
**SISC**), 38(5):A3264--A3290, 2016. - X. Yang, Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends, Journal of Computational Physics (
**JCP**), 327:294-316, 2016 - J. Zhao, X. Yang, J. Shen and Q. 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 (
**JCP**), 305(15), 539--556, 2016. - J. Zhao, Q. Wang and X. Yang, Numerical approximations to a new phase field model for two phase
flows of complex fluids, Computer Methods in Applied Mechanics and Engineering (
**CMAME**), 310:77--97, 2016. - M. Kapustina, D.Tsygakov, J. Zhao, J. Wessler, X. Yang, A. Chen, N. Roach, T. C. Elston, Q.Wang, K. Jacobson and M. G. Forest, Modeling the excess cell surface stored in a complex morphology of bleb-like protrusions, PLOS Computational Biology, 12(3):e1004841, 2016.
- R. Chen, G. Ji, X. Yang and H. Zhang, Decoupled energy stable schemes for phase-field vesicle membrane model, Journal of Computational Physics (
**JCP**), 302:509--523, 2015. - J. Shen, X. Yang and H. Yu, Efficient energy stable numerical schemes for a phase field moving contact line model, Journal of Computational Physics (
**JCP**), 284: 617--630, J2015. - J. Shen and X. Yang, Decoupled, Energy Stable Schemes for Phase-Field Models of Two-Phase Incompressible Flows, SIAM Journal on Numerical Analysis (
**SINUM**), 53:279--296, 2015. - C. Liu, J. Shen and X. Yang, Decoupled Energy Stable Schemes for a Phase-Field
Model of Two-Phase Incompressible Flows with Variable
Density, Journal of Scientific Computing (
**JSC**), 62:601--622, 2015. - J. Shen and X. Yang, Decoupled Energy Stable Schemes for Phase-Field Models of Two-Phase Complex Fluids, SIAM. Journal on Scientific Computing (
**SISC**), 36:B122--B145, 2014. - Y. Sun, X. Yang and Q. Wang, In-silico analysis on biofabricating vascular networks using kinetic Monte Carlo simulations, Biofabrication, 6:015008, 2014. (IF: 11.061)
- X. Yang, M. G. Forest, H. Li, C. Liu, J. Shen, Q. Wang and F. Chen, Modeling and simulations of drop pinch-off from liquid crystal filament and the leaky liquid crystal faucet immersed in viscous fluids, Journal of Computational Physics (
**JCP**), 236: 1--14, 2013. - J. Shen, X. Yang, Q. Wang, Mass and Volume Conservation in Phase Field
Models for Binary Fluids, 13: 1045--1065, Communications in Computational Physics (
**CICP**), 2013. - J. Shen and X. Yang, A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities, SIAM. Journal on Scientific Computing (
**SISC**), 32(3):1159--1179, 2010. - J. Shen and X. Yang, Numerical Approximations of Allen-Cahn and Cahn-Hilliard Equations, Discrete & Continuous Dynamical Systems (
**DCDS**), 28:1669--1691, 2010. - X. Yang, M. G. Forest, W. Mullins and Q. Wang, Dynamic defect morphology and hydrodynamics of sheared nematic polymers in two space dimensions, Journal of Rheology (
**JoR**), 53(3): 589--615, 2009. - J. Shen and X. Yang, An efficient moving mesh spectral method for the phase-field model of two-phase flows, Journal of Computational Physics (
**JCP**), 228: 2978--2992, 2009. - J. L. Guermond, J. Shen and X. Yang, Error analysis of fully discrete velocitycorrection methods for incompressible flows, Mathematics of Computation (
**Math. Comp.**), 77:1387--1405, 2008. - X. Yang, Z. Cui, M. G. Forest, Q. Wang and J. Shen, Dimensional Robustness & Instability of Sheared, Semi-Dilute, Nano-Rod Dispersions, SIAM. Multiscale Modeling and Simulation, 7:622-654, 2008.
- C. Liu, J. Shen and X. Yang, Dynamics of defect motion in nematic liquid crystal flow: modeling and numerical simulation, Communications in Computational Physics (
**CICP**), 2:1184--1198, 2007. - X. Yang, J. J. Feng, C. Liu and J. Shen, Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method, Journal of Computational Physics (
**JCP**), 218:417--428, 2006.