Publications
2022
A Modified Crank-Nicolson Numerical Scheme for the Flory-Huggins Cahn-Hilliard Model, Wenbin Chen; Jianyu Jing; Cheng Wang; Xiaoming Wang*; Steven M. Wise, Commun. Comput. Phys., 2022, 31(1)：60-93.doi: 10.4208/cicp.OA-2021-0074.
2021
Conservative unconditionally stable decoupled numerical schemes for the Cahn-Hilliard-Navier-Stokes-Darcy-Boussinesq system, Wenbin Chen, Daozhi Han, Xiaoming Wang*, Yichao Zhang, Numerical Methods for Partial Differential Equations, 10 September 2021, doi:10.1002/num.22841.
Energy stable ETD-MS methods for gradient flows, Wenbin Chen, Shufen Wang, Xiaoming Wang*, CSIAM Transaction, September 2021.doi:10.4208/csia m-am.2020-0033.
Stokes-Darcy system, small Darcy number behavior, and related interfacial conditions, Wenqi Lyu, Xiaoming Wang*, Journal of Fluid Mechanics, 922, A4. 02. July 2021.
Error estimate of a decoupled numerical scheme for the Cahn-Hilliard-Stokes-Darcy system, Wenbin Chen, Daozhi Han*, Cheng Wang, Shufen Wang, Xiaoming Wang, Yichao Zhang, IMA Numer Analysis, 23 June 2021.
Global weak solutions to the Navier--Stokes--Darcy--Boussinesq system for thermal convection in coupled free and porous media flows, Xiaoming Wang* and Hao Wu, Advances in Differential Equations, Volume 26, Number 1-2 (2021), 1-44.
2020
Dynamic transitions and bifurcations for thermal convection in the superposed free flow and porous media, Daozhi Han, Quan Wang, Xiaoming Wang*, Physica D, Volume 414, 15 December 2020.
Vanishing porosity limit of the coupled Stokes-Brinkman system, Mingwen Fei, Dongjuan Niu, and Xiaoming Wang, Journal of Mathematical Analysis and Applications, Vol. 486, no. 2, June 15 2020.
Uniquely solvable, energy stable decoupled numerical scheme for the Cahn-HilliardNavier-Stokes-Darcy-Boussinesq system, Wenbin Chen, Daozhi Han*, Xiaoming Wang, Yichao Zhang, Journal of Scientific Computing, 85, Paper No. 45, 04 November 2020.
Energy stable numerical schemes for ternary Cahn-Hilliard systems, Wenbin Chen, Cheng Wang*, Shufen Wang, Xiaoming Wang, Journal of Scientific Computing, 20 July 2020.
Energy stable higher-order linear ETD multi-step methods for gradient flows: application to thin fifilm epitaxy, Wenbin Chen, Weijia Li, Cheng Wang, Xiaoming Wang*, Majda 70th birthday issue, Res Math Sci 7, 29 June 2020, 13 (2020).
Vanishing porosity limit of the coupled Stokes-Brinkman system, Mingwen Fei, Dongjuan Niu, and Xiaoming Wang*, Journal of Mathematical Analysis and Applications, Vol. 486, no. 2, June 15 2020.
A stabilized second order exponential time differencing multistep method for thin film growth model without slope selection, Wenbin Chen, Weijia Li, Zhiwen Luo, Cheng Wang*, and Xiaoming Wang, ESAIM: Mathematical Modelling and Numerical Analysis, Volume 54, Number 3, May-June 2020, Page(s) 727 - 750.
2019
Convection in a Coupled Free Flow-Porous Media System, Matthew McCurdy, Matthew Nick Moore, Xiaoming Wang, SIAM Journal on Applied Mathematics, 79(6), 2313-2339, 2019.
Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential, Wenbin Chen, Cheng Wang*, Xiaoming Wang* and Steven Wise, Jour. Comp. Phys. X, vol.3, June 2019.
A second order BDF numerical scheme with variable steps for the Cahn-Hilliard equation, Wenbin Chen, Xiaoming Wang*, Yue Yan and Zhuying Zhang, SIAM Jour. Num. Anal., 57-1 (2019), pp. 495-525.
2018
A Second Order in Time, Decoupled, Unconditionally Stable Numerical Scheme for the Cahn-Hilliard-Darcy System, Daozhi Han* and Xiaoming Wang, J. Scientific Comp., 77(2), 1210–1233, 2018, DOI 10.1007/s10915-018-0748-0.
2017
Uniquely solvable and energy stable decoupled numerical schemes for the Cahn-Hilliard-Stokes-Darcy system for two-phase flows in karstic geometry, Wenbin Chen, Daozhi Han, and Xiaoming Wang, Numer. Math., accepted January, 2017. DOI:10.1007/s00211-017-0870-1.
Convergence Analysis and Error Estimates for a Second Order Accurate Finite Element Method for the Cahn-Hilliard-Navier-Stokes System, Amanda Diegel, Cheng Wang, Xiaoming Wang, and Steven Wise, Numer. Math., accepted March 2017. DOI 10.1007/s00211-017-0887-5
2016
An efficient and long-time accurate third-order algorithm for the Stokes-Darcy system, Wenbin Chen, Max Gunzburger, Dong Sun, and Xiaoming Wang, Numer.Math. (2016) 134(4), 857-879, DOI: 10.1007/s00211-015-0789-3.
Numerical algorithms for stationary statistical properties of dissipative dynamical systems, an invited paper dedicated to Prof. Peter Lax on the occasion of his 90th birthday, Discrete Continuous Dyn Syst Ser A, vol. 36 no.8, pp. 4599-4618, August 2016.
Initial boundary layer associated with the nonlinear Darcy-Brinkman-Oberbeck-Boussinesq system, Mingwen Fei, Daozhi Han, and Xiaoming Wang. Physica D, published online Aug. 2016. DOI: 10.1016/j.physd.2016.08.002
2015
Long-time dynamics of 2D double-diffusive convection: analysis and/or numerics, Florentina Tone, Xiaoming Wang, and Djoko Wirosoetisno. Numer. Math., July 2015, vol. 130, no.3, pp. 541-566,
A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn-Hilliard-Navier-Stokes equation, Daozhi Han and Xiaoming Wang, J. Comp. Phys., (2015), pp. 139-156.
2014
A linear iteration algorithm for a second-order energy stable scheme for a thin film model without slope selection, Wenbin Chen, Cheng Wang, Xiaoming Wang and Steven Wise, J. Sci. Comp., vol. 59 (3), 2014, 574-601.
Initial Boundary Layer Associated with the Nonlinear Darcy-Brinkman System, Daozhi Han and Xiaoming Wang, Jour. Diff. Eqn., Volume 256, Issue 2, 15 January 2014, Pages 609-639.
Two phase flows in karstic geometry, Daozhi Han, Dong Sun and Xiaoming Wang, Mathematical Methods in the Applied Sciences, Vol. 37, no.18, pages 3048-3063, Nov. 2014.
Existence and uniqueness of global weak solutions to a Cahn-Hilliard-Stokes-Darcy system for two phase incompressible flows in karstic geometry, Daozhi Han, Xiaoming Wang, and Hao Wu, Jour. Diff. Eqn., vol.257, no. 10, Nov. 2014, pp.3887-3933.
2013
Well-posedness of the Hele-Shaw-Cahn-Hilliard system, Xiaoming Wang and Zhifei Zhang, Annales de l’Institut Henri Poincaré (C) Analyse Non Linéaire., Volume 30, Issue 3, May and June 2013, Pages 367-384.
A bound on the vertical transport of heat in the ultimate state of slippery convection at large Prandtl numbers, Xiaoming Wang and Jared Whitehead, Journal of Fluid Mechanics, Volume 729 / August 2013, pp 103-122.
Efficient and long-time accurate second order schemes for the Stokes-Darcy system, Wenbin Chen, Max Gunzburger, Dong Sun, and Xiaoming Wang, SIAM J. Numer. Anal. 51-5 (2013), pp. 2563-2584.
2012
Experimental and computational validation and verification of the Stokes-Darcy and continuum pipe flow models for karst aquifers with dual porosity structure, Bill Hu, Xiaoming Wang, Max Gunzburger, Fei Hua and Yanzhao Cao, Hydrological Processes. Volume 26, Number 13, 30 June 2012 , pp. 2031-2040(10).
Long time stability of a classical efficient scheme for two dimensional Navier–Stokes equations, Sigal Gottlieb, Florentina Tone, Cheng Wang, Xiaoming Wang and Djoko Wirosoetisno, SIAM J. Numer. Anal. vol. 50, pp. 126-150, 2012.
Second-order convex splitting schemes for gradient flows with Enhrich-Schwoebel type energy: application to thin film epitaxy, Jie Shen, Cheng Wang, Xiaoming Wang and Steven Wise, SIAM J. Numer. Anal. vol. 50, no.1, pp.105-125, 2012.
Calibrating the exchange coefficient in the modified coupled continuum pipe-flow model for flow in karst aquifers, Nan Chen, Max Gunzburger, Bill Hu, Xiaoming Wang and Celestine Woodruff, J. Hydrology, 414-415 (2012) 294-301.
Boundary Layer for a Class of Nonlinear Pipe Flow, Daozhi Han, Anna Mazuccato, Dongjuan Niu and Xiaoming Wang, Jour. Diff. Equations., Volume 252, Issue 12, 15 June 2012, Pages 6387-6413. DOI:10.1016/j.jde.2012.02.012.
An efficient second order in time scheme for approximating long time statistical properties of the two dimensional Navier-Stokes equations, Xiaoming Wang, Numer. Math., Volume 121, Issue 4 (2012), Page 753-779.
Long-time Behavior for the Hele-Shaw-Cahn-Hilliard System, Xiaoming Wang and Hao Wu, Asymptotic Analysis, vol. 78, no.1, Aug. 2012, pp.217-245.
A linear energy stable numerical scheme for epitaxial thin film growth model without slope selection, Wenbin Chen, Sidafa Conde, Cheng Wang, Xiaoming Wang and Steven Wise, J. Sci. Comp.,(2012) 52: 546-562.
Boundary layers associated with a class of 3D nonlinear channel flows, Anna Mazzucato, Dongjuan Niu and Xiaoming Wang. Indiana U. Math. Jour., vol. 60, no.4, 2011, pp. 1113-1136.
2010
Approximation of stationary statistical properties of dissipative dynamical systems: time discretization. Math. Comp., vol. 79 (2010) 259-280.
Linear response theory for statistical ensembles in complex systems with time-periodic forcing. Andrew Majda and Xiaoming Wang, Comm. Math. Sci., special issue dedicated to Andy Majda, vol. 8, issue 1 (March 2010), p.145-172.
Coupled Stokes-Darcy model with Beavers-Joseph interface boundary condition, Yanzhao Cao, Max Gunzburger, Fei Hua and Xiaoming Wang, Communications in Mathematical Sciences, special issue dedicated Andrew Majda. Accepted July 2008. Vol. 8, issue 1 (March 2010), p.1-25.
On the coupled continuum pipe flow model (CCPF) for flows in karst aquifer, Discrete and Continuous Dynamical Systems-B, Volume: 13, Number: 2, March 2010, p. 489-501.
Finite element approximation of the Stokes-Darcy system with Beavers-Joseph interface interface boundary condition, Yanzhao Cao, Max Gunzburger, Bill Hu, Fei Hua, Xiaoming Wang and Weidong Zhao, SIAM J. Num. Anal., Volume 47, Issue 6, pp. 4239-4256 (2010).
Unconditionally stable schemes for thin film epitaxy, Cheng Wang, Xiaoming Wang and Steven Wise, Discrete and Continuous Dynamical Systems, ser. A vol. 28, no. 1, 2010, pp. 405-423. (an invited article in a special issue dedicated to Roger Témam).
Examples of boundary layers associated with the incompressible Navier-Stokes flows, Chin. Ann. Math. ser. B, vol. 31, no.5, pp.781–792, 2010.
2009
Upper semi-continuity of stationary statistical properties of dissipative systems, Discrete and Continuous Dynamical Systems -A, special issue dedicated to Prof. Li Ta-Tsien. Vol. 23, no.1/2, pp.521-540, 2009.
2008
Stationary statistical properties of Rayleigh-Bénard convection at large Prandtl number, Communications on Pure and Applied Mathematics, 61 (2008), no. 6, 789–815.
Bound on the vertical heat transport at large Prandtl number, Physica D, 237 (2008) 854-858.
A semi-implicit scheme for stationary statistical properties of the infinite Prandtl number model, W. Cheng and X. Wang, SIAM Jour. Num. Anal., vol.47, no.1, 250-270, 2008.
2007
Asymptotic behavior of global attractors to the Boussinesq system for Rayleigh-Bènard convection at large Prandtl number, Communications on Pure and Applied Mathematics, Volume 60, issue 9, pp.1293-1318, (September, 2007).
A discrete Kato type theorem on inviscid limit of Navier-Stokes flows, W. Cheng and X. Wang, J. Math. Phys. vol. 48, issue 6, pp. 065303-065303-14 (2007).
1993-2006
A Remark on the Characterization of the Gradient of Distributions, Applicable Analysis, Vol 51, 1993, 35-40.
An Energy Equation for Weakly Damped Driven Nonlinear Schrödinger Equations and Its Application to Their Attractors, Physica D 88 (1995) 167-175.
Upper Bound on the Dimension of the Attractor for the Nonhomogeneous Navier-Stokes Equations, Alain Miranville and Xiaoming Wang, Discrete and Continuous Dynamical Systems Vol 2, No. 1, 1996, pp. 95-110.
Time Averaged Energy Dissipation Rate of Boundary Driven Flows, Physica D 99 (1997) 555-563.
Attractors for Non-autonomous Non-homogeneous Navier-Stokes Equations, Alain Miranville and Xiaoming Wang, Nonlinearity 10 (1997) 1047-1061.
Attractors for Non-Compact Semigroups via Energy Equations, Ioana Moise, Ricardo Rosa and Xiaoming Wang, Nonlinearity, 11, 1998, 1369-1393.
Attractor Dimension Estimates for Two-dimensional Shear Flows, Charles Doering and Xiaoming Wang, Physica D, 123 (1998) 206-222.
On the Behavior of the Solutions of Navier-Stokes Equations at Vanishing Viscosity, Roger Témam and Xiaoming Wang, Annali della Scuola Normale Superiore di Pisa, vol. XXV, pp. 807-828, 1998.
Effect of tangential derivatives in the boundary layer on the energy dissipation rate, Physica D, 144(2000) 142-153.
A Kato type theorem on zero viscosity limit of Navier-Stokes flows, Xiaoming Wang, Indiana Univ. Math. Jour., Vol.50, No.1 (2001), 223-241.
Boundary Layer Associated with the Incompressible NavierStokes Equations: the non-characteristic boundary case, Roger Témam and Xiaoming Wang, J. Diff. Eqs., Vol.179, (2002), 647-686.
Infinite Prandtl number limit of Rayleigh-B´enard convection, Xiaoming Wang, Communications on Pure and Applied Mathematics Volume 57, Issue 10 (p 1265-1282), 2004.
Validity of the One and One-Half Layer Quasi-Geostrophic Model and Effective Topography, Andrew Majda and Xiaoming Wang, Communications in Partial Differential Equations, Volume 30, Number 9, 2005, pp. 1305 1314.
The emergence of large-scale coherent structure under small scale random bombardments, Andrew J. Majda and Xiaoming Wang, Communications on Pure and Applied Mathematics, Volume 59, Issue 4 (2006), pp.467-500.
Monograph
Nonlinear Dynamics and Statistical Theory for Basic Geophysical Flows, Andrew J. Majda and Xiaoming Wang, Cambridge University Press, 2006.
