Journal articles

Small random perturbations of Navier-Stokes equations
  • X. Wan ahd H. Yu, A dynamic-solver-consistent minimum action method: With an application to 2D Navier-Stokes equations, Journal of Computational Physics 331 (2017), pp. 209-226. [pdf]

  • X. Wan, H. Yu and W. E, Model the nonlinear instability of wall-bounded shear flows as a rare event: A study on two-dimensional Poiseuille flow, Nonlinearity, 28 (2015), pp. 1409-1440. [pdf]

  • X. Wan, A minimum action method for small random perturbations of two-dimensional parallel shear flows, Journal of Computational Physics, 235 (2013), pp. 497-514. [pdf]

Minimum action mehtods

  • X. Wan, H. Yu and J. Zhai, Convergence analysis of finite element approximation of large deviation principle, submitted.
  • X. Wan and X. Zhou, Asymptotically efficient simulation of elliptic problems with small random forcing, SIAM Journal on Scientific Computing, accepted.
  • X. Wan, B. Zheng and G. Lin, An hp adaptive minimum action method based on a posteriori error estimate, Communications in Computational Physics, 23(2) (2018), pp. 408-439. [pdf]

  • X. Wan, A minimum action method with optimal linear time scaling, Communications in Computational Physics, 18(5) (2015), pp. 1352-1379. [pdf]

  • X. Wan and G. Lin, Hybrid parallel computing of minimum action method, Parallel Computing, 39 (2013), pp. 638-651. [pdf]

  • X. Wan, An adaptive high-order minimum action method, Journal of Computational Physics, 230 (2011), pp. 8669-8682. [pdf]

  • X. Wan, X. Zhou and W. E, Study of the noise-induced transition and the exploration of the configuration space for the Kuramoto-Sivashinsky equation using the minimum action method, Nonlinearity, 23 (2010), pp. 475-493. [pdf]

Numerical methods of SPDE

  • X. Wan and B. Rozovskii, The Wick-Malliavin approximation of elliptic problems with log-normal random coefficients, SIAM Journal on Scientific Computing, 35(5) (2013), pp. A2370-A2392. [pdf]

  • D. Venturi, X. Wan, R. Mikulevicius, B. Rozovskii and G. Karniadakis, Wick-Malliavin approximation to nonlinear stochastic PDEs: analysis and simulations, Proceedings of the Royal Society A, 469 (2013), 20130001. [pdf]

  • X. Wan, A discussion on two stochastic elliptic modeling strategies, Communications in Computational Physics, 11 (2012), pp. 775-796. [pdf]

  • X. Wan, A note on stochastic elliptic models, Computer Methods in Applied Mechanics and Engineering, 199(45-48) (2010), pp. 2987-2995. [pdf]

  • S. V. Lototsky, B. L. Rozovskii and X. Wan, Elliptic equations of higher stochastic order, ESAIM: Mathematical Modeling and Numerical Analysis, 5/4 (2010), pp. 1135-1153. [pdf]

  • X. Wan, B. Rozovskii and G. E. Karniadakis, A stochastic modeling methodology based on weighted Wiener chaos and Malliavin calculus, Proceedings of the National Academy of Sciences, 106 (2009), pp. 14189-14194. [pdf]

Uncertainty Quantification

  • X. Yang, X. Wan and L. Lin, A general framework of enhancing sparsity of generalized polynomial chaos expansion, submitted.
  • M. Zheng, X. Wan and G. Karniadakis, Adaptive multi-element polynomial chaos with discrete measure: Algorithms and applications to SPDEs, Applied Numerical Mathematics, 90 (2015), pp. 91-110. [pdf]

  • H. Babaee, X. Wan and S. Acharya, Effect of uncertainty in blowing ratio on film cooling effectiveness, ASME Journal of Heat Transfer, 136(3) 2014, pp. 031701. [pdf]

  • G. Lin, M. Elizondo, S. Lu and X. Wan, Uncertainty quantification in dynamic simulations of large-scale power system models using the high-order probabilistic collocation method on sparse grids, International Journal for Uncertainty Quantification, 4(3) 2014, pp. 185-204. [pdf]

  • D. Venturi, X. Wan and G. E. Karniadakis, Stochastic bifurcation and stability of natural convective flows in bidimensional square enclosures, Journal of Fluid Mechanics, 650 (2010), pp. 391-413. [pdf]

  • X. Wan and G. E. Karniadakis, Solving elliptic problems with non-Gaussian spatially-dependent random coefficients: algorithms, error analysis and applications, Computer Methods in Applied Mechanics and Engineering, 198/21-26 (2009), pp. 1985-1995. [pdf]

  • X. Wan and G. E. Karniadakis, Error control in multi-element polynomial chaos method for elliptic problems with random coefficients, Communications in Computational Physics, 5/2-4 (2009), pp. 793-820. [pdf]

  • J. Foo, X. Wan and G. E. Karniadakis, The multi-element probabilistic collocation method: analysis and simulation, Journal of Computational Physics, 227 (2008), pp. 9572-9595. [pdf]

  • D. Venturi, X. Wan and G. E. Karniadakis, Stochastic low dimensional modeling of random laminar wake past a circular cylinder, Journal of Fluid Mechanics, 606 (2008), pp. 339-367. [pdf]

  • G. Lin, X. Wan, C.-H. Su and G. E. Karniadakis, Stochastic computational fluid mechanics, IEEE Computing in Science and Engineering Journal (CiSE), 9 (2007), pp. 21-29. [pdf]

  • X. Wan and G. E. Karniadakis, Stochastic heat transfer in a grooved channel, Journal of Fluid Mechanics, 565 (2006), pp. 255-278. [pdf]

  • X. Wan and G. E. Karniadakis, Long-term behavior of polynomial chaos in stochastic flow simulations, Computer Methods in Applied Mechanics and Engineering, 195 (2006), pp. 5582-5596. [pdf]

  • X. Wan and G. E. Karniadakis, Multi-element generalized polynomial chaos for arbitrary probability measures, SIAM Journal on Scientific Computing, 28 (2006), pp. 901-928. [pdf]

  • X. Wan and G. E. Karniadakis, Beyond Wiener-Askey expansions: handling arbitrary PDFs, Journal of Scientific Computing, 27 (2006), pp. 455-464. [pdf]

  • X. Wan and G. E. Karniadakis, An adaptive multi-element generalized polynomial chaos method for stochastic differential equations, Journal of Computational Physics, 209 (2005), pp. 617-642. [pdf]

  • X. Wan, D. Xiu and G. E. Karniadakis, Stochastic solutions for the two-dimensional advection-diffusion equation, SIAM Journal on Scientific Computing, 26 (2004), pp. 578-590. [pdf]

Miscellaneous topics

  • L. Zhu, Q. Chen and X. Wan, Optimization of non-hydrostatic Euler model for water waves, Coastal Engineering, 91 (2014), pp. 191-199. [pdf]

  • H. Babaee, S. Acharya and X. Wan, Optimization of forcing parameters of film cooling effectiveness, ASME Journal of Turbomachinery, ASME Journal of Turbomachinery, 136 (2014), 021016. [pdf]

  • X. Wan, Some improvements to the flux-type a posteriori error estimators, Computer Methods in Applied Mechanics and Engineering, 197/6-8 (2008), pp. 567-576. [pdf]

  • X. Wan and G. E. Karniadakis, A sharp error estimate for the Fast Gauss Transform [Short Note], Journal of Computational Physics, 219 (2006), pp. 7-12. [pdf]

Proceedings

  • H. Babaee, X. Wan and S. Acharya, Effect of uncertainty in blowing ratio on film cooling effectiveness, ASME Heat Transfer 2013, Minneapolis, July 14-19, 2013.
  • H. Babaee, S. Acharya and X. Wan, Optimization of forcing parameters of film cooling effectiveness, Proceedings of the ASME Tubo Expo 2013, San Antonio, June 3-7, 2013.
  • L. Zhu, Q. Chen and X. Wan, Numerical modeling of nonlinear water waves with Sigma coordinate and layer thickness optimization, Proceedings of XIX International Conference on Water Resources (CMWR 2012), University of Illinois at Urbana-Champaign, June 17-22, 2012.

  • X. Wan and G. E. Karniadakis, Recent advances in polynomial chaos methods, Proceedings of the Applied Vehicle Technology Panel (AVT) Symposium: Computational Uncertainty in Military Vehicle Design (NATO/PfP Unclassified) 2007.

  • X. Wan and G. E. Karniadakis, Spectral/hp element method in random space, Proceedings of 5th GRACM International Congress on Computational Mechanics 2005, p17-27.

  • X. Wan and G. E. Karniadakis, Simulation of heat transfer with uncertainty, Proceedings of the ASME 2005 Summer Heat Transfer Conference.

  • X. Wan, D. Xiu and G. E. Karniadakis, Modeling uncertainty in three-dimensional heat transfer problems, Advanced Computational Methods in Heat Transfer VIII (HEAT TRANSFER 2004), p15-24.