# 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]

*Journal of Computational Physics*331 (2017), pp. 209-226. [pdf]*Nonlinearity*, 28 (2015), pp. 1409-1440. [pdf]*Journal of Computational Physics*, 235 (2013), pp. 497-514. [pdf]### Minimum action mehtods

- X. Wan, H. Yu and J. Zhai, Convergence analysis of a finite element approximation of minimum action method, SIAM Journal on Numerical Analysis, accepted.
- X. Wan and X. Zhou, Asymptotically efficient simulation of elliptic problems with small random forcing,
*SIAM Journal on Scientific Computing*, 40(1) (2018), pp. A548-A572. [pdf] - 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

- J.-H. Liang, X. Wan, K. Rose, P. Sullivan and J. McWilliams, Horizontal dispersion
of buoyant materials in the ocean surface boundary layer, revised.
- 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.