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Articles written by Lin, G.

  1. Lin, G., Wan, X., Su, C.-H., and Karniadakis, G.E.. "Stochastic Computational Fluid Mechanics" Computing in Science and Engineering. 9 (2). 2007. pp. 21--29.


  2. Lin, G., Su, C.-H., and Karniadakis, G.E.. "Predicting shock dynamics in the presence of uncertainties" Journal of Computational Physics. 217 (1). 2006. pp. 260--276.

    We revisit the classical aerodynamics problem of supersonic flow past a wedge but subject to random inflow fluctuations or random wedge oscillations around its apex. We first obtain analytical solutions for the inviscid flow, and subsequently we perform stochastic simulations treating randomness both as a steady as well as a time-dependent process. We use a multi-element generalized polynomial chaos (ME-gPC) method to solve the two-dimensional stochastic Euler equations. A Galerkin projection is employed in the random space while WENO discretization is used in physical space. A key issue is the characteristic flux decomposition in the stochastic framework for which we propose different approaches. The results we present show that the variance of the location of perturbed shock grows quadratically with the distance from the wedge apex for steady randomness. However, for a time-dependent random process the dependence is quadratic only close to the apex and linear for larger distances. The multi-element version of polynomial chaos seems to be more effective and more efficient in stochastic simulations of supersonic flows compared to the global polynomial chaos method.


  3. Lin, G., Grinberg, L., and Karniadakis, G.E.. "Numerical studies of the stochastic Korteweg-de Vries equation" Journal of Computational Physics. 213 (2). 2006. pp. 676--703.

    We present numerical solutions of the stochastic Korteweg-de Vries equation for three cases corresponding to additive time-dependent noise, multiplicative space-dependent noise and a combination of the two. We employ polynomial chaos for discretization in random space, and discontinuous Galerkin and finite difference for discretization in physical space. The accuracy of the stochastic solutions is investigated by comparing the first two moments against analytical and Monte Carlo simulation results. Of particular interest is the interplay of spatial discretization error with the stochastic approximation error, which is examined for different orders of spatial and stochastic approximation.