Uncertainty modeling of Burgers' equation by generalized polynomial chaos

The solution of viscous Burgers' equation subjected to stochastic inputs is investigated numerically. The source of uncertain inputs includes viscosity and boundary conditions. The generalized polynomial chaos expansion is employed to represent the solution in random space. The expected spectral convergence rate of the generalized polynomial chaos expansion is observed for model problem. When small random perturbation is imposed on the boundary condition, the location of the transition layer exhibit noticeable change. This phenomenon is investigated, and is in analogy to the so-called 'supersensitivity' which occurs under deterministic perturbation on the boundary condition.