Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
A stable and conservative interface treatment of arbitrary spatial accuracy
Journal of Computational Physics
Journal of Computational Physics
High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates
Journal of Computational Physics
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Modeling uncertainty in flow simulations via generalized polynomial chaos
Journal of Computational Physics
Stable and Accurate Artificial Dissipation
Journal of Scientific Computing
Uncertainty analysis for the steady-state flows in a dual throat nozzle
Journal of Computational Physics
Computational Modeling of Uncertainty in Time-Domain Electromagnetics
SIAM Journal on Scientific Computing
Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics
Journal of Computational Physics
Uncertainty quantification for porous media flows
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Uncertainty quantification for chaotic computational fluid dynamics
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Uncertainty quantification of limit-cycle oscillations
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Journal of Scientific Computing
Subcell resolution in simplex stochastic collocation for spatial discontinuities
Journal of Computational Physics
A stochastic Galerkin method for the Euler equations with Roe variable transformation
Journal of Computational Physics
Hi-index | 31.46 |
The Burgers' equation with uncertain initial and boundary conditions is investigated using a polynomial chaos (PC) expansion approach where the solution is represented as a truncated series of stochastic, orthogonal polynomials. The analysis of well-posedness for the system resulting after Galerkin projection is presented and follows the pattern of the corresponding deterministic Burgers equation. The numerical discretization is based on spatial derivative operators satisfying the summation by parts property and weak boundary conditions to ensure stability. Similarly to the deterministic case, the explicit time step for the hyperbolic stochastic problem is proportional to the inverse of the largest eigenvalue of the system matrix. The time step naturally decreases compared to the deterministic case since the spectral radius of the continuous problem grows with the number of polynomial chaos coefficients. An estimate of the eigenvalues is provided. A characteristic analysis of the truncated PC system is presented and gives a qualitative description of the development of the system over time for different initial and boundary conditions. It is shown that a precise statistical characterization of the input uncertainty is required and partial information, e.g. the expected values and the variance, are not sufficient to obtain a solution. An analytical solution is derived and the coefficients of the infinite PC expansion are shown to be smooth, while the corresponding coefficients of the truncated expansion are discontinuous.