Numerical simulations for Stochastic convection-diffusion processes in concentration fields
We apply probabilistic approach (the stochastic Galerkin method) to numerically simulate the convection-diffusion processes in the concentration fields under uncertain inputs, I.e. random ow (transport) velocity or/and source (forcing) term. Two examples are given. The first is a test problem with random inputs (transport velocity and forcing term) examining the accuracy and convergence of the solver. The second simulates the convection and diffusion process of a deterministic cone-shaped initial concentration field under random ow (transport) velocity. Numerical study shows that simulations based on the probabilistic modeling provide the mean values of the solution together with their variances (likelihood) and higher statistical moments, which give valuable information (e.g. safety factors) for decision making in the engineering design. The cost paid here is the increased size of the equation system that needs to be solved. This poses a serious computational challenge in its practical engineering applications, and requires further investigation. The efficiency of the standard multigrid solver used in our work needs to be improved based on exploiting the structure of the stochastic equation system.
stochastic convection-diffusion equation numerical simulation stochastic Galerkin method
X.A.Ren W.Q.Wu
University of Shanghai for Science and Technology, Shanghai 200093, China
国际会议
The Fifth International Conference on Fluid Mechanics(第五届国际流体力学会议)
上海
英文
2007-08-15（万方平台首次上网日期，不代表论文的发表时间）