The practical computational and analytic modeling of stochastic fluid flow is a demanding challenge. We review several separate components of an integrated approach to this problem, drawing on recent results of the speaker, colleagues, and others.
Stochastic risk assessment of engineering systems motivates this study, as it requires stochastic fluid flow as an input. The use of multiple simulations to evaluate a stochastic ensemble places a strong premium on fast algorithms. Upscaling is a necessary approach to achieving fast algorithms in many cases. Upscaling can be understood as the opposite of multigrid methods in a multiscale problem: Finely gridded data is used to condition a coarsely gridded solution. Analytic, numerical, and experimental studies are needed to validate upscaling methodologies. Massively parallel computing based on a locally-assembled supercomputer with commodity components and public domain software is a cost effective solution for the still remaining large computational problems.
In combination, these methods appear to be capable of solving previously intractible stochastic fluid flow problems.