Joint Center for Fluid Mechanics & Division of Engineering Seminar
Abstract: Wake flows have been described by Morkovin as a kaleidoscope for complex fluid dynamic phenomena. Even at modest Reynolds numbers the wake dynamics is complex, three-dimensional and often exhibits a strong low-frequency unsteadiness in addition to the familiar Karman vortex shedding mechanism. We have investigated flow over several different bluff bodies; here we will focus on flow past a nominally two-dimensional flat plate held normal to the flow at Reynolds numbers up to 1000. The long time signature of lift and drag forces clearly show low frequency unsteadiness with a period approximately 10 shedding cycles. It is observed that the low frequency unsteadiness is associated with the flow gradually switching between two distinct states. The role of three- dimensional instabilities is observed to be very important.
In all these flows it has been reasonably well established that even at modest Reynolds numbers the flow is strongly three-dimensional. From a practical stand point, a two-dimensional computational projection, which accurately accounts for all the three-dimensional (spanwise) fluctuations, has great appeal. One can consider the two-dimensional projection as the limiting case of a large eddy simulation, where the homogeneous spanwise direction has been completely averaged out. The transport equation for the spanwise-averaged spanwise component of vorticity ($< \omega_z >$) is considered; the three-dimensional effects to be modeled appear as subgrid scale fluxes arising from spanwise fluctuations. Here we develop optimal linear and quadratic closures for the flux vector in terms of $< \omega_z >$, based on linear and quadratic stochastic estimation. Limitations of eddy viscosity and Smagorinski type models is explored.
IF YOU WOULD LIKE TO MEET WITH DR. BALACHANDAR PLEASE CONTACT MADELINE BREWSTER TO MAKE AN APPOINTMENT (863-1414)
Stochastic Systems Seminar
Abstract: When estimating expectations of rare events by simulation, a very large number of replications are needed to achieve a reasonable accuracy. The optimal parameters for the change of measure used in Importance Sampling are highly problem dependent and in many situations, they are calculated numerically, before the actual simulation is performed.
We present an example where simulation is used to price Asian options, and show that a change of measure can very significantly improve the precision when the option is deeply out of the money (so that exercising the option is a rare event). We also show that the simulation method itself can be used to find the optimal change of measure. This is done by incorporating a stochastic approximation procedure that uses the IPA estimate of the gradient of the variance of the estimator. Our method simultaneously estimates the option price and optimizes the Importance Sampling parameters towards faster simulations, which justifies our naming it "Accelerated Simulation".
Brown Analysis Seminar
Department of Mathematics Colloquium
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