Multiscale Computations and Engineering Applications


Yizhao Hou

10:00:00 - 11:00:00

Multiscale Computations and Engineering Applications

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Many problems of fundamental and practical importance contain multiple scale solutions. Composite materials, flow and transport in heterogeneous porous media, and turbulent flow are examples of this type. Direct numerical simulations of these multiscale problems are extremely difficult due to the wide range of length scales in the underlying physical problems. In this talk, I describe some of our recent efforts in developing multiscale computational methods to upscale two-phase flows in strongly heterogeneous porous media. For some challenging problems with long range scale interaction arising from engineering applications, we show how to use limited global information to improve the accuracy of the multiscale method. Another important application is how to quantify uncertainty in modeling the heterogeneous random media. We show that by using a coarse multiscale model to precondition the Markov Chain Monte Carlo method, we can significantly improve the efficiency of the MCMC method in generating the probability distribution of the random media subject to some production data. Finally, we will discuss some recent progress in developing multiscale methods for incompressible Navier-Stokes equations with high Reynolds number.