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Published March 2005 | metadata_only
Journal Article

Multiscale modelling and computation of fluid flow

Hou, Thomas Y.


Many problems of fundamental and practical importance have multiscale solutions. Direct numerical simulation of these multiscale problems is difficult due to the range of length scales in the underlying physical problems. Here, we describe two multiscale methods for computing nonlinear partial differential equations with multiscale solutions. The first method relies on constructing local multiscale bases for diffusion‐dominated problems. We demonstrate that such an approach can be used to upscale two‐phase flow in heterogeneous porous media. The second method is to construct semi‐analytic multiscale solutions local in space and time. We use these solutions to approximate the large‐scale solution for convection‐dominated transport. This approach overcomes the common difficulty due to the memory effect in deriving the averaged equations for convection‐dominated transport. Our multiscale analysis provides a useful guideline for designing effective numerical methods for incompressible flow.

Additional Information

© 2005 John Wiley & Sons, Ltd. Issue Online 04 March 2005; Version of Record online: 17 January 2005; Manuscript accepted: 03 November 2004; Manuscript revised: 07 September 2004; Manuscript received: 27 April 2004. This Research was in part supported by a NSF Grant No. ACI-0204932.

Additional details

August 22, 2023
August 22, 2023