Research
Finite element formulations for the transport equation
HENCH, J. L., and R. A. LUETTICH, JR., Analysis and application of Eulerian finite element methods for the transport equation, 1998. Proc. 5th Conference on Estuarine and Coastal Modeling, M. L. Spaulding and A. F. Blumberg (eds.), ASCE, pp. 138-152.
Abstract
A comparison of various Eulerian finite element schemes for the transport equation is made using Fourier analysis. The relative merits of each scheme are discussed and one scheme is selected for a two-dimensional field application. A series of runs are made to test global scalar mass conservation which is found to depend on the complexity of the flow field. Difficulties with global scalar mass conservation are related to local fluid mass errors. The results stress the importance to transport modeling of using hydrodynamic schemes which conserve fluid mass on both a local and global basis.
Image: Transport of a scalar plume in the vicinity of a tidal inlet. Strong horizontal velocity shear rapidly and severely distorts the concentration field. Nearshore advection dominated applications such as this pose significant challanges to traditional numerical schemes.