An adaptive finite element water column model using the Mellor-Yamada level 2.5 turbulence closure scheme

A one-dimensional water column model using the Mellor and Yamada level 2.5 parameterization of vertical turbulent fluxes is presented. The model equations are discretized with a mixed finite element scheme. Details of the finite element discrete equations are given and adaptive mesh refinement strategies are presented. The refinement criterion is an "a posteriori" error estimator based on stratification, shear and distance to surface. The model performances are assessed by studying the stress driven penetration of a turbulent layer into a stratified fluid. This example illustrates the ability of the presented model to follow some internal structures of the flow and paves the way for truly generalized vertical coordinates. (c) 2005 Elsevier Ltd. All rights reserved.

Implicit-factorization preconditioning and iterative solvers for regularized saddle-point systems

We consider conjugate-gradient like methods for solving block symmetric indefinite linear systems that arise from saddle-point problems or, in particular, regularizations thereof. Such methods require preconditioners that preserve certain sub-blocks from the original systems but allow considerable flexibility for the remaining blocks. We construct a number of families of implicit factorizations that are capable of reproducing the required sub-blocks and (some) of the remainder. These generalize known implicit factorizations for the unregularized case. Improved eigenvalue clustering is possible if additionally some of the noncrucial blocks are reproduced. Numerical experiments confirm that these implicit-factorization preconditioners can be very effective in practice.