Browsing by Author "Silvester, David"
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Item Efficient Preconditioning of the Linearized Navier-Stokes Equations}(1999-10-16) Silvester, David; Elman, Howard; Kay, David; Wathen, AndrewWe outline a new class of robust and efficient methods for solving subproblems that arise in the linearization and operator splitting of Navier-Stokes equations. We describe a very general strategy for preconditioning that has two basic building blocks; a multigrid V-cycle for the scalar convection-diffusion operator, and a multigrid V-cycle for a pressure Poisson operator. We present numerical experiments illustrating that a simple implementation of our approach leads to an effective and robust solver strategy in that the convergence rate is independent of the grid and the time-step, and only deteriorates very slowly as the Reynolds number is increased. (Also cross-referenced as UMIACS-TR-99-66)Item Least Squares Preconditioners for Stabilized Discretizations of the Navier-Stokes Equations(2006-04-20T16:09:59Z) Elman, Howard; Howle, Victoria E.; Shadid, John; Silvester, David; Tuminaro, RayThis paper introduces two stabilization schemes for the Least Squares Commutator (LSC) preconditioner developed by Elman, Howle, Shadid, Shuttleworth and Tuminaro [SIAM J. Sci. Comput., 27, 2006, pp. 1651--1668] for the incompressible Navier-Stokes equations. This preconditioning methodology is one of several choices that are effective for Navier-Stokes equations, and it has the advantage of being defined from strictly algebraic considerations. It has previously been limited in its applicability to div-stable discretizations of the Navier-Stokes equations. This paper shows how to extend the same methodology to stabilized low-order mixed finite element approximation methods.