COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > A Reynolds-robust preconditioner for the 3D stationary Navier-Stokes equations

## A Reynolds-robust preconditioner for the 3D stationary Navier-Stokes equationsAdd to your list(s) Download to your calendar using vCal - Patrick Farrell (University of Oxford)
- Thursday 31 October 2019, 16:00-17:00
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact info@newton.ac.uk. GCS - Geometry, compatibility and structure preservation in computational differential equations When approximating PDEs with the finite element method, large sparse linear systems must be solved. The ideal preconditioner yields convergence that is algorithmically optimal and parameter robust, i.e. the number of Krylov iterations required to solve the linear system to a given accuracy does not grow substantially as the mesh or problem parameters are changed. Achieving this for the stationary Navier-Stokes has proven challenging: LU factorisation is Reynolds-robust but scales poorly with degree of freedom count, while Schur complement approximations such as PCD and LSC degrade as the Reynolds number is increased. Building on ideas of Schöberl, Xu, Zikatanov, Benzi & Olshanskii, in this talk we present the first preconditioner for the Newton linearisation of the stationary Navier–Stokes equations in three dimensions that achieves both optimal complexity and Reynolds-robustness. The scheme combines augmented Lagrangian stabilisation to control the Schur complement, the convection stabilisation proposed by Douglas & Dupont, a divergence-capturing additive Schwarz relaxation method on each level, and a specialised prolongation operator involving non-overlapping local Stokes solves. The properties of the preconditioner are tailored to the divergence-free CG(k)-DG(k-1) discretisation and the appropriate relaxation is derived from considerations of finite element exterior calculus. We present 3D simulations with over one billion degrees of freedom with robust performance from Reynolds numbers 10 to 5000. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
- Featured lists
- INI info aggregator
- Isaac Newton Institute Seminar Series
- School of Physical Sciences
- Seminar Room 2, Newton Institute
- bld31
Note that ex-directory lists are not shown. |
## Other listsMechanisms of Language Change Research Cluster – student run event 2012 Number theory study group: Iwasawa theory Cambridge Canadian Club Events## Other talksAlternate Twentieth-Century Biotechnologies (Domestication Practices across History) A question of balance? Thinking about sexual health in medieval Europe Decoding the Heavens: The Antikythera Mechanism Air pollution and human health. Lessons learnt and challenges ahead. Bayesian analyses of galaxy surveys Stepping up climate change mitigation |