This repository contains implementations for scalable solvers for the steady Navier-Stokes equations, implemented in Firedrake. These solvers combine an augmented Lagrangian approach for the Schur complement with a custom robust multigrid scheme for the top-left block of the mixed system.
Currently we implement the following discretisations
[P_2]^2-P_0,[P_1+FacetBubble]^3-P_0,[P_2+FacetBubble]^3-P_0on simplices as described in Farrell, Mitchell, Wechsung, An Augmented Lagrangian Preconditioner for the 3D Stationary Incompressible Navier--Stokes Equations at High Reynolds Number[P_k]^d-P_{k-1}^{DG}Scott Vogelius elements and[P_k]^d-P_{k-1}Taylor-Hood elements for on barycentrically refined simplices fork⩾2as described in Farrell, Mitchell, Scott, Wechsung, A Reynolds-robust preconditioner for the Scott-Vogelius discretization of the stationary incompressible Navier-Stokes equations
Solvers for H(div)-L2 discretisations on both simplices and quads/hexes as well as solvers for Q_k-Q_{k-2}^{DG} and Q_k-P_{k-1}^{DG} discretisations on quads/hexes exist on branches and will be available soon.
Main development by
and with contributions by