(A)ugmented (L)agrangian based solvers for the Navier Stokes equation in (Fi)redrake

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_0 on 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 for k⩾2 as 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.

Developers

Main development by

• Florian Wechsung
• Patrick Farrell
• Lawrence Mitchell

and with contributions by

• Hamza Alawiye