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A Preconditioner for the Finite Element Approximation to the Arbitrary Lagrangian–Eulerian Navier–Stokes Equations

This paper examines the development of a preconditioner for the arbitrary Lagrangian-Eulerian (ALE) Navier-Stokes equations used to model ventricular flow in the heart. The ALE form introduces a transient change to the discrete linearized matrix operators, making the solution of these equations more costly to solve than their standard Navier-Stokes counterpart. In this paper, we extend the Fp-preconditioner for the first time to the ALE Navier-Stokes system, showing that this linear solver strategy produces bounded iteration counts with mesh refinement. This approach enables the solution of complex hemodynamics simulations by defining a solver strategy scaling linearly with problem size.