Abstract
This paper describes an adaptive preconditioner for numerical continuation of
incompressible Navier--Stokes flows. The preconditioner maps the identity (no
preconditioner) to the Stokes preconditioner (preconditioning by Laplacian)
through a continuous parameter and is built on a first order Euler
time-discretization scheme. The preconditioner is tested onto two fluid
configurations: three-dimensional doubly diffusive convection and a reduced
model of shear flows. In the former case, Stokes preconditioning works but a
mixed preconditioner is preferred. In the latter case, the system of equation
is split and solved simultaneously using two different preconditioners, one of
which is parameter dependent. Due to the nature of these applications, this
preconditioner is expected to help a wide range of studies.
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