ALADINS: an ALgebraic splitting time ADaptive solver for the incompressible Navier-Stokes equations

The heart beat induces in the vascular
ow the periodic sequence of a fast (systole) and a slow (diastole) transient. The duration of each phase depends on the patient and his specic conditions (e.g. exercise or rest). From the numerical viewpoint, this feature of blood
ow can be exploited for reducing the computational costs, resorting to time adaptivity.
Dierent time steps can be conveniently and automatically selected during the dierent phases
of the heart beat. The automatic selection of the step requires however a reliable error estimator.
In the talk, we will consider an estimator coming from a particular segregated solver for velocity
and pressure, formerly proposed by Saleri and Veneziani [1]. The strong point of this approach,
called ALADINS (ALgebraic ADaptive Incompressible Navier-Stokes) is that the estimator is a by-product of the velocity-pressure splitting and does not require any additional cost.
Basic features of the method (stability, accuracy) will be addressed together with implementation details and hints for the parallel formulation (PALADINS) [2, 3].
Several numerical tests (implemented in LifeV) will be presented with particular emphasis to
cardiovascular applications.

Keywords: Incompressible fluids , Time adaptivity, Segregated methods