CompMath Seminar - Cristóbal Bertoglio, University of Groningen

Title: Multiscale modeling of incompressible fluid flow (joint work with Jeremias Garay and David Nolte)

Abstract:

Lumped parameter models, serving as boundary conditions for 3D fluid flow models, offer flexibility in representing neglected domain influences but pose significant computational challenges. While time-explicit coupling in the forward problem leads to conditionally stable time integration schemes, time-implicit solutions necessitate non-local spatial coupling between 0D and 3D compartments, demanding tailored linear algebra methods and multiple 3D model solutions. Additionally, containing several parameters per boundary exacerbates computational complexity in the solution of the inverse problem. This talk introduces a new approach inspired by prior works on "Stokes-consistent" backflow stabilization (Bertoglio & Caiazzo 2016) and the method of asymptotic partial decomposition of a domain (Panassenko 1998, Bertoglio et al 2019). Termed "Stokes-enforcing," this boundary condition incorporates a weak integral term and constrains velocity perpendicular to the boundary, effectively extending outlets virtually with specific lengths. Blood flow simulations in a left coronary arterial tree serve as a pertinent example to demonstrate the efficacy and applicability of the proposed approach.