Fast solution of parametric incompressible flow problems with application to microfluidics

Abstract

The process of design in computational fluid dynamics often involves queries to a similar set of problems, which may be viewed together as a single problem with parametrized data. These parameters can be seen as extra variables of the model. The use of reduced-order modeling provides a low-dimensional approximation of this high-dimensional solution space of solutions, thus enabling a fast evaluation of the obtained approximation. The aim of this thesis is to apply the recent robust face-centered finite volume (FCFV) method together with the Proper Generalized Decomposition to solve Stokes flow problems where the geometry of the domain is governed by a set of parameters, circumventing the curse of dimensionality and allowing for a real-time computation of the solutions. Contrary to other finite volume methods, the FCFV is not sensitive to mesh distortion and stretching, making it suitable to model complex geometries. The potential of the proposed technique is shown through an example arising from microfluidics, the so-called push-me-pull-you microswimmer.