Computational Mathematics (CM)http://hdl.handle.net/20.500.11824/52022-10-01T13:37:08Z2022-10-01T13:37:08ZA numerical method for suspensions of articulated bodies in viscous flowsBalboa, F.Delmotte, B.http://hdl.handle.net/20.500.11824/15232022-09-29T22:20:46Z2022-09-01T00:00:00ZA numerical method for suspensions of articulated bodies in viscous flows
Balboa, F.; Delmotte, B.
An articulated body is defined as a finite number of rigid bodies connected by a set of arbitrary constraints that limit the relative motion between pairs of bodies. Such a general definition encompasses a wide variety of situations in the microscopic world, from bacteria to synthetic micro-swimmers, but it is also encountered when discretizing inextensible bodies, such as filaments or membranes. In this work we consider hybrid articulated bodies, i.e. constituted of both linear chains, such as filaments, and closed-loop chains, such as membranes. Simulating suspensions of such articulated bodies requires to solve the hydrodynamic interactions between large collections of objects of arbitrary shape while satisfying the multiple constraints that connect them. Two main challenges arise in this task: limiting the cost of the hydrodynamic solves, and enforcing the constraints within machine precision at each time-step. To address these challenges we propose a formalism that combines the body mobility problem in Stokes flow with a velocity formulation of the constraints, resulting in a mixed mobility-resistance problem. While resistance problems are known to scale poorly with the particle number, our preconditioned iterative solver is not sensitive to the system size, therefore allowing to study large suspensions with quasilinear computational cost. Additionally, constraint violations, e.g. due to discrete time-integration errors, are prevented by correcting the particles' positions and orientations at the end of each time-step. Our correction procedure, based on a nonlinear minimisation algorithm, has negligible computational cost and preserves the accuracy of the time-integration scheme. The versatility of our method allows to study a plethora of articulated systems within a unified framework. We showcase its robustness and scalability by exploring the locomotion modes of a model microswimmer inspired by the diatom colony Bacillaria Paxillifer, and by simulating large suspensions of bacteria interacting near a no-slip boundary. Finally, we provide a Python implementation of our framework in a collaborative publicly available code, where the user can prescribe a set of constraints through a single input file to study a wide spectrum of applications involving suspensions of articulated bodies.
2022-09-01T00:00:00ZAeroacoustic Analysis of a Subsonic Jet using the Discontinuous Galerkin MethodLindblad, D.Sherwin, S.Cantwell, C.Lawrence, J.Proença, A.Moragues, M.http://hdl.handle.net/20.500.11824/15222022-09-13T22:21:16Z2022-01-01T00:00:00ZAeroacoustic Analysis of a Subsonic Jet using the Discontinuous Galerkin Method
Lindblad, D.; Sherwin, S.; Cantwell, C.; Lawrence, J.; Proença, A.; Moragues, M.
In this work, the open-source spectral/hp element framework Nektar++ (www.nektar.info) is coupled with the Antares library (www.cerfacs.fr/antares/) to predict noise from a subsonic jet. Nektar++ uses the high-order discontinuous Galerkin method to solve the compressible Navier-Stokes equations on unstructured grids. Unresolved turbulent scales are modeled using an implicit Large Eddy Simulation approach. In this approach, the favourable dissipation properties of the discontinuous Galerkin method are used to remove the highest resolved wavenumbers from the solution. For time-integration, an implicit, matrix-free, Newton-Krylov method is used. To compute the far-field noise, Antares solves the Ffowcs Williams-Hawkings equation for a permeable integration surface in the time-domain using a source-time dominant algorithm. The simulation results are validated against experimental data obtained in the Doak Laboratory Flight Jet Rig, located at the University of Southampton.
2022-01-01T00:00:00ZZindler-type hypersurfaces in R^4Martinez-Maure, Y.Rochera, D.http://hdl.handle.net/20.500.11824/15192022-09-09T22:20:51Z2022-09-08T00:00:00ZZindler-type hypersurfaces in R^4
Martinez-Maure, Y.; Rochera, D.
In this paper the definition of Zindler-type hypersurfaces is introduced in $\mathbb{R}^4$ as a generalization of planar Zindler curves. After recalling some properties of planar Zindler curves, it is shown that Zindler hypersurfaces satisfy similar properties. Techniques from quaternions and symplectic geometry are used. Moreover, each Zindler hypersurface is fibrated by space Zindler curves that correspond, in the convex case, to some space curves of constant width lying on the associated hypersurface of constant width and with the same symplectic area.
2022-09-08T00:00:00ZThe DPG Method for the Convection-Reaction Problem, RevisitedDemkowicz, L.Roberts, N.V.Muñoz-Matute, J.http://hdl.handle.net/20.500.11824/15122022-08-28T22:20:58Z2022-01-01T00:00:00ZThe DPG Method for the Convection-Reaction Problem, Revisited
Demkowicz, L.; Roberts, N.V.; Muñoz-Matute, J.
We study both conforming and non-conforming versions of the practical DPG method for the convection-reaction problem. We determine that the most common approach for DPG stability analysis - construction of a local Fortin operator - is infeasible for the convection-reaction problem. We then develop a line of argument based on a direct proof of discrete stability; we find that employing a polynomial enrichment for the test space does not suffice for this purpose, motivating the introduction of a (two-element) subgrid mesh. The argument combines mathematical analysis with numerical experiments.
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