XLIII Olimpiada matemática española

Depto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasTRUEpu

Study of the Liebau effect for use in extracorporeal blood circulation devices

The Liebau effect is a phenomenon capable of generating a net flow without the need for valves. The mechanisms of the Liebau effect, impedance pumping and asymmetric pumping, involve a complex fluid-mechanical problem with many variables that influence the direction and amplitude of flow. However, Liebau effect pumps are devices with characteristics suitable for many applications, including the pumping of biofluids. Moreover, these pumps are easier to build. The research carried out during this doctoral thesis focuses on the study of the Liebau effect and its potential application in extracorporeal blood circulation assist devices. Much of the work focuses on the analysis of asymmetric pumping, which is the least studied mechanism of the Liebau effect. A deeper understanding of the Liebau effect will facilitate the design of such pumps.El efecto Liebau es un fenómeno capaz de generar un flujo neto sin necesidad de válvulas. Los mecanismos del efecto Liebau, el bombeo por impedancia y el bombeo asimétrico, entrañan un problema fluidomecánico complejo, con muchas variables involucradas en el fenómeno y todas con influencia en el sentido y amplitud del flujo. No obstante, las bombas de efecto Liebau son dispositivos con características idóneas para muchas aplicaciones, entre ellas el bombeo de biofluidos. Además, son sencillos de construir. La investigación desarrollada durante esta tesis doctoral se centra en el estudio del efecto Liebau y su potencial aplicación en dispositivos de asistencia a la circulación sanguínea extracorpórea. Gran parte del trabajo se centra en el análisis del bombeo asimétrico, que es el mecanismo del efecto Liebau menos estudiado. La comprensión más profunda del efecto Liebau, facilitará el diseño de este tipo de bombas.Escuela de DoctoradoDoctorado en Ingeniería Industria

Dimensional hyper-reduction of nonlinear finite element models via empirical cubature

We present a general framework for the dimensional reduction, in terms of number of degrees of freedom as well as number of integration points (“hyper-reduction”), of nonlinear parameterized finite element (FE) models. The reduction process is divided into two sequential stages. The first stage consists in a common Galerkin projection onto a reduced-order space, as well as in the condensation of boundary conditions and external forces. For the second stage (reduction in number of integration points), we present a novel cubature scheme that efficiently determines optimal points and associated positive weights so that the error in integrating reduced internal forces is minimized. The distinguishing features of the proposed method are: (1) The minimization problem is posed in terms of orthogonal basis vector (obtained via a partitioned Singular Value Decomposition) rather that in terms of snapshots of the integrand. (2) The volume of the domain is exactly integrated. (3) The selection algorithm need not solve in all iterations a nonnegative least-squares problem to force the positiveness of the weights. Furthermore, we show that the proposed method converges to the absolute minimum (zero integration error) when the number of selected points is equal to the number of internal force modes included in the objective function. We illustrate this model reduction methodology by two nonlinear, structural examples (quasi-static bending and resonant vibration of elastoplastic composite plates). In both examples, the number of integration points is reduced three order of magnitudes (with respect to FE analyses) without significantly sacrificing accuracy.Peer ReviewedPostprint (published version

gVOF: An open-source package for unsplit geometric volume of fluid methods on arbitrary grids

The gVOF package implements several accurate and efficient geometric volume of fluid (VOF) methods on arbitrary grids, either structured or unstructured with convex or non-convex cells, based on multidimensional unsplit advection and piecewise linear interface calculation (PLIC) schemes, with the purpose of facilitating and extending the use of advanced unsplit geometric VOF methods in new or existing computational fluid dynamics codes. The package includes a complete and self-contained set of routines for VOF initialization, interface reconstruction and fluid advection, and uses as external libraries a set of publicly available in-house tools to perform several analytical and geometrical operations. These operations may involve handling of high-complex non-convex flux polyhedra, even with self-intersecting faces, which are robustly and efficiently treated in this work without the need of costly techniques based on convex decomposition. Results for the accuracy, computational efficiency, and volume (local and global) conservation properties of different combinations of the implemented advection and reconstruction methods are presented for several numerical tests on structured and unstructured grids. An extensive comparison with results obtained by other authors using advanced geometric VOF methods shows the outstanding performance of the gVOF package in terms of efficiency and accuracy. To demonstrate the performance of the package in solving complex two-phase flow problems, the implemented methods are combined with an existing in-house code to simulate the impact of a water drop on a free surface.The authors gratefully acknowledge the joint support of the Spanish Ministerio de Ciencia, Innovación y Universidades - Agencia Estatal de Investigación and FEDER through projects DPI2017-87826-C2-1-P and DPI2017-87826-C2-2-P, and the Spanish Ministerio de Ciencia e Innovación - Agencia Estatal de Investigación (MCIN/ AEI / 10.13039/501100011033) through projects PID2020-120100GB-C21 and PID2020-120100GB-C22

Artículos científicos: tipos, secciones y publicación

Las revistas científicas han sido el principal vehículo de transmisión de conocimientos entre los investigadores y la comunidad científica. Investigar y publicar un artıculo científico son dos actividades íntimamente relacionadas. Saber los tipos de publicación existentes, las secciones de un articulo y donde publicarlo es el objetivo de este trabajo