Mathematical Aspects of Hydrodynamics

The workshop dealt with the partial differential equations that describe fluid motion and related topics. These topics included both inviscid and viscous fluids in two and three dimensions. Some talks addressed aspects of fluid dynamics such as the construction of wild weak solutions, compressible shock formation, inviscid limit and behavior of boundary layers, as well as both polymer/fluid and structure/fluid interaction

Stabilized finite element formulations for the three-field viscoelastic fluid flow problem

The Finite Element Method (FEM) is a powerful numerical tool, that permits the resolution of problems defined by partial differential equations, very often employed to deal with the numerical simulation of multiphysics problems. In this work, we use it to approximate numerically the viscoelastic fluid flow problem, which involves the resolution of the standard Navier-Stokes equations for velocity and pressure, and another tensorial reactive-convective constitutive equation for the elastic part of the stress, that describes the viscoelastic nature of the fluid. The three-field (velocity-pressure-stress) mixed formulation of the incompressible Navier-Stokes problem, either in the elastic and in the non-elastic case, can lead to two different types of numerical instabilities. The first is associated with the incompressibility and loss of stability of the stress field, and the second with the dominant convection. The first type of instabilities can be overcome by choosing an interpolation for the unknowns that satisfies the two inf-sup conditions that restrict the mixed problem, whereas the dominant convection requires a stabilized formulation in any case. In this work, different stabilized schemes of the Sub-Grid-Scale (SGS) type are proposed to solve the three-field problem, first for quasi Newtonian fluids and then for solving the viscoelastic case. The proposed methods allow one to use equal interpolation for the problem unknowns and to stabilize dominant convective terms both in the momentum and in the constitutive equation. Starting from a residual based formulation used in the quasi-Newtonian case, a non-residual based formulation is proposed in the viscoelastic case which is shown to have superior behavior when there are numerical or geometrical singularities. The stabilized finite element formulations presented in the work yield a global stable solution, however, if the solution presents very high gradients, local oscillations may still remain. In order to alleviate these local instabilities, a general discontinuity-capturing technique for the elastic stress is also proposed. The monolithic resolution of the three-field viscoelastic problem could be extremely expensive computationally, particularly, in the threedimensional case with ten degrees of freedom per node. A fractional step approach motivated in the classical pressure segregation algorithms used in the two-field Navier-Stokes problem is presented in the work.The algorithms designed allow one the resolution of the system of equations that define the problem in a fully decoupled manner, reducing in this way the CPU time and memory requirements with respect to the monolithic case. The numerical simulation of moving interfaces involved in two-fluid flow problems is an important topic in many industrial processes and physical situations. If we solve the problem using a fixed mesh approach, when the interface between both fluids cuts an element, the discontinuity in the material properties leads to discontinuities in the gradients of the unknowns which cannot be captured using a standard finite element interpolation. The method presented in this work features a local enrichment for the pressure unknowns which allows one to capture pressure gradient discontinuities in fluids presenting different density values. The stability and convergence of the non-residual formulation used for viscoelastic fluids is analyzed in the last part of the work, for a linearized stationary case of the Oseen type and for the semi-discrete time dependent non-linear case. In both cases, it is shown that the formulation is stable and optimally convergent under suitable regularity assumptions.El Método de los Elementos Finitos (MEF) es una herramienta numérica de gran alcance, que permite la resolución de problemas definidos por ecuaciones diferenciales parciales, comúnmente utilizado para llevar a cabo simulaciones numéricas de problemas de multifísica. En este trabajo, se utiliza para aproximar numéricamente el problema del flujo de fluidos viscoelásticos, el cual requiere la resolución de las ecuaciones básicas de Navier-Stokes y otra ecuación adicional constitutiva tensorial de tipo reactiva-convectiva, que describe la naturaleza viscoelástica del fluido. La formulación mixta de tres campos (velocidad-presión-tensión) del problema de Navier-Stokes, tanto en el caso elástico como en el no-elástico, puede conducir a dos tipos de inestabilidades numéricas. El primer grupo, se asocia con la incompresibilidad del fluido y la pérdida de estabilidad del campo de tensiones, y el segundo con la convección dominante. El primer tipo de inestabilidades, se puede solucionar eligiendo un tipo de interpolación entre las incógnitas que satisfaga las dos condiciones inf-sup que restringen el problema mixto, mientras que la convección dominante requiere del uso de formulaciones estabilizadas en cualquier caso. En el trabajo, se proponen diferentes esquemas estabilizados del tipo SGS (Sub-Grid-Scales) para resolver el problema de tres campos, primero para fluidos del tipo cuasi-newtonianos y luego para resolver el caso viscoelástico. Los métodos estabilizados propuestos permiten el uso de igual interpolación entre las incógnitas del problema y estabilizan la convección dominante, tanto en la ecuación de momento como en la ecuación constitutiva. Comenzando desde una formulación de tipo residual usada en el caso cuasi-newtoniano, se propone una formulación no-residual para el caso viscoelástico que muestra un comportamiento superior en presencia de singularidades numéricas y geométricas. En general, una formulación estabilizada produce una solución estable global, sin embargo, si la solución presenta gradientes elevados, oscilaciones locales se pueden mantener. Con el objetivo de aliviar este tipo de inestabilidades locales, se propone adicionalmente una técnica general de captura de discontinuidades para la tensión elástica. La resolución monolítica del problema de tres campos viscoelástico puede llegar a ser extremadamente costosa computacionalmente, sobre todo, en el caso tridimensional donde se tienen diez grados de libertad por nodo. Un enfoque de paso fraccionado motivado en los algorítmos clásicos de segregación de la presión usados en el caso del problema de dos campos de Navier-Stokes, se presenta en el trabajo, el cual permite la resolución del sistema de ecuaciones que definen el problema de una manera completamente desacoplada, lo que reduce los tiempos de cálculo y los requerimientos de memoria, respecto al caso monolítico. La simulación numérica de interfaces móviles que envuelve los problemas de dos fluidos, es un tópico importante en un gran número de procesos industriales y situaciones físicas. Si se resuelve el problema utilizando un enfoque de mallas fijas, cuando la interfaz que separa los dos fluidos corta un elemento, la discontinuidad en las propiedades materiales da lugar a discontinuidades en los gradientes de las incógnitas que no pueden ser capturados utilizando una formulación estándar de interpolación. Un enriquecimiento local para la presión se presenta en el trabajo, el cual permite la captura de gradientes discontinuos en la presión, asociados a fluidos de diferentes densidades. La estabilidad y la convergencia de la formulación no-residual utilizada para fluidos viscoelásticos es analizada en la última parte del trabajo, para un caso linealizado estacionario del tipo Oseen y para un problema transitorio no-lineal semi-discreto. En ambos casos, se logra mostrar que la formulación es estable y de convergencia óptima bajo supuestos de regularidad adecuados.Postprint (published version

Geophysical Fluid Dynamics

The workshop “Geophysical Fluid Dynamics” addressed recent advances in analytical, stochastic, modeling and computational studies of geophysical rotating fluids models. Of particular interest on the analytical and stochastic sides were the contributions concerning dispersive mechanism, regularity verses finite-time formation of singularities of certain viscous and inviscid geostrophic models, the primitive equations, Boussinesq approximation, boundary layers and fast rotating fluids. Model reductions, based on asymptotic, scaling analysis and variational methods, were presented. In addition, computational investigations were provided in support of the claim that three-dimensional geophysical turbulent flows exhibit two-dimensional features, at small Rosby numbers

Emerging Developments in Interfaces and Free Boundaries

The field of the mathematical and numerical analysis of systems of nonlinear partial differential equations involving interfaces and free boundaries is a well established and flourishing area of research. This workshop focused on recent developments and emerging new themes. By bringing together experts in these fields we achieved progress in open questions and developed novel research directions in mathematics related to interfaces and free boundaries. This interdisciplinary workshop brought together researchers from distinct mathematical fields such as analysis, computation, optimisation and modelling to discuss emerging challenges

The Effect of Malaysia General Election on Financial Network: An Evidence from Shariah-Compliant Stocks on Bursa Malaysia

Instead of focusing the volatility of the market, the market participants should consider on how the general election affects the correlation between the stocks during 14th general election Malaysia. The 14th general election of Malaysia was held on 9th May 2018. This event has a great impact towards the stocks listed on Bursa Malaysia. Thus, this study investigates the effect of 14th general election Malaysia towards the correlation between stock in Bursa Malaysia specifically the shariah-compliant stock. In addition, this paper examines the changes in terms of network topology for the duration, sixth months before and after the general election. The minimum spanning tree was used to visualize the correlation between the stocks. Also, the centrality measure, namely degree, closeness and betweenness were computed to identify if any changes of stocks that plays a crucial role in the network for the duration of before and after 14th general election Malaysia

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio