Loading...

Research Project

## Center for Mathematics, Fundamental Applications and Operations Research

## Funder

## Authors

## Publications

Kelvin-Voigt equations with anisotropic diffusion, relaxation and damping: Blow-up and large time behaviorExpand Expand

Publication . Antontsev, S.; Oliveira, H. B. de; Khompysh, Kh

A nonlinear initial and boundary-value problem for the Kelvin-Voigt equations with anisotropic diffusion, relaxation and absorption/damping terms is considered in this work. The global and local unique solvability of the problem was established in (J. Math. Anal. Appl. 473(2) (2019) 1122-1154). In the present work, we show how all the anisotropic exponents of nonlinearity and all anisotropic coefficients should interact with the problem data for the solutions of this problem display exponential and polynomial time-decays. We also establish the conditions for the solutions of this problem to blow-up in a finite time in three different cases: problem without convection, full anisotropic problem, and the problem with isotropic relaxation.

A strategy to assess water meter performanceExpand Expand

Publication . Cordeiro, Clara; Borges, Ana; Ramos, M. Rosário

A recurring problem that troubles water companies is that of timely detection of malfunctioning water meters. Indeed, defective water meters impair the management of water supply and diminish water companies’ revenues. The management of nonrevenue water (NRW) is one key issue for improving water use efficiency, reducing gaps
between water supply and demand (Ncube and Taigbenu 2019).
Water losses in the distribution system can be categorized as either real (leakage) or apparent (commercial) losses (Mutikanga et al. 2011). Water meter under-registration resulted in apparent losses and lost revenue (Moahloli et al. 2019; Fourie et al. 2020), being apparent losses one of the components of NRW. As Criminisi et al. (2009) explain, apparent losses are caused by unauthorized consumption and meter inaccuracies, corresponding not to physical but rather to financial losses. Since they are water volumes taken from the network and consumed but not accounted for, as a consequence, the company will be jeopardized by the unaccounted water volume, resulting in an important impact on the utility’s water and economic balances.
A long-known fact is that reducing apparent losses caused by meter inaccuracies can result in substantial short-term increases in utility revenue and lead to increasingly equitable service charges for long-term water consumers (Richards et al. 2010; Kadenge
et al. 2020). The accurate measurement of the water collected by meters is crucial in reducing any uncertainty affecting the water balance and has significant technical and economic implications (Pacheco et al. 2020). A cubic meter consumed but not measured
reduces the company revenue in quantity equal to the selling price of the last cubic meter of water consumed by that consumer (Arregui et al. 2018).
The water companies’ awareness for the responsible use of water has gained importance, with climate changes emphasizing this need. In the context of water scarcity, Oviedo-Ocana et al. ˜(2020) alert to the importance of assessing losses in water distribution systems since the compensation of water losses represents an increase in the source’s water supply. Enhancing that water use efficiency and conservation are priority alternatives to ensure, for example, universal access to drinking water and reducing the number of people suffering from water scarcity. Furthermore, Pacheco
et al. (2020) emphasize that water measurement will become an even more critical aspect in the near future because of the increase in the world’s water supplies due to population growth. In this context, one form of water companies to be aware of its important role is to steer the effective water consumption and guarantee an efficient manutention of its equipment, namely the water meters.
Current research confirms that several factors affect a water meter’s accuracy, particularly water meterage and total registered volume (Moahloli et al. 2019; Pacheco et al. 2020). Detecting the point in time in which water meters should be replaced implies
that they can be substituted proactively to minimize the impact of water consumption nonregistration and under-registration on NRW (Moahloli et al. 2019). There seems to be no specific determination and/or agreement on a water meter lifespan or optimal replacement period. Water meter producers only give a limited warranty against
manufacturing defects but do not specify the meters’ lifetime (Moahloli et al. 2019). It is believed that the premature replacement of water meters will result in a higher average life-cycle cost due to the initial fixed costs. However, if a meter is replaced too late, a
significant loss of revenue caused by meter nonregistration and under-registration will also increase the average life-cycle cost (Fontanazza et al. 2015). The main studies on this problem have adopted approaches based on laboratory studies, which may implicate two significant issues: (1) the high costs inherent to the laboratory, and (2) the conditions in which the tests are taken upon are far from the real scenario.

Cauchy problem for the Navier–Stokes–Voigt model governing nonhomogeneous flowsExpand Expand

Publication . Antontsev, S. N.; Oliveira, H. B. de

The Navier-Stokes-Voigt model that governs flows with non-constant density of incompressible fluids with elastic properties is considered in the whole space domain R-d and in the entire time interval. If d is an element of{2,3,4}, we prove the existence of weak solutions (velocity, density and pressure) to the associated Cauchy problem. We also analyse some issues of regularity of the weak solutions to the considered problem and the large time behavior in special unbounded domains.

Parabolic turbulence k-epsilon model with applications in fluid flows through permeable mediaExpand Expand

Publication . de Oliveira, H.B.

In this work, we study a one-equation turbulence k-epsilon model that governs fluid flows through permeable media. The model problem under consideration here is derived from the incompressible Navier-Stokes equations by the application of a time-averaging operator used in the k-epsilon modeling and a volume-averaging operator that is characteristic of modeling unsteady porous media flows. For the associated initial- and boundary-value problem, we prove the existence of suitable weak solutions (average velocity field and turbulent kinetic energy) in the space dimensions of physics interest.

## Organizational Units

## Description

## Keywords

## Contributors

## Funders

## Funding agency

Fundação para a Ciência e a Tecnologia

## Funding programme

6817 - DCRRNI ID

## Funding Award Number

UIDB/04561/2020