9h00 Open session

9h30-10h15 "Efficient very high-order accurate polyhedral mesh finite volume scheme for 3D conjugate heat transfer problems in curved domains", Ricardo Costa

Abstract. A very high-order accurate finite volume scheme is proposed to solve three-dimensional conjugate heat transfer problems in arbitrary curved domains. The proposed method preserves the accuracy and the convergence order with the sole use of polyhedral meshes, overcoming the main shortcomings of the standard curved mesh approaches. The implementation is also addressed and optimized calculations are derived to provide the same approximate solution at a significantly reduced computational cost. A set of numerical benchmarks addresses several situations of the conjugate heat transfer problem and proves that the optimal convergence order is effectively achieved and that substantial performance improvements are obtained from the proposed optimizations.

10h30-11h15 "A Mathematical Model for the Corneal Transparency Problem", Adérito Araújo

Abstract. This work aims to identify the conditions that lead to corneal opacity. The cornea is the transparent, protective front of the eye and maintaining its curvature and transparency is essential for good vision. This question is relevant because there are several pathologies that increase the scattering of light in the cornea, often requiring surgical intervention. Our objective is to develop a suitable mathematical model capable of representing the lamellar structure of the cornea and simulating different scenarios that may help to early identify the characteristics that lead to a loss of corneal transparency.

In this talk, we will use Maxwell's equations to model the propagation of light in ocular tissues and a discontinuous Galerkin method associated with an explicit Runge-Kutta method to simulate the propagation of light in normal corneas and corneas that reveal pathologies. The results obtained allow us to conclude that an increase in the diameter of some fibrils can result in a loss of corneal transparency.

11h30-12h15 "The stability of the coastal protection structures with focus on the Sines port", Saeid Lotfi

Abstract. This study is focused on the stability of different breakwaters. The final objective of this study is numerical modelling of coastal protection structures using FEM with focus on the breakwater of Sines port. The work begun with a literature review of guidelines which are available for different countries including the guidelines for sea defence structures, recommended design for a strong breakwater, ASCE 7 tsunami loads chapter, risk categories of buildings (ASCE 7), FEMA55, CCH and SMBTR codes for tsunami-induced loads. Moreover, different parameters and various aspects were accurately studied including building damage data, tsunami intensity data, numerical methods to define tsunami-induced forces on structure, tsunami mitigation strategies, tsunami terminology and debris impact. Much attention was devoted to breakwaters, failure mechanism and damage, countermeasures, harbours and finally, the stability of the structures of Sines Port. In this regard, a fully comprehensive study is conducted to take into account all the aspects. In the next stage, all of the existing formulae related to the stability of the different breakwaters are extracted accurately. The focus is on the shallow water equations, which are the most suitable assumptions for the tsunami action in the Sines Port. All types of armour units are studied properly. Different versions of Hudson formulae to use for the Sines port are uniquely investigated.

12h30-13h00 Activity report.

14h30-15h15 "Solving non-linear problems with curved boundaries on a Cartesian grid", Diogo Lopes

Abstract. A method to solve non-linear equations in a Cartesian grid with curved boundaries is presented. It combines the reconstruction off-site (ROD) method to calculate the values of the boundary cells (ghost cells) with an alternate direction implicit (ADI) method to compute the values of the inner cells. Given any type of boundary conditions and domain, this method employs both ROD and ADI in succession until the solution converges to a desirable degree. We present an example of the capacity for this method to solve non-linear problems by considering a steady-state convection-diffusion heat transfer problem, where the value of conductivity depends on the overall solution to the problem

15h30-16h15 "Compact time schemes for EDO and EDP", Gaspar Machado

Abstract. In this talk, we introduce new compact implicit schemes based on the physical equation and on a structural equation that links the function and its derivatives. The stability and accuracy are analysed and a detailed set of benchmarks are presented for the ordinary differential equation y'=lambda y as well as the linear convection-diffusion equation and the nonlinear Burgers equation.

16h30-17h00 Future and perspectives