Theoretical Analysis of the No-Slip Boundary Condition Enforcement in SPH Methods

The aim of the present work is to provide an in-depth analysis of the most representative mirroring techniques used in SPH to enforce boundary conditions (BC) along solid profiles. We specifically refer to dummy particles, ghost particles, and Takeda et al. [Prog. Theor. Phys. 92 (1994), 939] boundary integrals. The analysis has been carried out by studying the convergence of the first- and second-order differential operators as the smoothing length (that is, the characteristic length on which relies the SPH interpolation) decreases. These differential operators are of fundamental importance for the computation of the viscous drag and the viscous/diffusive terms in the momentum and energy equations. It has been proved that close to the boundaries some of the mirroring techniques leads to intrinsic inaccuracies in the convergence of the differential operators. A consistent formulation has been derived starting from Takeda et al. boundary integrals (see the above reference). This original formulation allows implementing no-slip boundary conditions consistently in many practical applications as viscous flows and diffusion problems.

On the non-slip boundary condition enforcement in SPH methods.

The implementation of boundary conditions is one of the points where the SPH methodology still has some work to do. The aim of the present work is to provide an in-depth analysis of the most representative mirroring techniques used in SPH to enforce boundary conditions (BC) along solid profiles. We specifically refer to dummy particles, ghost particles, and Takeda et al. [1] boundary integrals. A Pouseuille flow has been used as a example to gradually evaluate the accuracy of the different implementations. Our goal is to test the behavior of the second-order differential operator with the proposed boundary extensions when the smoothing length h and other dicretization parameters as dx/h tend simultaneously to zero. First, using a smoothed continuous approximation of the unidirectional Pouseuille problem, the evolution of the velocity profile has been studied focusing on the values of the velocity and the viscous shear at the boundaries, where the exact solution should be approximated as h decreases. Second, to evaluate the impact of the discretization of the problem, an Eulerian SPH discrete version of the former problem has been implemented and similar results have been monitored. Finally, for the sake of completeness, a 2D Lagrangian SPH implementation of the problem has been also studied to compare the consequences of the particle movement

Is there scope for a new project bond market in Europe? A promising opportunity for promoting transnational infrastructure

La Unión Europea acaba de lanzar una iniciativa para fomentar Participaciones Público Privadas (PPPs) mediante bonos de proyecto más atractivos a inversores institucionales para promover proyectos transeuropeos. Esto se logra a través de mecanismos de mejora crediticia como garantías de liquidez o tramos de deuda subordinada facilitados por el Banco Europeo de Inversiones. Esta iniciativa pretende evitar los problemas de liquidez experimentados actualmente por bancos comerciales en Europa para financiar megaproyectos. En este artículo exploramos las ventajas e inconvenientes de esta iniciativa para promover redes de infraestructuras transnacionales en Europa, y analizamos su aplicabilidad a otras áreas como Latino-América. The European Union recently launched an initiative to foster Public Private Partnerships (PPPs) for delivering Trans-European projects by making long-term project-bonds more appealing to institutional investors. This is achieved through credit-enhancement mechanisms such as partial stand-by liquidity guarantees, or layers of subordinated debt provided by the European Investment Bank. This initiative intends to circumvent the liquidity problems currently endured by commercial banks in Europe to fund megaprojects. In this paper we explore the advantages and drawbacks of this initiative for promoting transnational infrastructure networks in Europe, and analyse its applicability to other economic areas such as Latin America.