CFD investigation of a complete floating offshore wind turbine

This chapter presents numerical computations for floating offshore wind turbines for a machine of 10-MW rated power. The rotors were computed using the Helicopter Multi-Block flow solver of the University of Glasgow that solves the Navier-Stokes equations in integral form using the arbitrary Lagrangian-Eulerian formulation for time-dependent domains with moving boundaries. Hydrodynamic loads on the support platform were computed using the Smoothed Particle Hydrodynamics method. This method is mesh-free, and represents the fluid by a set of discrete particles. The motion of the floating offshore wind turbine is computed using a Multi-Body Dynamic Model of rigid bodies and frictionless joints. Mooring cables are modelled as a set of springs and dampers. All solvers were validated separately before coupling, and the loosely coupled algorithm used is described in detail alongside the obtained results

A conservative integration of the pseudo-incompressible equations with implicit turbulence parameterization

Durran’s pseudo-incompressible equations are integrated in a mass and momentum conserving way with a new implicit turbulence model. This system is soundproof, which has two major advantages over fully compressible systems: the Courant–Friedrichs–Lewy (CFL) condition for stable time advancement is no longer dictated by the speed of sound and all waves in the model are clearly gravity waves (GW). Thus, the pseudo-incompressible equations are an ideal laboratory model for studying GW generation, propagation, and breaking. Gravity wave breaking creates turbulence that needs to be parameterized. For the first time the adaptive local deconvolution method (ALDM) for implicit large-eddy simulation (ILES) is applied to non-Boussinesq stratified flows. ALDM provides a turbulence model that is fully merged with the discretization of the flux function. In the context of non-Boussinesq stratified flows this poses some new numerical challenges—the solution of which is presented in this text. In numerical test cases the authors show the agreement of the results with the literature (Robert’s hot–cold bubble test case), they present the sensitivity to the model’s resolution and discretization, and they demonstrate qualitatively the behavior of the implicit turbulence model for a 2D breaking gravity wave packet

A novel deterministic forecast model for COVID-19 epidemic based on a single ordinary integro-differential equation

In this paper we present a new approach to deterministic modelling of COVID-19 epidemic. Our model dynamics is expressed by a single prognostic variable which satisfies an integro-differential equation. All unknown parameters are described with a single, time-dependent variable R(t). We show that our model has similarities to classic compartmental models, such as SIR, and that the variable R(t) can be interpreted as a generalized effective reproduction number. The advantages of our approach are the simplicity of having only one equation, the numerical stability due to an integral formulation and the reliability since the model is formulated in terms of the most trustable statistical data variable: the number of cumulative diagnosed positive cases of COVID-19. Once this dynamic variable is calculated, other non-dynamic variables, such as the number of heavy cases (hospital beds), the number of intensive-care cases (ICUs) and the fatalities, can be derived from it using a similarly stable, integral approach. The formulation with a single equation allows us to calculate from real data the values of the sample effective reproduction number, which can then be fitted. Extrapolated values of R(t) can be used in the model to make reliable forecasts, though under the assumption that measures for reducing infections are maintained. We have applied our model to more than 15 countries and the ongoing results are available on a web-based platform [1]. In this paper, we focus on the data for two exemplary countries, Italy and Germany, and show that the model is capable of reproducing the course of the epidemic in the past and forecasting its course for a period of four to five weeks with a reasonable numerical stability

Accuracy in a finite volume godunov type method

The standard Godunov type method used in computational fluid dynamics shows accuracy problems for low Mach number flows and for the kinetic energy at the highest wave numbers resolvable on a given grid. Both drawbacks become visible when simulating the decay of isotropic turbulence at the low Mach numbers typical for the respective experimental investigations. A modification to cure both problems is proposed by Thornber et al. [10] with a mathematical motivation in case of a special fifth order reconstruction. The theoretical results are repeated here. Numerical results are achieved for schemes not investigated in that literature, namely AUSMDV and AUSM + -up which includes already modifications for low Mach number flows. First experiences with Thornber's modification confirm the positive influence in combination with AUSMDV even if the reconstruction is only of second order. In combination with AUSM + -up Thornber's modification provides too little damping when used without subgrid scale modelling. textcopyright 2013 Springer-Verlag Berlin Heidelberg