Friction decoupling and loss of rotational invariance in flooding models

Friction decoupling, i.e. the computation of friction vector components making separate use of the corresponding velocity components, is common in staggered grid models of the SWE simplifications (Zero-Inertia and Local Inertia Approximation), due to the programming simplicity and to the consequent calculations speed-up. In the present paper, the effect of friction decoupling has been studied from the theoretical and numerical point of view. First, it has been found that friction vector decoupling causes the reduction of the computed friction force and the rotation of the friction force vector. Second, it has been demonstrated that decoupled-friction models lack of rotational invariance, i.e. model results depend on the alignment of the reference framework. These theoretical results have been confirmed by means of numerical experiments. On this basis, it is evident that the decoupling of the friction vector causes a major loss of credibility of the corresponding mathematical and numerical models. Despite the modest speed-up of decoupled-friction computations, classic coupled-friction models should be preferred in every case

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 two-layer shallow water model for bedload sediment transport: convergence to Saint-Venant-Exner model

A two-layer shallow water type model is proposed to describe bedload sediment transport. The upper layer is filled by water and the lower one by sediment. The key point falls on the definition of the friction laws between the two layers, which are a generalization of those introduced in Fern\'andez-Nieto et al. (ESAIM: M2AN, 51:115-145, 2017). This definition allows to apply properly the two-layer shallow water model for the case of intense and slow bedload sediment transport. Moreover, we prove that the two-layer model converges to a Saint-Venant-Exner system (SVE) including gravitational effects when the ratio between the hydrodynamic and morphodynamic time scales is small. The SVE with gravitational effects is a degenerated nonlinear parabolic system. This means that its numerical approximation is very expensive from a computational point of view, see for example T. Morales de Luna et al. (J. Sci. Comp., 48(1): 258-273, 2011). In this work, gravitational effects are introduced into the two-layer system without such extra computational cost. Finally, we also consider a generalization of the model that includes a non-hydrostatic pressure correction for the fluid layer and the boundary condition at the sediment surface. Numerical tests show that the model provides promising results and behave well in low transport rate regimes as well as in many other situations

Demonstration of a coupled floating offshore wind turbine analysis with high-fidelity methods

This paper presents results of numerical computations for floating off-shore wind turbines using, as an example, a machine of 10-MW rated power. The aerodynamic loads on the rotor are computed using the Helicopter Multi-Block flow solver developed at the University of Liverpool. The method 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 are computed using the Smoothed Particle Hydrodynamics method, which is mesh-free and represents the water and floating structures by a set of discrete elements, referred to as 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 results are presented in this paper. The importance of coupling is assessed and the loosely coupled algorithm used is described in detail alongside the obtained results

Multilayer shallow water models with locally variable number of layers and semi-implicit time discretization

We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in which the number of vertical layers and their distribution are allowed to change in different regions of the computational domain. Furthermore, semi-implicit schemes are employed for the time discretization, leading to a significant efficiency improvement for subcritical regimes. We show that, in the typical regimes in which the application of multilayer shallow water models is justified, the resulting discretization does not introduce any major spurious feature and allows again to reduce substantially the computational cost in areas with complex bathymetry. As an example of the potential of the proposed technique, an application to a sediment transport problem is presented, showing a remarkable improvement with respect to standard discretization approaches

Coupling shallow water models with three-dimensional models for the study of fluid-structure interaction problems using the particle finite element method

(English) This thesis investigates numerical methods for the simulation of surface water flows, focusing on the interaction between the large scale and the local scale and its application to natural hazards. Several families of numerical methods for the approximation of large scale phenomena and the coupling with the local scale have been analyzed. The general motion of a fluid mass is governed by the Navier-Stokes equations, which can accurately solve the local scale phenomena. However, the same level of accuracy is not required by the large scale solution of the water-related events. In this context, the shallow water equations are defined. In contrast to the extensive use of the Finite Element Method for solving the Navier-Stokes equations, the shallow-water equations are usually solved with the Finite Volume Method. Thus, an effort have been done to solve both equations in an unified framework. The first part of this thesis is devoted to study stabilized formulations of Finite Element Method for the different forms of the shallow water equations. Stabilized formulations arise from the need to mitigate the various instabilities inherent in numerical approximations. The first source of instability is the incompatibility of the equal interpolation of the variables. The second source of instability is the presence of shocks due to the change of regime or hydraulic jumps. Finally, Gibbs oscillations may appear on the moving shoreline and monotonic properties of the physical system are lost by the numerical approximation. The second part of the thesis is committed to the coupling strategies of the numerical methods for the Navier-Stokes and the shallow water equations. The case of a coupling from the local scale to the large scale is analyzed. This type of coupling corresponds to the generation of cascading natural hazard. The proposed strategy combines a Lagrangian Navier Stokes multi-fluid solver with an Eulerian method based on the Boussinesq equations, an extension of the shallow water equations. Finally, the proposed technique is applied to the numerical simulation of landslide-generated impulse waves. The Particle Finite Element Method has been used to model the landslide runout, its impact against the water body and the consequent wave generation. The results of this fully-resolved analysis are stored at selected interfaces and then used as input for the modelling of waves propagation on the far-field. This one-way coupling scheme drastically reduces the computational cost of the analyses while maintaining high accuracy in reproducing the key phenomena of cascading natural hazards.(Español) En esta tesis se investigan métodos numéricos para la simulación de flujos de aguas superficiales, haciendo énfasis en la interacción entre las distintas escalas y su aplicación a desastres naturales. Se han analizado diversas familias de métodos numéricos para aproximar los fenómenos a gran escala y su acoplamiento con la escala local. El movimiento general de una masa de fluido se rige por las ecuaciones de Navier-Stokes, que pueden resolver con precisión los fenómenos a escala local. Sin embargo, la solución numérica a gran escala de dichos fenómenos, no requiere el mismo nivel de precisión. En este ámbito, se definen las acuaciones de agua poco profundas. En contraste con el amplio uso del Método de los Elementos Finitos para aproximar las ecuaciones de Navier-Stokes, las ecuaciones de aguas poco profundas se suelen resolver con el Método de los Volúmenes Finitos. Por ello, se ha realizado un esfuerzo para resolver ambas ecuaciones en un marco unificado. La primera parte de esta tesis está dedicada a estudiar formulaciones estabilizadas para el Método de los Elementos Finitos aplicado a las diferentes formas de las ecuaciones de aguas someras. Las formulaciones estabilizadas surgen de la necesidad de mitigar las diferentes inestabilidades inherentes a las aproximaciones numéricas. La primera fuente de inestabilidad es la incompatibilidad debida a la interpolación de las variables. La segunda fuente de inestabilidad es la presencia de discontinuidades debidos al cambio de régimen o a los saltos hidráulicos. Por último, pueden aparecer oscilaciones de Gibbs en la línea de costa en movimiento, dado que las propiedades monótonas del sistema físico se pierden por la aproximación numérica. La segunda parte de la tesis está dedicada a las estrategias de acoplamiento de los métodos numéricos para las ecuaciones de Navier-Stokes y de aguas poco profundas. Se ha analizado el caso de acoplamiento desde la escala local a la escala global. Este tipo de acoplamiento corresponde a la generación de desastres naturales en cascada. La estrategia propuesta combina un solver Lagrangiano de Navier Stokes para multi-fluidos con un método Euleriano basado en las ecuaciones de Boussinesq, una extensión de las ecuaciones de aguas someras. Finalmente, la técnica propuesta se ha aplicado a la simulación numérica de olas generadas por deslizamientos. El deslizamiento de ladera, su impacto contra la masa de agua y la consiguiente generación de olas se ha modelado con el Método de Elementos Finitios de Partículas. Los resultados de este análisis detallado se almacenan en las interfaces seleccionadas que, luego, se utilizan como punto de entrada para modelar la propagación de olas en el campo lejano. Este esquema de acoplamiento unidireccional reduce drásticamente el coste computacional, a la vez que se mantiene una alta precisión en la simulación de los fenómenos clave de desastres naturales.Postprint (published version