Robert Jan Labeur

Energy Stable and Momentum Conserving Hybrid Finite Element Method for the Incompressible Navier-Stokes Equations

A hybrid method for the incompressible Navier-Stokes equations is presented. The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can be used for the velocity and pressure fields, and mass can be conserved locally. Using continuous Lagrange multiplier spaces to enforce flux continuity across cell facets, the number of global degrees of freedom is the same as for a continuous Galerkin method on the same mesh. Different from our earlier investigations on the approach for the Navier-Stokes equations, the pressure field in this work is discontinuous across cell boundaries. It is shown that this leads to very good local mass conservation and, for an appropriate choice of finite element spaces, momentum conservation. Also, a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed, even in the absence of a pointwise solenoidal velocity field. Mass conservation, momentum conservation, and global energy stability are proved for the time-continuous case and for a fully discrete scheme. The presented analysis results are supported by a range of numerical simulations.

Movement of tidal watersheds in the Wadden Sea and its consequences on the morphological development

Abstract The Wadden Sea consists of a series of tidal lagoons which are connected to the North Sea by tidal inlets. Boundaries of each lagoon are the mainland coast, the barrier islands on both sides of the tidal inlet, and the tidal watersheds behind the two barrier islands. Behind each Wadden Island there is a tidal watershed separating two adjacent tidal lagoons. The locations of the tidal watersheds in the Wadden Sea are not fixed. Especially after a human interference in one of the tidal lagoons, a tidal watershed can move and thereby influence the distribution of area between the lagoons. This appears to be important for the morphological development in not only the basin in which the interference takes place, but also in the adjacent basins. This paper describes theoretical analyses and numerical modelling aimed at improving the insights into the location of the tidal watersheds, their movements, and the impact of the movements of tidal watersheds on the morphological development of a multi-basin system like the Wadden Sea.

A hybridized discontinuous Galerkin framework for high-order particle–mesh operator splitting of the incompressible Navier–Stokes equations

Abstract A generic particle–mesh method using a hybridized discontinuous Galerkin (HDG) framework is presented and validated for the solution of the incompressible Navier–Stokes equations. Building upon particle-in-cell concepts, the method is formulated in terms of an operator splitting technique in which Lagrangian particles are used to discretize an advection operator, and an Eulerian mesh-based HDG method is employed for the constitutive modeling to account for the inter-particle interactions. Key to the method is the variational framework provided by the HDG method. This allows to formulate the projections between the Lagrangian particle space and the Eulerian finite element space in terms of local (i.e. cellwise) l 2 -projections efficiently. Furthermore, exploiting the HDG framework for solving the constitutive equations results in velocity fields which excellently approach the incompressibility constraint in a local sense. By advecting the particles through these velocity fields, the particle distribution remains uniform over time, obviating the need for additional quality control. The presented methodology allows for a straightforward extension to arbitrary-order spatial accuracy on general meshes. A range of numerical examples shows that optimal convergence rates are obtained in space and, given the particular time stepping strategy, second-order accuracy is obtained in time. The model capabilities are further demonstrated by presenting results for the flow over a backward facing step and for the flow around a cylinder.

Development of a hybrid particle-mesh method for simulating free-surface flows

In this work the feasibility of a numerical wave tank using a hybrid particle-mesh method is investigated. Based on the fluid implicit particle method (FLIP) a formulation for the hybrid method is presented for incompressible multiphase flows involving large density jumps and wave generating boundaries. The performance of the method is assessed for a standing wave and for the generation and propagation of a solitary wave over a flat and a sloping bed. A comparison is made with results obtained with a well-established SPH package. The tests demonstrate that the method is a promising and attractive tool for simulating the nearshore propagation of waves.

Surfing waves generated by a hull

In this paper a new wave pool concept is presented using ship hulls as wave generators. To evaluate the potential of such a concept a towing tank experiment is conducted to investigate ship wave generation in a confined space. In the towing tank experiment various hull sizes and velocities are examined to maximize the generated wave height. The laboratory data shows that when blocking of the cross section of the pool by the hull is large, the large return flow significantly influences the wave height. This is in contrast to the open water case where the return flow is much smaller and therefore is not incorporated in wave height predictions. Based on the results of the physical model tests an optimum hull size and velocity are derived to maximize the potential use for surfing and a preliminary design of the wave pool is proposed.