A Very High-Order Accurate Staggered Finite Volume Scheme for the Stationary Incompressible Navier–Stokes and Euler Equations on Unstructured Meshes

International audienceWe propose a sixth-order staggered finite volume scheme based on polynomial reconstructions to achieve high accurate numerical solutions for the incompressible Navier-Stokes and Euler equations. The scheme is equipped with a fixed-point algorithm with solution relaxation to speed-up the convergence and reduce the computation time. Numerical tests are provided to assess the effectiveness of the method to achieve up to sixth-order con-2 Ricardo Costa et al. vergence rates. Simulations for the benchmark lid-driven cavity problem are also provided to highlight the benefit of the proposed high-order scheme

A generalised immersed boundary method for flows of dense suspension of solid particles

Immersed boundary method (IBM) provides computational advantages in approximating moving solid surfaces on fixed numerical meshes. It has been widely used for fully-resolved simulations of particulate flows. This thesis proposes a generalised formulation of IBM with improved applicability to flows with dense concentrations of particles and unstructured meshes. The new IBM formulation, which is based on the smooth-interface direct forcing approach, directly uses the algebraic discretised terms of the momentum equations in the evaluation of the forces on Lagrangian immersed boundary (IB) points, and evaluate the integral Lagrangian volumes based on these forces. Appropriate reconstructions of the boundary forces are adopted to ensure the compatibility with the momentum-weighted interpolation used for the finite-volume discretisation with a collocated mesh arrangement. A modified direct forcing formulation is also proposed, which results in an efficiency gain of a devised segregated flow-particle coupling scheme. The novel framework is applied to flows with stationary and moving IBs on both Cartesian and arbitrary triangular/tetrahedral meshes, and the results are similar or better than other related methods that are mostly developed for Cartesian meshes. Accurate and stable enforcement of the no-slip condition on the IB at every time-step is demonstrated, even for flows with strong transient behaviour and high velocity and pressure gradients. Local continuity in the vicinity of the IB is also preserved, ensuring local and global mass conservation alongside the local no-slip condition. Adaptations devised for unstructured meshes results in an accuracy close to that obtained on Cartesian meshes. The framework is successfully applied in the simulations of fluidisation of dense particle bed and a rising pack of light particles, showing robust stability. The issues related to the interfering regularised forces of different particle surfaces are not significant using the present formulation, hence eliminate unphysical flow patterns between aggregated particles.Open Acces

Computational modelling of ice floe dynamics in the Antarctic marginal ice zone.

The contribution of Antarctic sea ice in global climate models requires a more accurately estimation, as a relatively large part, approximately 4% of the Earth's surface in the winter season, is covered by sea ice. Understanding the dynamic and thermodynamic processes of sea ice, results in a better comprehension of sea ice behaviour in the Antarctic marginal ice zone (MIZ) and thus leads to better predictions. Large-scale sea ice models operate at regions of 10-100km2 , describing sea ice in a smeared model approach. However, the highly dynamic sea ice behaviour in the Antarctic MIZ, which is represented by the area where sea ice and ocean waves interact, still eludes reliable prediction. A heterogeneous morphology, consisting of relatively small and mobile ice floes, governed by collisional dynamics and fracture mechanics, requires detailed finer-scale sea ice dynamics models. Therefore, this project focuses on small-scale modelling of sea ice dynamics in the Antarctic MIZ. A more detailed model implies a heterogeneous sea ice material composition, considering separately ice floes and grease ice with their distinct properties. The material behaviour of ice floes is implemented using a Hookean-like flow rule, whereas grease ice is governed by a viscous-plastic material law. The small-scale model assumes that sea ice is isothermal, as only small time windows of less than a minute are considered. As a result, thermodynamic effects, such as sea ice melt and growth, are not taken into account. This work describes key aspects of ice floe collision dynamics in wavy conditions, considering skin drag, the Froude-Krylov force acting at the circumference of ice floes from the wave pressure gradient, and form drag due to the surrounding grease ice deeper into the Antarctic MIZ in a low to medium wave energy regime. Ice floes that interact with each other and the interaction between ice floes and grease ice are analysed. The behaviour of the sea ice rheology of both ice floes and grease ice are studied in realistic sea ice layouts, subjected to different wave properties and grease ice viscosity values. The influence of inertia on the phase shift between the motion of the sea ice cover and the orbital wave velocity of the water layer underneath, is one of the most important aspects in the small-scale model. The phase shift directly affects the interrelation between the sea ice velocity, wave elevation and the ice floe collision dynamics. Additionally, the collision dynamics shows that the ice floe collision pattern in the sea ice domain becomes more random for larger wave periods, due to an increase of the kinetic wave energy. Lastly, strain rates exhibit high localised gradients due to form drag at the interface between ice floes and grease ice, which corresponds to low viscosity values. The small-scale model, demonstrated in this study, shows the general applicability of a detailed continuum framework, contributing to the current research to small-scale atmosphere-ocean physical processes in the Antarctic MIZ. The obtained results provide insights into high resolution behaviour of sea ice on the floe-scale. Furthermore, the newly-developed model can provide for the parametrisation of large-scale models, improving existing global climate models