Héloïse Beaugendre

An immersed boundary method using unstructured anisotropic mesh adaptation combined with level-sets and penalization techniques

The interest on embedded boundary methods increases in Computational Fluid Dynamics (CFD) because they simplify the mesh generation problem in the case of the Navier-Stokes equations. The same simplifications occur for the simulation of multi-physics flows, the coupling of fluid-solid interactions in situation of large motions or deformations, to give a few examples. Nevertheless an accurate treatment of the wall boundary conditions remains an issue of the method. In this work, the wall boundary conditions are easily taken into account through a penalization technique, and the accuracy of the method is recovered using mesh adaptation, thanks to the potential of unstructured meshes. Several classical examples are used to demonstrate that claim.

Computation of ice shedding trajectories using cartesian grids, penalization, and level sets

We propose to model ice shedding trajectories by an innovative paradigm that is based on cartesian grids, penalization and level sets. The use of cartesian grids bypasses the meshing issue, and penalization is an efficient alternative to explicitly impose boundary conditions so that the body-fitted meshes can be avoided, making multifluid/multiphysics flows easy to set up and simulate. Level sets describe the geometry in a nonparametric way so that geometrical and topological changes due to physics and in particular shed ice pieces are straight forward to follow. The model results are verified against the case of a free falling sphere. The capabilities of the proposed model are demonstrated on ice trajectories calculations for flow around iced cylinder and airfoil.

Aerodynamic force evaluation for ice shedding phenomenon using vortex in cell scheme, penalisation and level set approaches

In this work, we propose a formulation to evaluate aerodynamic forces for flow solutions based on Cartesian grids, penalisation and level set functions. The formulation enables the evaluation of forces on closed bodies moving at different velocities. The use of Cartesian grids bypasses the meshing issues, and penalisation is an efficient alternative to explicitly impose boundary conditions so that the body fitted meshes can be avoided. Penalisation enables ice shedding simulations that take into account ice piece effects on the flow. Level set functions describe the geometry in a non-parametric way so that geometrical and topological changes resulting from physics, and particularly shed ice pieces, are straightforward to follow. The results obtained with the present force formulation are validated against other numerical formulations for circular and square cylinder in laminar flow. The capabilities of the proposed formulation are demonstrated on ice trajectory calculations for highly separated flow behind a bluff body, representative of inflight aircraft ice shedding.

Silicic acid flux to the ocean from tidal permeable sediments: A modeling study

Sandy sediments of tidal beaches are poor in reactive substances because they are regularly flushed by significant flow caused by tidal forcing. This transport process may significantly affect the flux of reactive solutes to the ocean. A two dimensional model coupling the Richards equation that describes the flow in permeable sediments and the conservation equation of the silicic acid was developed to simulate the evolution of the silicic acid concentration into a variably saturated porous media submitted to tidal forcing. A detailed algorithm of drainage zone under tidal forcing and numerical methods needed to solve it are properly presented. Flux to the ocean has been estimated. The silicic acid concentration displays a permanent lens with low silicic acid concentration at the top of the tidal zone. This lens that results from the tidal forcing, presents weak variations of area during the tidal cycle. Silicic outflux to the ocean increases with increasing beach slope, hydraulic conductivity and tidal range. Simulations reveal that the total silicic acid flux to the ocean from the coastal marine sands can be considered as significant compared to the flux supplied by the rivers. These results may alter the previously published global budget of the silicic acid to the ocean.

Simulation of ice shedding around an airfoil

In this work we propose to model ice shedding by an innovative paradigm that is based on cartesian grids, penalization and level sets. The use of cartesian grids bypass the meshing issue in complex geometries and moreover allows extensions to higher order accuracy in a natural and simple way. Penalization is an efficient alternative to explicitly impose boundary conditions so that the body fitted meshes can be avoided, making multi fluid/multi physics flows easy to set up and simulate. Level sets describe the geometry in a non-parametric way so that geometrical and topological changes due to physics and in particular ice-shedding are straight forward to follow.

Coupling particle sets of contours and streamline methods for solving convection problems

In this work a particle sets of contours method is coupled with a streamline technique in order to obtain accurate approximations of transport problems. A modified streamline technique is proposed and several bench tests arising in the field of porous media are then simulated to validate the new method.

Finite volume box scheme for a certain class of nonlinear conservation laws in mixed form

We develop a finite volume box scheme to approximate a certain class of nonlinear conservation laws in the form \(\partial_t \psi(p) - \nabla \cdot u(p,\nabla p) = f\). The proposed scheme was first introduced in [1] for the Poisson equation (for which \(\psi(p) \equiv 0\) and \(u(p, \nabla p) = \nabla p\). The principles of the scheme are first to use degrees of freedom located on mesh faces (or edges in two dimensions) for both the primal variable p and its flux u, and second to build the discrete equations by averaging the continuous ones onto “boxes”. In this sense the scheme can be viewed as a finite volume scheme ensuring a local conservation property at the mesh level.

Combined Finite Element — Particles Discretisation for Simulation of Transport-Dispersion in Porous Media

Combining finite element together with particle methods provide one of the best compromise for solving transport problem in porous media. Saturated or non-saturated flows are determined by boundary condition and the media permeability. 1For real terrain, permeability can consist in various almost constant and imbricated zones with complex shapes. Thus, it is of some interest that the boundary between two adjacent zones coincides with a natural mesh interface and that each element is entirely contains in one such zone. Beside this, solving transport equation by means of particle methods offers two distinctive advantages. The method is unconditionally stable when applied to a pure convective equation, and it does not contain any numerical diffusion if the particle trajectories are correctly computed. Therefore the combination of finite elements and particle method appears to be a straightforward application of the principle: “the right method at the right place”.

FENSAP-ICE: Roughness Effects on Ice Accretion Prediction

FENSAP-ICE is a 3D in-flight icing simulation system, built in a modular and interlinked way to successively solve each of flow, impingement, accretion, heat loads and performance degradation via new models based on the Euler/Navier-Stokes equations for the clean and degraded flow and new partial differential equations for the other three icing processes. This paper presents a number of improvements in calibrating the roughness in the flow module, FENSAP, and the evaluation of its influence on ice shape prediction. The paper also presents new 3D results of FENSAP-ICE.

Construction of a p-Adaptive Continuous Residual Distribution Scheme

A p-adaptive continuous residual distribution scheme is proposed in this paper. Under certain conditions, primarily the expression of the total residual on a given element K into residuals on the sub-elements of K and the use of a suitable combination of quadrature formulas, it is possible to change locally the degree of the polynomial approximation of the solution. The discrete solution can then be considered non continuous across the interface of elements of different orders, while the numerical scheme still verifies the hypothesis of the discrete Lax–Wendroff theorem which ensures its convergence to a correct weak solution. We detail the theoretical material and the construction of our p-adaptive method in the frame of a continuous residual distribution scheme. Different test cases for non-linear equations at different flow velocities demonstrate numerically the validity of the theoretical results.