Title : Free surface models for marine energy applications and numerical results.

Abstract : We are interested in the modeling of the free surface for marine energy applications. In Shallow Water systems, the assumption on an hydrostatic pressure leads to solving the system as a compressible system since an algebraic equation is explicitly given for the pressure. In this talk we focus on Shallow Water systems which take into account a pressure playing the role of a Lagrangian multiplier under a non-classical constraint. The idea is to rewrite the constraint under the form of a free divergence constraint in order to apply classical numerical methods developed for the Navier-Stokes Equations. Comparisons with analytical solutions and classical test cases are performed to evaluate the efficiency of our approach.

Title: A POD-based Reduced Order Model of Wind Turbine Wakes (S. J. Andersen, J. N. Sørensen, and R. F. Mikkelsen)

Abstract: The turbulence deep inside large wind farms is simulated using Large Eddy Simulation and the Actuator Line technique implemented model wind turbines in the Navier-Stokes equations. The simulations are carried out for 'infinitely' long rows of turbines simulated by applying cyclic boundary conditions at the inlet and outlet. The wind turbines inherently generated turbulence and a Reduced Order Model describing the highly dynamic flow is proposed based on a Proper Orthogonal Decomposition. The reconstructed flow is shown to capture the large scale motions of the highly turbulent flow and predict the loads well.

Title: A hybrid DNS/ROM approach for wind and ocean wave energy converters (Michel Bergmann, Andrea Ferrero and Angelo Iollo)

Abstract: We present a numerical method to solve fluid flows with interfaces like fluid structure interactions. The incompressible Navier-Stokes equations are discretized on Cartesian grids coupled with immersed boundary and level set methods. Several applications will be presented starting from 2D fish like swimming to 3D power extraction like a Wave Energy Converter and windtubines. The CPU costs required for these kind of applications can be prohibitive. Indeed, large computational domains have to be used due to complex outflow boundary conditions. We thus present a method based on POD ROM (Proper Orthogonal Decomposition Reduced Order Models) that allows to use significant smaller DNS domains. This hybrid DNS/ROM approach finally allows to concentrate efforts (DNS) where accuracy is needed (near boundary) and to approximate the solution on robust POD basis (computed offline) elsewhere.

Title : Lagrangian stochastic approach for wind farm simulation.

Abstract: In this talk, we introduce a Lagrangian stochastic approach for atmospheric boundary layer simulation. Such Lagrangian stochastic method is based on a turbulent-fluid-particle model, generally used for the description of the turbulent subgrid scales. We show that such Lagrangian particle approach is an interesting alternative for some applications, in particular in the context of down-scaling simulation from a LES in meteorology. This approach will be also illustrated by numerical results obtained for the computation of circulation around wind turbines, with Lagrangian versions of actuator disk methods.

Title: Calibrated Reduced Order Modeling

Abstract:

Title : Anisotropic mesh adaptation and immersed method toward offshore wind turbine simulation (T. Coupez, L. Doutreau, H. Digonnet, L. Silva)

Abstract : A wider use of numerical simulation is still depending on meshing and adaptive meshing capabilities when complex geometry, multi-domain, moving interface and multiphase flow are involved as in offshore wind turbine simulation. This task becomes more and more difficult when it is combined with a posteriori adaptive meshing or/and dealing with boundary layers. In order to overcome the lack of flexibility of the common body fitted method, the alternative proposed here, is based on an implicit representation of the interfaces by a truncated distance function using a hyperbolic tangent filter [1]. Therefore, the geometries can be interpolated and contribute to the numerical error which is detected by an a posteriori error estimator [2]. This approach favors the full usage of anisotropic adaptive meshing techniques providing an optimal capture of the interfaces within the volume mesh, whatever is the complexity of the geometry involved. From the flow solver side, the interface condition transfer is enforced by following the immersed boundary (IBM) or immersed volume (IVM) methodologies for respectively fluid solid and or fluid structure interaction [3]. The multiphase flow solver, including a related local level set technique [4], is based on a stabilized finite element method (VMS) that can afford with anisotropic meshing with high aspect ratio elements [5]. First steps toward offshore wind turbine simulation within such a framework will be discussed.

[1] T. Coupez, L. Silva, E. Hachem, Implicit boundary and adaptive anisotropic meshing, SEMA SIMAI Springer Series, Vol. 5, pp. 1-18, (2014)
[2] T. Coupez, Metric construction by length distribution tensor and edge based error for anisotropic adaptive meshing, J. of Comp. Physics Vol 23, pp. 2391-2405 (2011)
[3] E. Hachem, S. Feghali, R. Codina, T. Coupez, Anisotropic adaptive meshing and monolithic Variational Multiscale method for fluid--structure interaction}, Comp. Strut., Vol. 122, pp. 88- 100, 2013
[4] L. Ville, L. Silva, T. Coupez, Convected level set method for the numerical simulation of fluid buckling, International Journal for Numerical Methods in Fluids, Vol. 66 (3) pp. 324-344 (2011)
[5] T. Coupez, E. Hachem, "Solution of high Reynolds Incompressible Flow with Stabilized Finite Element and Adaptive Anisotropic Meshing", Comp. Meth. in App. Mech. and Engng Vol. 267, pp. 65-85, (2013)

Title: Parallel finite element framework for the numerical simulation of multiphase flows involving moving solids (Mehdi Khalloufi, Rudy Valette, Youssef Mesri and Elie Hachem)

Abstract: We propose in this work an adaptive finite element method for complex multiphase flows with surface tension and moving solids. The proposed framework is based on a new conservative level-set method used to provide a precise position of the interfaces. It is combined with an implicit implementation of the surface tension and anisotropic parallel mesh adaptation. The obtained system is solved using a unified compressible-incompressible variational multiscale stabilized finite element method designed to handle the abrupt changes at the interface and large density and viscosity ratios. Combined with an a posteriori error estimator, we show that the proposed framework yields accurate 3D modeling for turbulent multiphase flows.

Title: Partial mechanics of far fields for nonlinear vibration (D.T. Le, D. Ryckelynck)

Abstract: Nonlinear dynamical analyses are generally complex due to the time integration of the nonlinear motion equations. For a system with a large number of degrees of freedom, these nonlinear dynamical analyses are time consuming and expensive.
Model reduction techniques such as the proper orthogonal decomposition (POD) [1] method can be used to reduce the computational effort of simulations by reducing the number of degrees of freedom. For medium problems, the classical Galerkin formulation of the nonlinear reduced equations do not provide sufficient speed-up. It is mainly because the repeated computation of residuals and tangent stiffness matrices, which remains affected by the complexity of the original model. Hyper-reduction methods aim to generate reduced-order model whose complexity does not depend on the complexity of the original model by introducing a reduced integration domain (RID) [2], [3]. This RID is created by selecting few elements of the mesh to perform the local integration of the nonlinear motion equations. The introduction of RID can reduce the number of integration points, but inevitably leads to the problems of accuracy in some domains. To ensure the high fidelity solution in some zones of interest (IZ), we propose to couple hyper-reduction with finite element approximation as an extension of the works proposed in [4],[5], [6].
A 2D elastic beam model is considered to illustrate the capabilities of the method. Large deformation of the beam is the nature of nonlinearity in the problem. We use a Newmark integration scheme and a Newton Raphson algorithm for the solution of the nonlinear time dependent equations. The displacement fields outside IZ of the first 50 time-steps are used as snapshots to build the first part of POD basis. The second part of the POD basis is the finite element basis whose support is located inside IZ. The RID obtained from the discrete empirical interpolation method (DEIM) with the new POD basis automatically contains IZ. To compare with the finite element solutions, the error related to maximum displacement is only 0.05% and to the maximum stress inside IZ is only 0.003%. The computational time saving is about 50%.

[1] L. Sirovich. "Turbulence and the dynamics of coherent structures. Part I: Coherent structures". Quarterly of applied mathematics 45.3 (1987), pp. 561–571.
[2] D Ryckelynck. "A priori hyperreduction method: an adaptive approach". Journal of computational physics 202.1 (2005), pp. 346–366.
[3] D. Ryckelynck. "Hyper-reduction of mechanical models involving internal variables". International Journal for Numerical Methods in Engineering 77.1 (2009), pp. 75–89.
[4] P. Kerfriden, J.-C. Passieux, and S. P.-A. Bordas. "Local/global model order reduction strategy for the simulation of quasi-brittle fracture". International Journal for Numerical Methods in Engineering 89.2 (2012), pp. 154–179.
[5] A. Radermacher and S. Reese. "Model reduction in elastoplasticity: proper orthogonal decomposition combined with adaptive sub-structuring". Computational Mechanics 54.3 (2014), pp. 677–687.
[6] A. Ammar et al. "Coupling finite elements and reduced approximation bases". European Journal of Computational Mechanics/Revue Européenne de Mécanique Numérique 18.5-6 (2009), pp. 445–463.

Title: Reduced Basis Approaches for data assimilation and data mining

Abstract:

Title : 3D Flow Separation on Wind Turbine Airfoils and Blades

Abstract : Although the assumption of two-dimensionality is widely used in wind turbine industry for both research and design, the reality is that it doesn't hold under separated flow conditions, when Stall Cells form on the suction side of airfoils and blades. Stall Cells are large scale three-dimensional coherent vortical structures that appear for a vast range of chord Reynolds numbers. In this talk, the latest research on Stall Cells will be discussed, including both experimental and numerical approaches.

Title : Some mathematical results abtout "The Blade Element Momentum"

Abstract : The Blade Element Momentum Theory provides a model that enables to evaluate numerically the efficiency of a propeller. The advantage of the related algorithm lies in the decomposition of the computation into two parts : a 2D model that reports lift and drag forces associated with the profile under consideration, and a system of scalar equations that describes the macroscopic forces applied on the propeller. In this talk, we will present necessary assumptions on the 2D model to obtain existence of solution(s) of the latter system. In addition, we prove the convergence of a fixed point algorithm that can be used to solve it numerically.

Title: A Reduced Basis technique for Turbulent Flows

Abstract: For turbulent flows, estimation of the entire solution trajectory through a low-dimensional Reduced Order Model might be unfeasible due to the slow convergence of the Kolmogorov N-width, and due to the sensitivity of the dynamical system to perturbations. Nevertheless, it might still be possible to estimate the time-averaged solution and associated quantities of interest.
In this talk, we propose a Reduced-Basis technique for the estimation of long-time-averaged solutions of parametrized turbulent flows. The key elements of our approach are (i) a Greedy technique for the construction of a low-dimensional reduced space, and (ii) a stabilized POD-Galerkin formulation of the reduced solution. The Greedy technique relies on a novel residual indicator for the error in the long-time-averaged solution.
We present a number of numerical examples to illustrate our approach, and to demonstrate the effectivity of the error indicator.