Modelling supporting truss structure for wind turbine blade

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Lattice Boltzman Method with Adaptative Mesh Refinement strategy to solve the transport equation

International audienceIntroductionThe Lattice Boltzmann Method (LBM) is a widelyused method for solving the transport equation inmedia with complex geometry. This popularity stemsboth from its simplicity of implementation and fromits intrinsically parallelizable algorithm, which makesit a highly efficient High-Performance Computing(HPC) numerical method.The main drawback of this method, in its basic form,is the use of a lattice similar to a regular Cartesianmesh, which can lead to use a large number of siteswith a level of discretization that is much too high inareas of low interest. We propose here to use anAdaptive Mesh Refinement method for the LBM withthe strong objective of not reducing the HPCefficiency of LBM.HPC strategyOur main objective is to develop a high-levellanguage portable simulation tool on different parallelCPU and GPU architectures without having to rewriteit with each new processors technological advance.To do this, we have developed our code in C++coupled with the Kokkos library that allows us toobtain an executable that runs on several kinds ofarchitectures (as multicores x86 multicores, GPUNVIDIA®, AMD GPU or ARM processor) [1,2].LBM on non-conformal gridsIn order to modify a LB numerical scheme to a nonconforminglattice, we choose to use a Lax-Wendroffdiscretization approach for replacing the streamingstep. The LB algorithm then reads (1) for collisionstep where Ωi is the transport collision operator and(2) for the streaming step.$f^*_i (x,t) = f_i (x,t) - \Omega_i$ (1)$f_i (x, t+\Delta t) = f^*_i (x,t) - \chi(f^*_i (x,t) - f^*_i (x-e_i \Delta x,t)) - 0.5 \chi (1-\chi)(f^*_i (x+e_i \Delta x,t) - 2f^*_i (x,t) + f^*_i (x-e_i \Delta x,t))$(2)_This scheme is stable for $\chi<1$, which we impose bychoice of Δt on the finest network and thus guaranteestability on all refinement levels.The mesh is organised in blocks of a given number ofcells in an octree structure. The communicationbetween neighboring blocks is done via ghost cells.For neighboring blocks of different refinement level,the ghost layers are filled using quadraticinterpolation.Adaptive Mesh Refinement criteriaIn order to compute the transport as accurately aspossible, we have chosen to refine as much aspossible the high concentration gradient zones andhave therefore chosen to use a criterion based on thegradient to refine or to coarsen each block componentof the lattice.When the mesh adaptation criteria requires to refine agiven block, the values to be assigned to the refinedlattice are obtained by projection and when thecriterion value asks for coarsening, the value to beassigned is obtained by averaging.References[1] Compatibilities of kokkos library (2020).https://github.com/kokkos/kokkos/wiki/Compiling(Web link accessible on March 8, 2022).[2] Verdier, W., Kestener, P., & Cartalade, A. (2020).Performance portability of lattice Boltzmannmethods for two-phase flows with phase change.Computer Methods in Applied Mechanics andEngineering, 370, 113266

Multi-architecture implementation of Adaptive Mesh Refinement for Lattice-Boltzmann Method

International audienceThe research work presented herein proposes an implementation of a Lattice Boltzmann Method [1] (LBM), coupled with an Adaptive Mesh Refinement (AMR) algorithm, with main focus on the portability and the optimisation of the code on different high performance computing (HPC) architectures. To preserve the efficiency of LBM for HPC when using the adaptive grid, as well as to optimally exploit the available HPC resources and keep up-to-date with their progress, the developed computational tool is built atop of Kokkos [2] C++ library for scientific computing. Kokkos handles automatically the adaptation and optimisation of a single piece of software on different computer architectures, such as CPUs, GPUs, shared and distributed memory systems alike. The proposed method uses the BGK collision operator but alters the streaming step. Instead of using multiple time-steps [3], a single time-step with a Lax-Wendroff [4] spatial discretisation scheme is employed, which accommodates computational cells of different sizes, while sub-iterations per computation step and variable scaling between different grids are avoided, and data sweeps and exchanges are minimised. The computational domain is discretised by a cell-centred mesh, which is organised in a block-based octree structure. Computations, as well as refinement andcoarsening operations, are performed on each block separately. Block communication and boundary condition imposition are realised through layers of ghost cells filled by quadratic polynomial interpolations. Preliminary assessment and validation tests, on transport problems of a Gaussian distribution profile, for which analytical solutions exist, show that the AMR approach with respect to a fully refined uniform mesh simulation, can reduce the total number of computational cells, and therefore the mean time of a single computational iteration, 5 times, without loss of accuracy. In addition, hard disk I/O processes get accelerated. The normalised gradient of the concentration was used as a refinement criterion and coarsening occurred automatically on neighbouring blocks that did not require refinement.These encouraging results, indicate the great potential of the method’s application on more complex physical problems, such as porous media or multiphase flows and dissolution modelling, coupled with Navier-Stokes equations

Multi-architecture adaptive Mesh Refinement Lattice-Boltzmann method for multi-phase and porous media flows

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