Design and Analysis of a Task-based Parallelization over a Runtime System of an Explicit Finite-Volume CFD Code with Adaptive Time Stepping

FLUSEPA (Registered trademark in France No. 134009261) is an advanced simulation tool which performs a large panel of aerodynamic studies. It is the unstructured finite-volume solver developed by Airbus Safran Launchers company to calculate compressible, multidimensional, unsteady, viscous and reactive flows around bodies in relative motion. The time integration in FLUSEPA is done using an explicit temporal adaptive method. The current production version of the code is based on MPI and OpenMP. This implementation leads to important synchronizations that must be reduced. To tackle this problem, we present the study of a task-based parallelization of the aerodynamic solver of FLUSEPA using the runtime system StarPU and combining up to three levels of parallelism. We validate our solution by the simulation (using a finite-volume mesh with 80 million cells) of a take-off blast wave propagation for Ariane 5 launcher.Comment: Accepted manuscript of a paper in Journal of Computational Scienc

Numerical simulation of model problems in plasticity based on field dislocation mechanics

The aim of this paper is to investigate the numerical implementation of the field dislocation mechanics (FDM) theory for the simulation of dislocation-mediated plasticity. First, the mesoscale FDM theory of Acharya and Roy (2006 J. Mech. Phys. Solids 54 1687-710) is recalled which permits to express the set of equations under the form of a static problem, corresponding to the determination of the local stress field for a given dislocation density distribution, complemented by an evolution problem, corresponding to the transport of the dislocation density. The static problem is solved using FFT-based techniques (Brenner et al 2014 Phil. Mag. 94 1764-87). The main contribution of the present study is an efficient numerical scheme based on high resolution Godunov-type solvers to solve the evolution problem. Model problems of dislocation-mediated plasticity are finally considered in a simplified layer case. First, uncoupled problems with uniform velocity are considered, which permits to reproduce annihilation of dislocations and expansion of dislocation loops. Then, the FDM theory is applied to several problems of dislocation microstructures subjected to a mechanical loading

A coupled implicit-explicit time integration method for compressible unsteady flows

This paper addresses how two time integration schemes, the Heun's scheme for explicit time integration and the second-order Crank-Nicolson scheme for implicit time integration, can be coupled spatially. This coupling is the prerequisite to perform a coupled Large Eddy Simulation / Reynolds Averaged Navier-Stokes computation in an industrial context, using the implicit time procedure for the boundary layer (RANS) and the explicit time integration procedure in the LES region. The coupling procedure is designed in order to switch from explicit to implicit time integrations as fast as possible, while maintaining stability. After introducing the different schemes, the paper presents the initial coupling procedure adapted from a published reference and shows that it can amplify some numerical waves. An alternative procedure, studied in a coupled time/space framework, is shown to be stable and with spectral properties in agreement with the requirements of industrial applications. The coupling technique is validated with standard test cases, ranging from one-dimensional to three-dimensional flows

Numerical implementation of static Field Dislocation Mechanics theory for periodic media

This paper investigates the implementation of Field Dislocation Mechanics theory for media with a periodic microstructure (i.e. the Nye dislocation tensor and the elastic moduli tensor are considered as spatially periodic continuous elds). In this context, the uniqueness of the stress and elastic distortion elds is established. This allows to propose an e cient numerical scheme based on Fourier transform to compute the internal stress eld, for a given spatial distribution of dislocations and applied macroscopic stress. This numerical implementation is assessed by comparison with analytical solutions for homogeneous as well as heterogeneous elastic media. A particular insight is given to the critical case of stress-free dislocation microstructures which represent equilibrium solutions of the Field Dislocation Mechanics theory

Multiple-correction hybrid k -exact schemes for high-order compressible RANS-LES simulations on fully unstructured grids

A Godunov's type unstructured finite volume method suitable for highly compressible turbulent scale-resolving simulations around complex geometries is constructed by using a successive correction technique. First, a family of k-exact Godunov schemes is developed by recursively correcting the truncation error of the piecewise polynomial representation of the primitive variables. The keystone of the proposed approach is a quasi-Green gradient operator which ensures consistency on general meshes. In addition, a high-order single-point quadrature formula, based on high-order approximations of the successive derivatives of the solution, is developed for flux integration along cell faces. The proposed family of schemes is compact in the algorithmic sense, since it only involves communications between direct neighbors of the mesh cells. The numerical properties of the schemes up to fifth-order are investigated, with focus on their resolvability in terms of number of mesh points required to resolve a given wavelength accurately. Afterwards, in the aim of achieving the best possible trade-off between accuracy, computational cost and robustness in view of industrial flow computations, we focus more specifically on the third-order accurate scheme of the family, and modify locally its numerical flux in order to reduce the amount of numerical dissipation in vortex-dominated regions. This is achieved by switching from the upwind scheme, mostly applied in highly compressible regions, to a fourth-order centered one in vortex-dominated regions. An analytical switch function based on the local grid Reynolds number is adopted in order to warrant numerical stability of the recentering process. Numerical applications demonstrate the accuracy and robustness of the proposed methodology for compressible scale-resolving computations. In particular, supersonic RANS/LES computations of the flow over a cavity are presented to show the capability of the scheme to predict flows with shocks, vortical structures and complex geometries.A Godunov's type unstructured finite volume method suitable for highly compressible turbulent scale-resolving simulations around complex geometries is constructed by using a successive correction technique. First, a family of k-exact Godunov schemes is developed by recursively correcting the truncation error of the piecewise polynomial representation of the primitive variables. The keystone of the proposed approach is a quasi-Green gradient operator which ensures consistency on general meshes. In addition, a high-order single-point quadrature formula, based on high-order approximations of the successive derivatives of the solution, is developed for flux integration along cell faces. The proposed family of schemes is compact in the algorithmic sense, since it only involves communications between direct neighbors of the mesh cells. The numerical properties of the schemes up to fifth-order are investigated, with focus on their resolvability in terms of number of mesh points required to resolve a given wavelength accurately. Afterwards, in the aim of achieving the best possible trade-off between accuracy, computational cost and robustness in view of industrial flow computations, we focus more specifically on the third-order accurate scheme of the family, and modify locally its numerical flux in order to reduce the amount of numerical dissipation in vortex-dominated regions. This is achieved by switching from the upwind scheme, mostly applied in highly compressible regions, to a fourth-order centered one in vortex-dominated regions. An analytical switch function based on the local grid Reynolds number is adopted in order to warrant numerical stability of the recentering process. Numerical applications demonstrate the accuracy and robustness of the proposed methodology for compressible scale-resolving computations. In particular, supersonic RANS/LES computations of the flow over a cavity are presented to show the capability of the scheme to predict flows with shocks, vortical structures and complex geometries

MPMD parallelization of an aerodynamic code with bodies in relative motion

International audienceFLUSEPA is an advanced simulation tool which performs a large panel of aerodynamic studies. It is the unstructured finite-volume solver developed by Airbus Defence & Space company to calculate compressible, multidimensional, unsteady, viscous and reactive flows around bodies in relative motion. The numerical strategy in FLUSEPA is designed for highly compressible flows and keeps its accuracy in non-Cartesian grids. According the desired accuracy, a second-order accurate shock-capturing scheme is generally used for RANS and URANS simulations and a fourth order accurate vortex-centered scheme is used for hybrid RANS/LES simulations. The meshing strategy is based on multi-overlapping grid intersection which is conservative and allows to quickly and properly mesh 3D complex geometries. It can be seen as a CHIMERA strategy without interpolation. Each body is meshed independently and immersed in background grids.MPMD parallelisation of this code is presented

Task-based parallelization of a CFD code over a Runtime System

International audienceFLUSEPA is an advanced simulation tool which performs a large panel of aerodynamic studies. It is the unstructured nite-volume solver developed by Airbus Defence & Space company to calculate compressible, multidimensional, unsteady, viscous and reactive flows around bodies in relative motion [2](Figure 1). The numerical strategy in FLUSEPA is designed for highly compressible tlows and to remain accurate when using non-Cartesian grids. The meshing strategy is based on multi-overlapping grid intersection which is conservative and allows to quickly mesh 3D complex geometries. The time integration in FLUSEPA is done using an explicit temporal adaptive method [3]. Instead of using a time step imposed by the slowest cell, cells are grouped inside temporal classes according to their maximum allowed time step. This method allows to perform a fewer number of operations at the expense of some complexity. An iteration of the aerodynamic solver is separated into several sub-iterations. Every cell is not integrated during each sub-iteration but cells which share a face with a slower one are interpolated. At the end of the iteration, each cell has reached the same time. Between iterations, temporal classes can evolve.The current version of FLUSEPA is parallelized using a classical MPI-OpenMP approach and domain decomposition: border faces are duplicated and ghost cells are used. However, the way the time is integrated leads to important time wasted in synchronization despite computation-communication overlapping. The time integration implies an order for the cells to be processed depending on their temporal class: neighbor cells must be at the same time during processing. This locality information is partially lost with the current parallelization. In this paper, we present a way to overcome this issue by working on sub-domains inside each process. We capture the dependencies more precisely through the use of a task-based parallel expression with the help of a well suited runtime system

Hybrid-dimensional modelling of two-phase flow through fractured porous media with enhanced matrix fracture transmission conditions

International audienceIn this work, we extend, to two-phase flow, the single-phase Darcy flow model proposed in [26], [12] in which the (d − 1)-dimensional flow in the fractures is coupled with the d-dimensional flow in the matrix. Three types of so called hybrid-dimensional two-phase Darcy flow models are proposed. They all account for fractures acting either as drains or as barriers, since they allow pressure jumps at the matrix-fracture interfaces. The models also permit to treat gravity dominated flow as well as discontinuous capillary pressure at the material interfaces. The three models differ by their transmission conditions at matrix fracture interfaces: while the first model accounts for the nonlinear two-phase Darcy flux conservations, the second and third ones are based on the linear single phase Darcy flux conservations combined with different approximations of the mobilities. We adapt the Vertex Approximate Gradient (VAG) scheme to this problem, in order to account for anisotropy and heterogeneity aspects as well as for applicability on general meshes. Several test cases are presented to compare our hybrid-dimensional models to the generic equi-dimensional model, in which fractures have the same dimension as the matrix, leading to deep insight about the quality of the proposed reduced models