Pierre KESTENER
Ingénieur-Chercheur en calcul haute performance appliquée à la mécanique des fluides numériques, expertise sur les modèles de programmation pour la portabilité de performance.
Computer Methods in Applied Mechanics and Engineering , 2020
abstract
Abstract
Numerical codes using the lattice Boltzmann methods (LBM) for simulating one- or two-phase flows are widely compiled and run on graphical process units. However, those computational units necessitate to re-write the program by using a low-level language which is suited to those architectures (e.g. CUDA for GPU NVIDIA®or OpenCL). In this paper we focus our effort on the performance portability of LBM i.e. the possibility of writing LB algorithms with a high-level of abstraction while remaining efficient on a wide range of architectures such as multicores x86, GPU NVIDIA®, ARM, and so on. For such a purpose, implementation of LBM is carried out by developing a unique code, LBM_saclay written in the C++ language, coupled with the Kokkos library for performance portability in the context of High Performance Computing. In this paper, the LBM is used to simulate a phase-field model for two-phase flow problems with phase change. The mathematical model is composed of the incompressible Navier–Stokes equations coupled with the conservative Allen–Cahn model. Initially developed in the literature for immiscible binary fluids, the model is extended here to simulate phase change occurring at the interface between liquid and gas. For that purpose, a heat equation is added with a source term involving the time derivative of the phase field. In the phase-field equation a source term is added to approximate the mass production rate at the interface. Several validations are carried out to check step-by-step the implementation of the full model. Finally, computational times are compared on CPU and GPU platforms for the physical problem of film boiling.
PHYSICAL REVIEW E 99(5), 2019
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Abstract
It is still not known whether solutions to the Navier-Stokes equation can develop singularities from regular initial conditions. In particular, a classical and unsolved problem is to prove that the velocity field is Hölder continuous with some exponent h<1 (i.e., not necessarily differentiable) at small scales. Different methods have already been proposed to explore the regularity properties of the velocity field and the estimate of its Hölder exponent h. A first method is to detect potential singularities via extrema of an “inertial” dissipation D*=limℓ→0DℓI that is independent of viscosity [Duchon and Robert, Nonlinearity 13, 249 (2000)]. Another possibility is to use the concept of multifractal analysis that provides fractal dimensions of the subspace of exponents h. However, the multifractal analysis is a global statistical method that only provides global information about local Hölder exponents, via their probability of occurrence. In order to explore the local regularity properties of a velocity field, we have developed a local statistical analysis that estimates locally the Hölder continuity. We have compared outcomes of our analysis with results using the inertial energy dissipation DℓI. We observe that the dissipation term indeed gets bigger for velocity fields that are less regular according to our estimates. The exact spatial distribution of the local Hölder exponents however shows nontrivial behavior and does not exactly match the distribution of the inertial dissipation.
The Astrophysical Journal, Volume 876, Number 2 (144), 2019
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Abstract
By generalizing the theory of convection to any type of thermal and compositional source terms (diabatic processes), we show that thermohaline convection in Earth's oceans, fingering convection in stellar atmospheres, and moist convection in Earth's atmosphere are derived from the same general diabatic convective instability. We also show that "radiative convection" triggered by the CO/CH4 transition with radiative transfer in the atmospheres of brown dwarfs is analogous to moist and thermohaline convection. We derive a generalization of the mixing-length theory to include the effect of source terms in 1D codes. We show that CO/CH4 "radiative" convection could significantly reduce the temperature gradient in the atmospheres of brown dwarfs similarly to moist convection in Earth's atmosphere, thus possibly explaining the reddening in brown dwarf spectra. By using idealized 2D hydrodynamic simulations in the Ledoux unstable regime, we show that compositional source terms can indeed provoke a reduction of the temperature gradient. The L/T transition could be explained by a bifurcation between the adiabatic and diabatic convective transports and seen as a giant cooling crisis: an analog of the boiling crisis in liquid/steam-water convective flows. This mechanism, with other chemical transitions, could be present in many giant and Earth-like exoplanets. The study of the impact of different parameters (effective temperature, compositional changes) on CO/CH4 radiative convection and the analogy with Earth moist and thermohaline convection is opening the possibility of using brown dwarfs to better understand some aspects of the physics at play in the climate of our own planet.
The Astrophysical Journal, Volume 875, Number 2, 2019
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Abstract
Convection is an important physical process in astrophysics well-studied using numerical simulations under the Boussinesq and/or anelastic approximations. However, these approaches reach their limits when compressible effects are important in the high-Mach flow regime, e.g., in stellar atmospheres or in the presence of accretion shocks. In order to tackle these issues, we propose a new high-performance and portable code called “ARK” with a numerical solver well suited for the stratified compressible Navier–Stokes equations. We take a finite-volume approach with machine precision conservation of mass, transverse momentum, and total energy. Based on previous works in applied mathematics, we propose the use of a low-Mach correction to achieve a good precision in both low and high-Mach regimes. The gravity source term is discretized using a well-balanced scheme in order to reach machine precision hydrostatic balance. This new solver is implemented using the Kokkos library in order to achieve high-performance computing and portability across different architectures (e.g., multi-core, many-core, and GP-GPU). We show that the low-Mach correction allows to reach the low-Mach regime with a much better accuracy than a standard Godunov-type approach. The combined well-balanced property and the low-Mach correction allowed us to trigger Rayleigh–Bénard convective modes close to the critical Rayleigh number. Furthermore, we present 3D turbulent Rayleigh–Bénard convection with low diffusion using the low-Mach correction leading to a higher kinetic energy power spectrum. These results are very promising for future studies of high Mach and highly stratified convective problems in astrophysics.
Journal of Physics: Conference Series, Volume 1125, Joint Varenna-Lausanne International Workshop on the Theory of Fusion Plasmas 2018 27–31 August 2018, Varenna, Italy, 2018
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Abstract
This contribution deals with the fluid modeling of multicomponent magnetized plasmas in thermo-chemical non-equilibrium from the partially- to fully-ionized collisional regimes, aiming at the predictive simulation of magnetic reconnection in Sun chromosphere conditions. Such fluid models are required for large-scale simulations by relying on high performance computing. The fluid model is derived from a kinetic theory approach, yielding a rigorous description of the dissipative and non-equilibrium effects and a well-identified mathematical structure. We start from a general system of equations that is obtained by means of a multiscale Chapman-Enskog method, based on a non-dimensional analysis accounting for the mass disparity between the electrons and heavy particles, including the influence of the electromagnetic field and transport properties. The latter are computed by using a spectral Galerkin method based on a converged Laguerre-Sonine polynomial approximation. Then, in the limit of small Debye length with respect to the characteristic scale in the Sun chromosphere, we derive a two-temperature single-momentum multicomponent diffusion model coupled to Maxwell's equations, which is able to describe fully- and partially-ionized plasmas, beyond the multi-fluid model of Braginskii, valid for the whole range of the Sun chromosphere conditions. The second contribution is the development and verification of an accurate and robust numerical strategy that is based on CanoP, a massively parallel code with adaptive mesh refinement capability, which is able to cope with the full spectrum of scales of the magnetic reconnection process, without additional constraint on the time steps compared to single-fluid Magnetohydrodynamics (MHD) models. The final contribution is a study of the physics of magnetic reconnection in collaboration with the heliophysics team of NASA Ames Research Center. We show that the model and methods allow us to retrieve the results of usual single-fluid MHD models in the highly collisional case at equilibrium, while achieving a more detailed physics description relevant to such applications in the weakly collisional case, where non-equilibrium effects become important.
The Astrophysical Journal, Volume 840, Number 1, 2017
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Abstract
Magnetohydrodynamic (MHD) turbulence driven by the magnetorotational instability can provide diffusive transport of angular momentum in astrophysical disks, and a widely studied computational model for this process is the ideal, stratified, isothermal shearing box. Here we report results of a convergence study of such boxes up to a resolution of $N = 256$ zones per scale height, performed on blue waters at NCSA with ramses-gpu. We find that the time and vertically integrated dimensionless shear stress $\overline{\alpha} \sim N^{-1/3}$, i.e. the shear stress is resolution dependent. We also find that the magnetic field correlation length decreases with resolution, $\lambda \sim N^{-1/2}$. This variation is strongest at the disk midplane. We show that our measurements of $\alpha$ are consistent with earlier studies. We discuss possible reasons for the lack of convergence.
Communications in Mathematical Sciences, Volume 15, Number 3, 2017
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Abstract
This work focuses on the numerical approximation of the shallow water equations (SWE) using a Lagrange-projection type approach. We propose to extend to this context the recent implicit-explicit schemes developed in [C. Chalons, M. Girardin, and S. Kokh, SIAM J. Sci. Comput., 35(6):a2874–a2902, 2013], [C. Chalons, M. Girardin, and S. Kokh, Commun. Comput. Phys., to appear, 20(1):188–233, 2016] in the framework of compressible flows, with or without stiff source terms. These methods enable the use of time steps that are no longer constrained by the sound velocity thanks to an implicit treatment of the acoustic waves, and maintain accuracy in the subsonic regime thanks to an explicit treatment of the material waves. In the present setting, a particular attention will be also given to the discretization of the non-conservative terms in SWE and more specifically to the wellknown well-balanced property. We prove that the proposed numerical strategy enjoys important non linear stability properties and we illustrate its behaviour past several relevant test cases.