One of the more promising recent approaches to turbulence modelling is the Variational Multiscale Large Eddy Simulation (VMS LES) method proposed by Hughes et al. [Comp. Visual. Sci., vol. 3, pp. 47-59, 2000]. This method avoids several conceptual issues of traditional filter-based LES by employing a priori scale partitioning in the discretization of the Navier-Stokes equations.
Most applications of VMS LES reported to date have been based on hierarchical bases, in particular global spectral methods, in which scale partitioning is straightforward. In the present work we describe the implementation of the methodology in a three-dimensional high-order spectral element method with a nodal basis. We report results from coarse grid simulations of turbulent channel flow at different Reynolds numbers to assess the performance of the model.
Key words: Large eddy simulation, variational multiscale method, spectral element method, incompressible flow 1991 MSC: 76F65, 65M60, 65M70 PACS: 47.27.Eq, 02.70.Hm, 02.70.Dh
This article presents a formulation that extends the variational multiscale modelling for compressible large-eddy simulation to a vast family of compact nodal numerical methods represented by the high-order flux reconstruction scheme. The theoretical aspects of the proposed formulation are laid down via rigorous mathematical derivations which clearly expose the underlying assumptions and approximations and provide sufficient details for accurate reproduction of the methodology. The final form is assessed on a Taylor-Green vortex benchmark with Reynolds number of 5000 and compared to filtered d…
The deformation and dynamics of a single droplet in isotropic turbulence is studied using a Lattice Boltzmann diffuse interface model involving exact boundary flow conditions to allow for the creation of an external turbulent flow. We focus on a small, sub-Kolmogorov droplet, whose scale is much smaller than the Kolmogorov length scale of the turbulent flow. The external flow field is obtained via pseudo-spectral simulation data describing the trajectory of a passive tracer in isotropic turbulence. In this way we combine the microscopic scale of the droplet and the macroscopic scale of the tur…
An open-sourced multiphase Darcy-Brinkman approach is proposed to simulate two-phase flow in hybrid systems containing both solid-free regions and porous matrices. This micro-continuum model is rooted in elementary physics and volume averaging principles, where a unique set of partial differential equations is used to represent flow in both regions and scales. The crux of the proposed model is that it tends asymptotically towards the Navier-Stokes volume-of-fluid approach in solid-free regions and towards the multiphase Darcy equations in porous regions. Unlike existing multiscale multiphase s…
Numerical schemes for wave-like systems with small dissipation are often inaccurate and unstable due to truncation errors and numerical roundoff errors. Hence, numerical simulations of wave-like systems lacking proper handling of these numerical issues often fail to represent the physical characteristics of wave phenomena. This challenge gets even more intricate for multiscale modelling, especially in multiple dimensions. When using the usual collocated grid, about two-thirds of the resolved wave modes are incorrect with significant dispersion. But, numerical schemes on staggered grids (with a…
New large eddy simulation (LES) turbulence models for incompressible magnetohydrodynamics (MHD) derived from the variational multiscale (VMS) formulation for finite element simulations are introduced. The new models include the variational multiscale formulation, a residual-based eddy viscosity model, and a mixed model that combines both of these component models. Each model contains terms that are proportional to the residual of the incompressible MHD equations and is therefore numerically consistent. Moreover, each model is also dynamic, in that its effect vanishes when this residual is smal…
Atomistic-continuum multiscale modelling is becoming an increasingly popular tool for simulating the behaviour of materials due to its computational efficiency and reliable accuracy. In the case of ferromagnetic materials, the atomistic approach handles the dynamics of spin magnetic moments of individual atoms, while the continuum approximations operate with volume-averaged quantities, such as magnetisation. One of the challenges for multiscale models in relation to physics of ferromagnets is the existence of the long-range dipole-dipole interactions between spins. The aim of the present paper…
In multiscale modelling, multiple models are used simultaneously to describe scale-dependent phenomena in a system of interest. Here we introduce a machine learning (ML)-based multiscale modelling framework for modelling hierarchical multiscale problems. In these problems, closure relations are required for the macroscopic problem in the form of constitutive relations. However, forming explicit closures for nonlinear and hysteretic processes remains challenging. Instead, we provide a framework for learning constitutive mappings given microscale data generated according to micro and macro trans…
The recent surge in machine learning augmented turbulence modelling is a promising approach for addressing the limitations of Reynolds-averaged Navier-Stokes (RANS) models. This work presents the development of the first open-source dataset, curated and structured for immediate use in machine learning augmented turbulence closure modelling. The dataset features a variety of RANS simulations with matching direct numerical simulation (DNS) and large-eddy simulation (LES) data. Four turbulence models are selected to form the initial dataset: $k$-$\varepsilon$, $k$-$\varepsilon$-$ϕ_t$-$f$, $k$-$ω$…
In this investigation, a data-driven turbulence closure framework is introduced and deployed for the sub-grid modelling of Kraichnan turbulence. The novelty of the proposed method lies in the fact that snapshots from high-fidelity numerical data are used to inform artificial neural networks for predicting the turbulence source term through localized grid-resolved information. In particular, our proposed methodology successfully establishes a map between inputs given by stencils of the vorticity and the streamfunction along with information from two well-known eddy-viscosity kernels. Through th…
Data-driven turbulence modelling approaches are gaining increasing interest from the CFD community. However, the introduction of a machine learning (ML) model introduces a new source of uncertainty, the ML model itself. Quantification of this uncertainty is essential since the predictive capability of a data-driven model diminishes when predicting physics not seen during training. In this work, we explore the suitability of Mondrian forests (MF's) for data-driven turbulence modelling. MF's are claimed to possess many of the advantages of the commonly used random forest (RF) machine learning al…
Modular multiscale approach to modelling high-harmonic generation in gases
ELI Beamlines Facility, The Extreme Light Infrastructure ERIC（极亮基础设施欧洲研究联盟 ELI 光束线设施）；Czech Technical University in Prague（布拉格捷克理工大学）；Université Claude Bernard Lyon 1（里昂第一大学克洛德·贝尔纳大学）；CNRS（法国国家科学研究中心）；Institut Lumière Matière（光物质研究所）；Centre Lasers Intenses et Applications（高强度激光及应用中心）；Université de Bordeaux-CNRS-CEA（波尔多大学-CNRS-CEA）
The Closure Challenge: a benchmark task for machine learning in turbulence modelling
Center for Computational Science and Engineering, Massachusetts Institute of Technology（麻省理工学院计算科学与工程中心）；Aerodynamics Group, Faculty of Aerospace Engineering, TU Delft（代尔夫特理工大学航空航天工程学院空气动力学组）；Institut Jean Le Rond D’Alembert, Sorbonne University（索邦大学让·勒朗·达朗贝尔研究所）
Morphologies of adsorbed molecular films are of interest in a wide range of applications. To study the epitaxial growth of these systems in computer simulations requires access to long time and length scales and one typically resorts to kinetic Monte Carlo (KMC) simulations. However, KMC simulations require as input transition rates and their dependence on external parameters (such as temperature). Experimental data allows only limited and indirect access to these rates, and models are often oversimplified. Here we follow a bottom-up approach and aim to systematically construct all relevant ra…
A multi-resolution bead-spring model for polymer dynamics is developed as a generalization of the Rouse model. A polymer chain is described using beads of variable sizes connected by springs with variable spring constants. A numerical scheme which can use different timesteps to advance the positions of different beads is presented and analyzed. The position of a particular bead is only updated at integer multiples of the timesteps associated with its connecting springs. This approach extends the Rouse model to a multiscale model on both spatial and temporal scales, allowing simulations of loca…
In this paper, we train turbulence models based on convolutional neural networks. These learned turbulence models improve under-resolved low resolution solutions to the incompressible Navier-Stokes equations at simulation time. Our study involves the development of a differentiable numerical solver that supports the propagation of optimisation gradients through multiple solver steps. The significance of this property is demonstrated by the superior stability and accuracy of those models that unroll more solver steps during training. Furthermore, we introduce loss terms based on turbulence phys…
The reliability and safety of lithium-ion batteries can be affected by overheating issues. Phase change materials like paraffin due to their large heat capacities are among the best solutions for the thermal management of batteries. In this investigation, multiscale modelling techniques were developed to explore the efficiency in the thermal management of rechargeable batteries through employing the paraffin composite structures. A combined atomistic-continuum multiscale modelling was conducted to evaluate the thermal conductivity of paraffin reinforced with graphene or hexagonal boron-nitride…
