Direct numerical simulation of backward-facing step flow at Ret = 395 and expansion ratio 2

Backward-facing step (BFS) constitutes a canonical configuration to study wallbounded flows subject to massive expansions produced by abrupt changes in geometry. Recirculation flow regions are common in this type of flow, driving the separated flow to its downstream reattachment. Consequently, strong adverse pressure gradients arise through this process, feeding flow instabilities. Therefore, both phenomena are strongly correlated as the recirculation bubble shape defines how the flow is expanded, and how the pressure rises. In an incompressible flow, this shape depends on the Reynolds value and the expansion ratio. The influence of these two variables on the bubble length is widely studied, presenting an asymptotic behaviour when both parameters are beyond a certain threshold. This is the usual operating point of many practical applications, such as in aeronautical and environmental engineering. Several numerical and experimental studies have been carried out regarding this topic. The existing simulations considering cases beyond the above-mentioned threshold have only been achieved through turbulence modelling, whereas direct numerical simulations (DNS) have been performed only at low Reynolds numbers. Hence, despite the great importance of achieving this threshold, there is a lack of reliable numerical data to assess the accuracy of turbulence models. In this context, a DNS of an incompressible flow over a BFS is presented in this paper, considering a friction Reynolds number (Reτ) of 395 at the inflow and an expansion ratio 2. Finally, the elongation of the Kelvin–Helmholtz instabilities along the shear layer is also studied.Postprint (published version

Noise radiated by an open cavity at low Mach number: Effect of the cavity oscillation mode

The present work focuses on the study of noise generation and radiation of an infinite open three-dimensional cavity at low Mach number with laminar upstream conditions that is of interest to understand noise generation mechanisms in wall-bounded separated flows. A particular feature of this configuration is the oscillatory mode: shear layer mode or wake mode. For the parameters considered in the present study it is seen that while in shear layer mode the flow shows a two-dimensional behavior, in the wake mode the flow is three-dimensional, resulting in significantly different sound sources. The influence of the acoustic feedback mechanism in the shear layer mode has also been investigated comparing the results between different momentum thickness values at the cavity inlet. This paper presents results of sound radiated by a three-dimensional infinite open cavity with aspect ratio L/D = 4 at Reynolds number based on the cavity depth of ReD = 1500 and Mach number of M = 0.15, both for shear layer (L/θ = 67) and wake (L/θ = 84) oscillation modes. To do so, Curle integral evaluated as a post-process of an incompressible solution will be used. The results are compared with the resulting Curle post-process of a two-dimensional incompressible simulationPeer ReviewedPostprint (author's final draft

An OpenCL-based parallel CFD code for simulations on hybrid systems with massively-parallel accelerators

A parallel finite-volume CFD algorithm for modeling of incompressible flows on hybrid supercomputers is presented. It is based on a symmetry-preserving high-order numerical scheme for structured meshes. A multilevel approach that combines di erent parallel models is used for large-scale simulations on computing systems with massively-parallel accelerators. MPI is used on the first level within the distributed memory model to couple computing nodes of a supercomputer. On the second level OpenMP is used to engage multiple CPU cores of a computing node. The third level exploits the computing potential of massively-parallel accelerators such as GPU (Graphics Processing Units) of AMD and NVIDIA, or Intel Xeon Phi accelerators of the MIC (Many Integrated Core) architecture. The hardware independent OpenCL standard is used to compute on accelerators of di erent architectures within a general model for a combination of a central processor and a math co-processor.Peer ReviewedPostprint (published version

Portable implementation model for CFD simulations. Application to hybrid CPU/GPU supercomputers

Nowadays, high performance computing (HPC) systems experience a disruptive moment with a variety of novel architectures and frameworks, without any clarity of which one is going to prevail. In this context, the portability of codes across different architectures is of major importance. This paper presents a portable implementation model based on an algebraic operational approach for direct numerical simulation (DNS) and large eddy simulation (LES) of incompressible turbulent flows using unstructured hybrid meshes. The strategy proposed consists in representing the whole time-integration algorithm using only three basic algebraic operations: sparse matrix–vector product, a linear combination of vectors and dot product. The main idea is based on decomposing the nonlinear operators into a concatenation of two SpMV operations. This provides high modularity and portability. An exhaustive analysis of the proposed implementation for hybrid CPU/GPU supercomputers has been conducted with tests using up to 128 GPUs. The main objective consists in understanding the challenges of implementing CFD codes on new architectures.Peer ReviewedPostprint (author's final draft

Spectrally-consistent regularization modeling of wind farm boundary layers

The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, attempts at performing direct simulations are limited to relatively low-Reynolds numbers because of the almost numberless small scales produced by the non-linear convective term. Alternatively, a dynamically less complex formulation is proposed here. Namely, regularizations of the Navier-Stokes equations that preserve the symmetry and conservation properties exactly. To do so, both convective and diffusive term are altered in the same vein. In this way, the convective production of small scales is effectively restrained whereas the modified diffusive term introduces a hyperviscosity effect and consequently enhances the destruction of small scales. In practise, the only additional ingredient is a self-adjoint linear filter whose local filter length is determined from the requirement that vortex-stretching must stop at the smallest grid scale. In the present work, the performance of the above-mentioned recent improvements is assessed through application to homogeneous isotropic turbulence, a turbulent channel flow and a turbulent boundary layer. As a final application, regularization modelling will be applied for large-scale numerical simulation of the atmospheric boundary layer through wind farms.Peer ReviewedPostprint (published version

Symmetry-preserving regularization of wall-bounded turbulent flows

The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, attempts at performing direct simulations are limited to relatively low-Reynolds numbers because of the almost numberless small scales produced by the non-linear convective term. Alternatively, a dynamically less complex formulation is proposed here. Namely, regularizations of the Navier-Stokes equations that preserve the symmetry and conservation properties exactly. To do so, both convective and diffusive term are altered in the same vein. In this way, the convective production of small scales is effectively restrained whereas the modified diffusive term introduces an hyper-viscosity effect and consequently enhances the destruction of small scales. In practice, the only additional ingredient is a self-adjoint linear filter whose local filter length is determined from the requirement that vortex-stretching must stop at the smallest grid scale. To do so, a new criterion based on the invariants of the local strain tensor is proposed here. Altogether, the proposed method constitutes a parameter-free turbulence model.Peer ReviewedPostprint (published version

Towards proper subgrid-scale model for jet aerodynamics and aeroacoustics

This article presents the investigation of different grey-area mitigation (GAM) techniques towards achieving accurate subsonic turbulent round jet aerodynamics and aeroacoustics results. Combinations of new adapting subgrid length scales with 2D detecting LES models are used as the GAM technique. The numerical simulations are carried out on a set of refining meshes using two different scale-resolving codes: NOISEtte and OpenFOAM. The results show that all the considered techniques provide appropriate accuracy to predict the noise generated and the importance of both the numerical scheme and how subgrid eddy viscosity is modelled.The work of J.R.P. and F.X.T. has been financially supported by the project RETOtwin (PDC2021-120970-I00) funded by MCIN/AEI/10.13039/501100011033 and European Union Next Generation EU/PRTR. J.R.P. is supported by a FI-DGR 2015 predoctoral contract financed by Generalitat de Catalunya, Spain.Peer ReviewedPostprint (published version

Symmetry-preserving discretization of Navier-Stokes on unstructured grids: collocated vs staggered

The essence of turbulence are the smallest scales of motion. They result from a subtle balance between convective transport and diffusive dissipation. Mathematically, these terms are governed by two differential operators differing in symmetry: the convective operator is skew-symmetric, whereas the diffusive is symmetric and positive-definite. On the other hand, accuracy and stability need to be reconciled for numerical simulations of turbulent flows around complex configurations. With this in mind, a fully-conservative discretization method for general unstructured grids was proposed [Trias et al., J.Comp.Phys. 258, 246-267, 2014]: it exactly preserves the symmetries of the underlying differential operators on a collocated mesh. However, any pressure-correction method on collocated grids suffer from the same drawbacks: the cell-centered velocity field is not exactly incompressible and some artificial dissipation is inevitable introduced. On the other hand, for staggered velocity fields, the projection onto a divergence-free space is a well-posed problem: given a velocity field, it can be uniquely decomposed into a solenoidal vector and the gradient of a scalar (pressure) field. This can be easily done without introducing any dissipation as it should be from a physical point-of-view. In this work, we explore the possibility to build up staggered formulations based on collocated discrete operators.F.X.T., N.V. and A.O. have been financially supported by the Ministerio de Economía y Competitividad, Spain, ANUMESOL project (ENE2017-88697-R). F.X.T. and A.O. are supported by the Generalitat de Catalunya RIS3CAT-FEDER, FusionCAT project (001-P-001722). N.V. was supported by an FI AGAUR-Generalitat de Catalunya fellowship (2017FI B 00616). Calculations were performed on the IBM MareNostrum 4 supercomputer at the BSC. The authors thankfully acknowledge these institutions.Peer ReviewedPostprint (published version

On Preconditioning Variable Poisson Equation with Extreme Contrasts in the Coefficients

It is well known that the solution by means of iterative methods of very ill-conditioned systems leads to very poor convergence rates. In this context, preconditioning becomes crucial in order to modify the spectrum of the system being solved and improve the performance of the solvers. A proper balance between the reduction in the number of iterations and the overhead of the construction and application of the preconditioner needs to be sought to actually decrease the total execution time of the solvers. This is particularly important when considering variable coefficients matrices as, in general, its preconditioners will also be variable and need to be updated regularly at an affordable cost. In this work we present a family of variable preconditioners designed for the effective solution of variable Poisson equation with extreme contrasts in the coefficients, which represents a particularly challenging case as it translates into a variable and extremely ill-conditioned system arising in many situations such as with multiphase flows presenting high density ratios or in the presence of highly-stretched adaptive mesh refinements. Finally, the results of the numerical experiments performed are presented and discussed, confirming our preconditioners as extremely affordable, highly-parallelizable and easy-to-implement alternatives to the more standard (and usually unfeasible) preconditioners, still showing great improvements in the rate of convergence of the solvers without requiring the variable coefficients matrix to be explicitly rebuilt at each iteration.Àdel Alsalti-Baldellou, F. Xavier Trias and Assensi Oliva have been financially supported by a competitive R+D project (ENE2017-88697-R) by the Spanish Research Agency. Àdel Alsalti-Baldellou is also supported by predoctoral grants DIN2018-010061 and 2019-DI-90, given by, respectively, the Spanish Ministry of Science, Innovation and Universities (MICINN) and the Catalan Agency for Management of University and Research Grants (AGAUR).Postprint (published version