A. Gorobets

Building proper invariants for eddy-viscosity subgrid-scale models

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

ABSTRACT 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.

A new subgrid characteristic length for turbulence simulations on anisotropic grids

Direct numerical simulations of the incompressible Navier-Stokes equations are not feasible yet for most practical turbulent flows. Therefore, dynamically less complex mathematical formulations are necessary for coarse-grained simulations. In this regard, eddy-viscosity models for Large-Eddy Simulation (LES) are probably the most popular example thereof. This type of models requires the calculation of a subgrid characteristic length which is usually associated with the local grid size. For isotropic grids this is equal to the mesh step. However, for anisotropic or unstructured grids, such as the pancake-like meshes that are often used to resolve near-wall turbulence or shear layers, a consensus on defining the subgrid characteristic length has not been reached yet despite the fact that it can strongly affect the performance of LES models. In this context, a new definition of the subgrid characteristic length is presented in this work. This flow-dependent length scale is based on the turbulent, or subgrid stress, tensor and its representations on different grids. The simplicity and mathematical properties suggest that it can be a robust definition that minimizes the effects of mesh anisotropies on simulation results. The performance of the proposed subgrid characteristic length is successfully tested for decaying isotropic turbulence and a turbulent channel flow using artificially refined grids. Finally, a simple extension of the method for unstructured meshes is proposed and tested for a turbulent flow around a square cylinder. Comparisons with existing subgrid characteristic length scales show that the proposed definition is much more robust with respect to mesh anisotropies and has a great potential to be used in complex geometries where highly skewed (unstructured) meshes are present.

A priori study of subgrid-scale features in turbulent Rayleigh-Bénard convection

At the crossroad between flow topology analysis and turbulence modeling, a priori studies are a reliable tool to understand the underlying physics of the subgrid-scale (SGS) motions in turbulent flows. In this paper, properties of the SGS features in the framework of a large-eddy simulation are studied for a turbulent Rayleigh-Benard convection (RBC). To do so, data from direct numerical simulation (DNS) of a turbulent air-filled RBC in a rectangular cavity of aspect ratio unity and π spanwise open-ended distance are used at two Rayleigh numbers Ra∈{108,1010} [Dabbagh et al., “On the evolution of flow topology in turbulent Rayleigh-Benard convection,” Phys. Fluids 28, 115105 (2016)]. First, DNS at Ra = 108 is used to assess the performance of eddy-viscosity models such as QR, Wall-Adapting Local Eddy-viscosity (WALE), and the recent S3PQR-models proposed by Trias et al. [“Building proper invariants for eddy-viscosity subgrid-scale models,” Phys. Fluids 27, 065103 (2015)]. The outcomes imply that the eddy-...

On the evolution of flow topology in turbulent Rayleigh-Bénard convection

Small-scale dynamics is the spirit of turbulence physics. It implicates many attributes of flow topology evolution, coherent structures, hairpin vorticity dynamics, and mechanism of the kinetic energy cascade. In this work, several dynamical aspects of the small-scale motions have been numerically studied in a framework of Rayleigh-Benard convection (RBC). To do so, direct numerical simulations have been carried out at two Rayleigh numbers Ra = 108 and 1010, inside an air-filled rectangular cell of aspect ratio unity and π span-wise open-ended distance. As a main feature, the average rate of the invariants of the velocity gradient tensor (QG, RG) has displayed the so-called “teardrop” spiraling shape through the bulk region. Therein, the mean trajectories are swirling inwards revealing a periodic spin around the converging origin of a constant period that is found to be proportional to the plumes lifetime. This suggests that the thermal plumes participate in the coherent large-scale circulation and the tu...

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.

Building proper invariants for large eddy simulation

where u denotes the velocity field, p represents the kinematic pressure and ν is the kinematic viscosity. In the foreseeable future, numerical simulations of turbulent flows will have to resort to models of the small scales because the non-linear convective term produces too many scales of motion. Large-Eddy Simulation (LES) is probably the most popular example thereof. In short, LES equations result from applying a spatial filter, with filter length ∆ , to the NS Eqs.(1)

Building Proper Invariants for Eddy-Viscosity Models

Direct numerical simulations of the incompressible Navier-Stokes equations are limited to relatively low-Reynolds numbers. Therefore, dynamically less complex mathematical formulations are necessary for coarse-grain simulations. Regularization and eddy-viscosity models for LES are examples thereof. They rely on differential operators that should capture well different flow configurations (laminar and 2D flows, near-wall behavior, transitional regime ...). Most of them are based on the combination of invariants of a symmetric second-order tensor that is derived from the gradient of the resolved velocity field. In the present work, they are presented in a framework where the models are represented as a combination of elements of a 5D phase space of invariants. In this way, new models can be constructed by imposing appropriate restrictions in this space.

New Differential Operators for Large-Eddy Simulation and Regularization Modeling

where u denotes the velocity field, p represents the pressure, the non-linear convective term is given by C uv = (u · ∇) v, and the diffusive term reads Du = νΔu, where ν is the kinematic viscosity. Direct simulations at high Reynolds numbers are not feasible because the convective term produces far too many scales of motion. Hence, in the foreseeable future numerical simulations of turbulent flows will have to resort to models of the small scales. The most popular example thereof is the Large-Eddy Simulation (LES). Shortly, LES equations result from filtering the NS equations in space ∂t u + C (u,u) = Du −∇ p − ∇ · τ(u) ; ∇ · u = 0, (2)

Spectrally-consistent regularization modeling of turbulent natural convection 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 terms 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 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. In the present work, the performance of the above-mentioned recent improvements is assessed through application to turbulent natural convection flows by means of comparison with DNS reference data.