An efficient Two-Layer wall model for accurate numerical simulations of aeronautical applications

Two-Layer wall models have been widely studied since they allow wall modeled Large Eddy Simulationsof general non-equilibrium flows. However, they are plagued by two persistent problems, the "log-layermismatch" and the resolved Reynolds stresses inflow. Several methodologies have been proposed so far todeal with these problems separately. In this work, a time-filtering methodology is used to tackle both issuesat once with a single and low-computational-cost step, easily applicable to complex three-dimensionalgeometries. Additionally, it is shown that the techniques intended to suppress the Reynolds stresses inflowproposed so far, were not sufficient to completely mitigate their detrimental effects.Peer ReviewedPostprint (published version

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

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

A checkerboard-free symmetry-preserving conservative method for magnetohydrodynamic flows

Simulating MHD flows at high Hartmann numbers and low magnetic Reynolds numbers is of high interest for the design of a nuclear fusion breeding blanket, for which high accuracy and conservation of physical properties are of great importance. In this work, a solver is developed that offers these properties through the symmetry-preserving method, while at the same time warranting unconditional stability. Since this method uses predictor values for the pressure and electric potential fields, it can be prone to checkerboarding. Therefore it is extended to include a dynamical checkerboarding solution, which balances this problem with numerical dissipation. This is done through run-time measurements of the intensity of checkerboarding, which is then used as a negative feedback onto the predictor values. The symmetry-preserving discretisation and the dynamical solution to checkerboarding were successfully tested using an magnetohydrodynamic Taylor-Green vortex. The newly introduced method shows results free from numerical dissipation in smooth cases, whereas it avoids checkerboarding in more challenging cases. Finally, the method shows to be unconditionally stable, even on highly distorted meshes.This work is supported by the SIMEX project (PID2022-142174OB-I00) of Ministerio de Ciencia e Innovación, Spain and the RETOtwin project (PDC2021-120970-I00) of Ministerio de Economía y Competitividad, Spain. J.A.H. is supported by the predoctoral grant FI 2023 (2023 FI B1 00204) of the Catalan Agency for Management of University and Research Grants (AGAUR).Peer ReviewedPostprint (published version

On the properties of discrete spatial filters for CFD

© 2016. This version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/The spatial filtering of variables in the context of Computational Fluid Dynamics (CFD) is a common practice. Most of the discrete filters used in CFD simulations are locally accurate models of continuous operators. However, when filters are adaptative, i.e. the filter width is not constant, or meshes are irregular, discrete filters sometimes break relevant global properties of the continuous models they are based on. For example, the principle of maxima and minima reduction or conservation are eventually infringed. In this paper, we analyze the properties of analytic continuous convolution filters and extract those we consider to define filtering. Then, we impose the accomplishment of these properties on explicit discrete filters by means of constraints. Three filters satisfying the derived conditions are deduced and compared to common differential discrete CFD filters on synthetic fields. Tests on the developed discrete filters show the fulfillment of the imposed properties. In particular, the problem of maxima and minima generation is resolved for physically relevant cases. The tests are conducted on the basis of the eigenvectors of graph Laplacian matrices of meshes. Thus, insight into the relations between filtering and oscillation growth on general meshes is provided. Further tests on singularity fields and on isentropic vortices have also been conducted to evaluate the performance of filters on basic CFD fields. Results confirm that imposing the proposed conditions makes discrete filters properties consistent with those of the continuous ones.Peer ReviewedPostprint (author's final draft

NUMA-Aware Strategies for the Heterogeneous Execution of SPMV on Modern Supercomputers

The sparse matrix-vector product is a widespread operation amongst the scientific computing community. It represents the dominant computational cost in many large-scale simulations relying on iterative methods, and its performance is sensitive to the sparse pattern, the storage format, and kernel implementation, and the target computing architecture. In this work, we are devoted to the efficient execution of the sparse matrix-vector product on (potentially hybrid) modern supercomputers with non-uniform memory access configurations. A hierarchical parallel implementation is proposed to minimize the number of processes participating in distributed-memory parallelization. As a result, a single process per computing node is enough to engage all its hardware and ensure efficient memory access on manycore platforms. The benefits of this approach have been demonstrated on up to 9,600 cores of MareNostrum 4 supercomputer, at Barcelona Supercomputing Center.The work of A. Gorobets has been funded by the Russian Science Foundation, project 19- 11-00299. The work of X. Alvarez-Farr ´ e, F. X. Trias and A. Oliva has been financially supported ´ by the ANUMESOL project (ENE2017-88697-R) by the Spanish Research Agency (Ministerio de Economía y Competitividad, Secretaría de Estado de Investigacion, Desarrollo e Inno- ´ vacion), and the FusionCAT project (001-P-001722) by the Government of Catalonia (RIS3CAT ´ FEDER). The studies of this work have been carried out using the MareNostrum 4 supercomputer of the Barcelona Supercomputing Center (projects IM-2020-2-0029 and IM-2020-3-0030); the TSUBAME3.0 supercomputer of the Global Scientific Information and Computing Center at Tokyo Institute of Technology; the Lomonosov-2 supercomputer of the shared research facilities of HPC computing resources at Lomonosov Moscow State University; the K-60 hybrid cluster of the collective use center of the Keldysh Institute of Applied Mathematics. The authors thankfully acknowledge these institutions for the compute time and technical support.Postprint (published version

Symmetry-preserving discretisation methods for magnetohydrodynamics

In this work, the symmetry-preserving method [1, 2, 3] is extended to include magnetohydrodynamic effects, using the collocated grid arrangement of Ni et al. [4, 5]. The electromagnetic part is solved explicitly using the induction-less approximation and an electric potential Poisson equation. The proposed solver is implemented in OpenFOAM and tested for accuracy and stability, and compared to the method of Ni et al. [4, 5]. A new benchmark case using a Taylor-Green vortex in a transverse magnetic field is used, for which kinetic energy budget terms are compared to the analytical solutions. Finally, Hunt’s case is used to compare flow profiles to the analytical solutions. Influence of the spatial discretisation on accuracy and stability is also examined by solving both cases on meshes with variable degrees of distortion. The symmetry-preserving method showed accuracy on Cartesian meshes and stability even on extremely distorted meshes, whereas the method of Ni et al. [4, 5] showed less accurate conservation of current density and was not able to produce stable solutions on the extremely distorted meshes.This project is part of the RIS3CAT-FEDER, FusionCAT project (001- P-001722) of Generalitat de Catalunya and the RETOtwin project (PDC2021-120970-I00) of Ministerio de Economía y Competitividad, Spain. J.A.H. is supported by the predoctoral grant FI 2022 (2022 FI B1 00204) of the Catalan Agency for Management of University and Research Grants (AGAUR).Peer ReviewedPostprint (published version

Exploiting spatial symmetries for solving Poisson's equation

This paper presents a strategy to accelerate virtually any Poisson solver by taking advantage of s spatial reflection symmetries. More precisely, we have proved the existence of an inexpensive block diagonalisation that transforms the original Poisson equation into a set of 2s fully decoupled subsystems then solved concurrently. This block diagonalisation is identical regardless of the mesh connectivity (structured or unstructured) and the geometric complexity of the problem, therefore applying to a wide range of academic and industrial configurations. In fact, it simplifies the task of discretising complex geometries since it only requires meshing a portion of the domain that is then mirrored implicitly by the symmetries’ hyperplanes. Thus, the resulting meshes naturally inherit the exploited symmetries, and their memory footprint becomes 2s times smaller. Thanks to the subsystems’ better spectral properties, iterative solvers converge significantly faster. Additionally, imposing an adequate grid points’ ordering allows reducing the operators’ footprint and replacing the standard sparse matrix-vector products with the sparse matrixmatrix product, a higher arithmetic intensity kernel. As a result, matrix multiplications are accelerated, and massive simulations become more affordable. Finally, we include numerical experiments based on a turbulent flow simulation and making state-of-theart solvers exploit a varying number of symmetries. On the one hand, algebraic multigrid and preconditioned Krylov subspace methods require up to 23% and 72% fewer iterations, resulting in up to 1.7x and 5.6x overall speedups, respectively. On the other, sparse direct solvers’ memory footprint, setup and solution costs are reduced by up to 48%, 58% and 46%, respectively.This work has been financially supported by two competitive R+D projects: RETOtwin (PDC2021-120970-I00), given by MCIN/AEI/10.13039/501100011033 and European Union Next GenerationEU/PRTR, and FusionCAT (001-P-001722), given by Generalitat de Catalunya RIS3CAT-FEDER. Àdel Alsalti-Baldellou has also been supported by the predoctoral grants DIN2018-010061 and 2019-DI-90, given by MCIN/AEI/10.13039/501100011033 and the Catalan Agency for Management of University and Research Grants (AGAUR), respectively.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 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