Parallel algorithms for computational fluid dynamics on unstructured meshes

La simulació numèrica directa (DNS) de fluxos complexes és actualment una utopia per la majoria d'aplicacions industrials ja que els requeriments computacionals son massa elevats. Donat un flux, la diferència entre els recursos computacionals necessaris i els disponibles és cobreix mitjançant la modelització/simplificació d'alguns termes de les equacions originals que regeixen el seu comportament. El creixement continuat dels recursos computacionals disponibles, principalment en forma de super-ordinadors, contribueix a reduir la part del flux que és necessari aproximar. De totes maneres, obtenir la eficiència esperada dels nous super-ordinadors no és una tasca senzilla i, per aquest motiu, part de la recerca en el camp de la Mecànica de Fluids Computacional es centra en aquest objectiu. En aquest sentit, algunes contribucions s'han presentat en el marc d'aquesta tesis. El primer objectiu va ser el desenvolupament d'un codi de CFD de propòsit general i paral·lel, basat en la metodologia de volums finits en malles no estructurades, per resoldre problemes de multi-física. Aquest codi, anomenat TermoFluids (TF), té un disseny orientat a objectes i pensat per ser usat de forma altament eficient en els super-ordinadors actuals. Amb el temps, ha esdevingut pel grup una eina fonamental en projectes tant de recerca bàsica com d'interès industrial. En el context d'aquesta tesis, el treball s'ha focalitzat en el desenvolupament de dos de les llibreries més bàsiques de TermoFluids: i) La Basics Objects Library (BOL), que es una plataforma de software sobre la qual estan programades la resta de llibreries del codi, i que conté els mètodes algebraics i geomètrics fonamentals per la implementació paral·lela dels algoritmes de discretització, ii) la Linear Solvers Library (LSL), que conté un gran nombre de mètodes per resoldre els sistemes d'equacions lineals derivats de les discretitzacions. El primer capítol d'aquesta tesi conté les principals idees subjacents al disseny i la implementació de la BOL i la LSL, juntament amb alguns exemples i algunes aplicacions industrials. En els capítols posteriors hi ha una explicació detallada de solvers específics per algunes aplicacions concretes. En el segon capítol, es presenta un solver paral·lel i directe per la resolució de l'equació de Poisson per casos en els quals una de les direccions del domini té condicions d'homogeneïtat. En la simulació de fluxos incompressibles, l'equació de Poisson es resol almenys una vegada en cada pas de temps, convertint-se en una de les parts més costoses i difícils de paral·lelitzar del codi. El mètode que proposem és una combinació d'una descomposició directa de Schur (DDS) i una diagonalització de Fourier. La darrera descompon el sistema original en un conjunt de sub-sistemes 2D independents que es resolen mitjançant l'algorisme DDS. Atès que no s'imposen restriccions a les direccions no periòdiques del domini, aquest mètode és aplicable a la resolució de problemes discretitzats mitjançat l'extrusió de malles 2D no estructurades. L'escalabilitat d'aquest mètode ha estat provada amb èxit amb un màxim de 8192 CPU per malles de fins a ~10⁹ volums de control. En el darrer capitol capítol, es presenta un mètode de resolució per l'equació de Transport de Boltzmann (BTE). La estratègia emprada es basa en el mètode d'Ordenades Discretes i pot ser aplicat en discretitzacions no estructurades. El flux per a cada ordenada angular es resol amb un mètode de substitució equivalent a la resolució d'un sistema lineal triangular. La naturalesa seqüencial d'aquest procés fa de la paral·lelització de l'algoritme el principal repte. Diversos algorismes de substitució han estat analitzats, esdevenint una de les heurístiques proposades la millor opció en totes les situacions analitzades, amb excel·lents resultats. Els testos d'eficiència paral·lela s'han realitzat usant fins a 2560 CPU.Direct Numerical Simulation (DNS) of complex flows is currently an utopia for most of industrial applications because computational requirements are too high. For a given flow, the gap between the required and the available computing resources is covered by modeling/simplifying of some terms of the original equations. On the other hand, the continuous growth of the computing power of modern supercomputers contributes to reduce this gap, reducing hence the unresolved physics that need to be attempted with approximated models. This growth, widely relies on parallel computing technologies. However, getting the expected performance from new complex computing systems is becoming more and more difficult, and therefore part of the CFD research is focused on this goal. Regarding to it, some contributions are presented in this thesis. The first objective was to contribute to the development of a general purpose multi-physics CFD code. referred to as TermoFluids (TF). TF is programmed following the object oriented paradigm and designed to run in modern parallel computing systems. It is also intensively involved in many different projects ranging from basic research to industry applications. Besides, one of the strengths of TF is its good parallel performance demonstrated in several supercomputers. In the context of this thesis, the work was focused on the development of two of the most basic libraries that compose TF: I) the Basic Objects Library (BOL), which is a parallel unstructured CFD application programming interface, on the top of which the rest of libraries that compose TF are written, ii) the Linear Solvers Library (LSL) containing many different algorithms to solve the linear systems arising from the discretization of the equations. The first chapter of this thesis contains the main ideas underlying the design and the implementation of the BOL and LSL libraries, together with some examples and some industrial applications. A detailed description of some application-specific linear solvers included in the LSL is carried out in the following chapters. In the second chapter, a parallel direct Poisson solver restricted to problems with one uniform periodic direction is presented. The Poisson equation is solved, at least, once per time-step when modeling incompressible flows, becoming one of the most time consuming and difficult to parallelize parts of the code. The solver here proposed is a combination of a direct Schur-complement based decomposition (DSD) and a Fourier diagonalization. The latter decomposes the original system into a set of mutually independent 2D sub-systems which are solved by means of the DSD algorithm. Since no restrictions are imposed in the non-periodic directions, the overall algorithm is well-suited for solving problems discretized on extruded 2D unstructured meshes. The scalability of the solver has been successfully tested using up to 8192 CPU cores for meshes with up to 10 9 grid points. In the last chapter, a solver for the Boltzmann Transport Equation (BTE) is presented. It can be used to solve radiation phenomena interacting with flows. The solver is based on the Discrete Ordinates Method and can be applied to unstructured discretizations. The flux for each angular ordinate is swept across the computational grid, within a source iteration loop that accounts for the coupling between the different ordinates. The sequential nature of the sweep process makes the parallelization of the overall algorithm the most challenging aspect. Several parallel sweep algorithms, which represent different options of interleaving communications and calculations, are analyzed. One of the heuristics proposed consistently stands out as the best option in all the situations analyzed. With this algorithm, good scalability results have been achieved regarding both weak and strong speedup tests with up to 2560 CPUs

Parallel load balancing strategy for Volume-of-Fluid methods on 3-D unstructured meshes

© 2016. This version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/l Volume-of-Fluid (VOF) is one of the methods of choice to reproduce the interface motion in the simulation of multi-fluid flows. One of its main strengths is its accuracy in capturing sharp interface geometries, although requiring for it a number of geometric calculations. Under these circumstances, achieving parallel performance on current supercomputers is a must. The main obstacle for the parallelization is that the computing costs are concentrated only in the discrete elements that lie on the interface between fluids. Consequently, if the interface is not homogeneously distributed throughout the domain, standard domain decomposition (DD) strategies lead to imbalanced workload distributions. In this paper, we present a new parallelization strategy for general unstructured VOF solvers, based on a dynamic load balancing process complementary to the underlying DD. Its parallel efficiency has been analyzed and compared to the DD one using up to 1024 CPU-cores on an Intel SandyBridge based supercomputer. The results obtained on the solution of several artificially generated test cases show a speedup of up to similar to 12x with respect to the standard DD, depending on the interface size, the initial distribution and the number of parallel processes engaged. Moreover, the new parallelization strategy presented is of general purpose, therefore, it could be used to parallelize any VOF solver without requiring changes on the coupled flow solver. Finally, note that although designed for the VOF method, our approach could be easily adapted to other interface-capturing methods, such as the Level-Set, which may present similar workload imbalances. (C) 2014 Elsevier Inc. Allrights reserved.Peer ReviewedPostprint (author's final draft

HPC compact quasi-Newton algorithm for interface problems

In this work we present a robust interface coupling algorithm called Compact Interface quasi-Newton (CIQN). It is designed for computationally intensive applications using an MPI multi-code partitioned scheme. The algorithm allows to reuse information from previous time steps, feature that has been previously proposed to accelerate convergence. Through algebraic manipulation, an efficient usage of the computational resources is achieved by: avoiding construction of dense matrices and reduce every multiplication to a matrix-vector product and reusing the computationally expensive loops. This leads to a compact version of the original quasi-Newton algorithm. Altogether with an efficient communication, in this paper we show an efficient scalability up to 4800 cores. Three examples with qualitatively different dynamics are shown to prove that the algorithm can efficiently deal with added mass instability and two-field coupled problems. We also show how reusing histories and filtering does not necessarily makes a more robust scheme and, finally, we prove the necessity of this HPC version of the algorithm. The novelty of this article lies in the HPC focused implementation of the algorithm, detailing how to fuse and combine the composing blocks to obtain an scalable MPI implementation. Such an implementation is mandatory in large scale cases, for which the contact surface cannot be stored in a single computational node, or the number of contact nodes is not negligible compared with the size of the domain. \c{opyright} Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Comment: 33 pages: 23 manuscript, 10 appendix. 16 figures: 4 manuscript, 12 appendix. 10 Tables: 3 manuscript, 7 appendi

Distributed tabulation of flamelet lookup tables

One of the fundamental questions in combustion simulation is how to account for detailed chemistry effects, while controlling both the error of the chemical scheme and the computational cost. Combustion chemistry is important for resolving processes such as flame propagation and pollutant formation, which are non-linear processes that can be computationally expensive. The direct solution of the governing equations of turbulent reacting flows can be prohibitively expensive as the chemical integration is often stiff. Tabulated chemistry methods with flamelet modelling emerge as an alternative to perform direct integration of the chemical source terms and has been extended to a wide range of conditions [1]. In flamelet methods, the chemical time scale is assumed smaller than the time scales of the turbulence, so the flame structure is not affected by the turbulence. In flamelet methods, the thermochemical states of the flame are computed in a preprocessing step, and these values are retrieved from a lookup table loaded into memory at the beginning of the simulation. The flame structure can be recovered through the use of controlling variables, which represent dimensions along the multidimensional space of the flame manifold

Parallel Adaptive Mesh Refinement Simulation of the Flow Around a Square Cylinder at Re = 22000

AbstractIn this paper a parallel adaptive mesh refinement for LES simulation of turbulent flows is presented. The AMR scheme applies a cell- based refinement technique to get enough grid-resolution to solve the small scales structures, adapting the mesh according to physics- based refinement criteria. A flexible tree data structure is used to keeping track of the mesh adaptation and an edge-based data structure to save and search cell connectivity. The AMR framework is combined with parallel algorithms for partitioning and balancing of the computational mesh. Numerical results for turbulent flow around a square cylinder at Re = 22000 are compared to experimental data

Parallel SFC-based mesh partitioning and load balancing

Modern supercomputers allow the simulation of complex phenomena with increased accuracy. Eventually, this requires finer geometric discretizations with larger numbers of mesh elements. In this context, and extrapolating to the Exascale paradigm, meshing operations such as generation, adaptation or partition, become a critical bottleneck within the simulation workflow. In this paper, we focus on mesh partitioning. In particular, we present some improvements carried out on an in-house parallel mesh partitioner based on the Hilbert Space-Filling Curve. Additionally, taking advantage of its performance, we present the application of the SFC-based partitioning for dynamic load balancing. This method is based on the direct monitoring of the imbalance at runtime and the subsequent re-partitioning of the mesh. The target weights for the optimized partitions are evaluated using a least-squares approximation considering all measurements from previous iterations. In this way, the final partition corresponds to the average performance of the computing devices engaged.Comment: 10 pages, 9 figures. arXiv admin note: text overlap with arXiv:2005.0589

Communication-aware sparse patterns for the factorized approximate inverse preconditioner

The Conjugate Gradient (CG) method is an iterative solver targeting linear systems of equations Ax=b where A is a symmetric and positive definite matrix. CG convergence properties improve when preconditioning is applied to reduce the condition number of matrix A. While many different options can be found in the literature, the Factorized Sparse Approximate Inverse (FSAI) preconditioner constitutes a highly parallel option based on approximating A-1. This paper proposes the Communication-aware Factorized Sparse Approximate Inverse preconditioner (FSAIE-Comm), a method to generate extensions of the FSAI sparse pattern that are not only cache friendly, but also avoid increasing communication costs in distributed memory systems. We also propose a filtering strategy to reduce inter-process imbalance. We evaluate FSAIE-Comm on a heterogeneous set of 39 matrices achieving an average solution time decrease of 17.98%, 26.44% and 16.74% on three different architectures, respectively, Intel Skylake, Fujitsu A64FX and AMD Zen 2 with respect to FSAI. In addition, we consider a set of 8 large matrices running on up to 32,768 CPU cores, and we achieve an average solution time decrease of 12.59%.Marc Casas is supported by Grant RYC-2017-23269 funded by MCIN/AEI/ 10.13039/501100011033 and by “ESF Investing in your future”. This work has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 955606. This work has been supported by the Computación de Altas Prestaciones VIII (BSC-HPC8) project. It has also been partially supported by the EXCELLERAT project funded by the European Commission’s ICT activity of the H2020 Programme under grant agreement number: 823691 and by the Spanish Ministry of Science and Innovation (Nucleate, Project PID2020-117001GB-I00).Peer ReviewedPostprint (author's final draft