Download or read book OpenACC Acceleration of an Unstructured CFD Solver Based on a Reconstructed Discontinuous Galerkin Method for Compressible Flows written by and published by . This book was released on 2015 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here, an OpenACC directive-based graphics processing unit (GPU) parallel scheme is presented for solving the compressible Navier-Stokes equations on 3D hybrid unstructured grids with a third-order reconstructed discontinuous Galerkin method. The developed scheme requires the minimum code intrusion and algorithm alteration for upgrading a legacy solver with the GPU computing capability at very little extra effort in programming, which leads to a unified and portable code development strategy. A face coloring algorithm is adopted to eliminate the memory contention because of the threading of internal and boundary face integrals. A number of flow problems are presented to verify the implementation of the developed scheme. Timing measurements were obtained by running the resulting GPU code on one Nvidia Tesla K20c GPU card (Nvidia Corporation, Santa Clara, CA, USA) and compared with those obtained by running the equivalent Message Passing Interface (MPI) parallel CPU code on a compute node (consisting of two AMD Opteron 6128 eight-core CPUs (Advanced Micro Devices, Inc., Sunnyvale, CA, USA)). Speedup factors of up to 24× and 1.6× for the GPU code were achieved with respect to one and 16 CPU cores, respectively. The numerical results indicate that this OpenACC-based parallel scheme is an effective and extensible approach to port unstructured high-order CFD solvers to GPU computing.

Download or read book 2023 Asia Pacific International Symposium on Aerospace Technology APISAT 2023 Proceedings written by Song Fu and published by Springer Nature. This book was released on with total page 1975 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book High Performance Computing written by Michela Taufer and published by Springer. This book was released on 2016-10-05 with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes revised selected papers from 7 workshops that were held in conjunction with the ISC High Performance 2016 conference in Frankfurt, Germany, in June 2016. The 45 papers presented in this volume were carefully reviewed and selected for inclusion in this book. They stem from the following workshops: Workshop on Exascale Multi/Many Core Computing Systems, E-MuCoCoS; Second International Workshop on Communication Architectures at Extreme Scale, ExaComm; HPC I/O in the Data Center Workshop, HPC-IODC; International Workshop on OpenPOWER for HPC, IWOPH; Workshop on the Application Performance on Intel Xeon Phi – Being Prepared for KNL and Beyond, IXPUG; Workshop on Performance and Scalability of Storage Systems, WOPSSS; and International Workshop on Performance Portable Programming Models for Accelerators, P3MA.

Download or read book A high order discontinuous Galerkin method for unsteady compressible flows with immersed boundaries written by Stephan Krämer-Eis and published by Cuvillier Verlag. This book was released on 2017-10-20 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Um die komplexe Physik in kompressiblen Strömungen genauer zu verstehen, kommen vermehrt Simulationen zum Einsatz. Jedoch können weit verbreitete kommerzielle Softwarepakete die Physik aufgrund ihrer niedrigen Genauigkeit oft nicht korrekt erfassen. In dieser Arbeit wird eine diskontinuierliche Galerkin Methode mit hoher Ordnung entwickelt, welche eine hohe Genauigkeit erzielt. Dabei werden insbesondere zwei Probleme, die im Kontext von Verfahren mit hoher Ordnung auftreten, behandelt. Zum einen wird die Gittergenerierung durch das Verwenden einer Immersed Boundary Methode deutlich vereinfacht. Dies bedeutet, dass die Problemgeometrie aus einem deutlich einfacheren Hintergrundgitter herausgeschnitten wird. Die Geometrie wird mit Hilfe einer Level-Set Funktion dargestellt, und die Integration auf den entstehenden geschnittenen Zellen wird mittels einer hierarchischen Moment-Fitting Quadratur durchgeführt. Das Problem der sehr kleinen oder stark gekrümmten Zellen wird durch Zellagglomeration gelöst. Zum zweiten wird die starke Zeitschrittbeschränkung durch anisotrope Gitter mit Hilfe eines lokalen Zeitschrittverfahrens behoben. Diverse numerische Experimente bestätigen die hohe Genauigkeit, Effizienz und geometrische Flexibilität der vorgestellten Methode.

Download or read book An Adaptive Discontinuous Galerkin Solver for Aerodynamic Flows written by Nicholas K. Burgess and published by . This book was released on 2011 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work considers the accuracy, efficiency, and robustness of an unstructured high-order accurate discontinuous Galerkin (DG) solver for computational fluid dynamics (CFD). Recently, there has been a drive to reduce the discretization error of CFD simulations using high-order methods on unstructured grids. However, high-order methods are often criticized for lacking robustness and having high computational cost. The goal of this work is to investigate methods that enhance the robustness of high-order discontinuous Galerkin (DG) methods on unstructured meshes, while maintaining low computational cost and high accuracy of the numerical solutions. This work investigates robustness enhancement of high-order methods by examining effective non-linear solvers, shock capturing methods, turbulence model discretizations and adaptive refinement techniques. The goal is to develop an all encompassing solver that can simulate a large range of physical phenomena, where all aspects of the solver work together to achieve a robust, efficient and accurate solution strategy. The components and framework for a robust high-order accurate solver that is capable of solving viscous, Reynolds Averaged Navier-Stokes (RANS) and shocked flows is presented. In particular, this work discusses robust discretizations of the turbulence model equation used to close the RANS equations, as well as stable shock capturing strategies that are applicable across a wide range of discretization orders and applicable to very strong shock waves. Furthermore, refinement techniques are considered as both efficiency and robustness enhancement strategies. Additionally, efficient non-linear solvers based on multigrid and Krylov subspace methods are presented. The accuracy, efficiency, and robustness of the solver is demonstrated using a variety of challenging aerodynamic test problems, which include turbulent high-lift and viscous hypersonic flows. Adaptive mesh refinement was found to play a critical role in obtaining a robust and efficient high-order accurate flow solver. A goal-oriented error estimation technique has been developed to estimate the discretization error of simulation outputs. For high-order discretizations, it is shown that functional output error super-convergence can be obtained, provided the discretization satisfies a property known as dual consistency. The dual consistency of the DG methods developed in this work is shown via mathematical analysis and numerical experimentation. Goal-oriented error estimation is also used to drive an hp -adaptive mesh refinement strategy, where a combination of mesh or h -refinement, and order or p -enrichment, is employed based on the smoothness of the solution. The results demonstrate that the combination of goal-oriented error estimation and hp-adaptation yield superior accuracy, as well as enhanced robustness and efficiency for a variety of aerodynamic flows including flows with strong shock waves. This work demonstrates that DG discretizations can be the basis of an accurate, efficient, and robust CFD solver. Furthermore, enhancing the robustness of DG methods does not adversely impact the accuracy or efficiency of the solver for challenging and complex flow problems. In particular, when considering the computation of shocked flows, this work demonstrates that the available shock capturing techniques are sufficiently accurate and robust, particularly when used in conjunction with adaptive mesh refinement . This work also demonstrates that robust solutions of the Reynolds Averaged Navier-Stokes (RANS) and turbulence model equations can be obtained for complex and challenging aerodynamic flows. In this context, the most robust strategy was determined to be a low-order turbulence model discretization coupled to a high-order discretization of the RANS equations. Although RANS solutions using high-order accurate discretizations of the turbulence model were obtained, the behavior of current-day RANS turbulence models discretized to high-order was found to be problematic, leading to solver robustness issues. This suggests that future work is warranted in the area of turbulence model formulation for use with high-order discretizations. Alternately, the use of Large-Eddy Simulation (LES) subgrid scale models with high-order DG methods offers the potential to leverage the high accuracy of these methods for very high fidelity turbulent simulations. This thesis has developed the algorithmic improvements that will lay the foundation for the development of a three-dimensional high-order flow solution strategy that can be used as the basis for future LES simulations.

Download or read book Towards High performance Discontinuous Galerkin Simulations of Reacting Flows Using Legion written by Kihiro Bando and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: High-fidelity scale-resolving computational fluid dynamics (CFD) simulations may provide a path towards predictive capabilities for many engineering-relevant applications, in particular those involving the interaction between multiple physics such as turbulent multi-component reacting flows. However, their routine use is hindered by their cost. The throughput of the fastest supercomputers is fortunately still increasing but this comes at the cost of specialized devices and hardware heterogeneity. Modern supercomputing thus imposes new requirements onto numerical algorithms and their implementation for leveraging the available compute while significantly complicating the design, development, and maintenance of massively parallel computational physics software. This dissertation focuses on addressing numerical and implementation challenges of CFD of multi-component reacting flows. It considers high-order discontinuous Galerkin (DG) discretization methods as a way towards a more efficient use of modern compute architectures for performing high-fidelity simulations of configurations involving complex geometries. Both the high accuracy requirement and the ability to accommodate unstructured meshes are key motivations for investigating this class of numerical schemes. The entire content of this manuscript is based on DG-Legion, a novel unstructured DG CFD solver for the compressible Navier-Stokes equations written on top of the Legion system for targeting distributed heterogeneous architectures. The main challenge related to the computer science aspect was to scale the code on GPU supercomputers. An explicit ghost formulation is proposed which results in performance competitive with state-of-the-art solvers based on the message-passing interface (MPI) system while the application code remains free of explicit communication and synchronization, i.e. it has sequential semantics. The contribution related to the numerics addresses two important questions. First, the issue of spurious pressure oscillations generated by fully-conservative schemes for thermally perfect mixtures is analyzed in detail. A generic framework is developed in order to generate systematic variations of the baseline scheme with improved properties. When applied to the problem at hand, several techniques that were previously proposed independently are recovered as special cases in a rigorous way. Finally, a hybrid strategy for preserving the positivity of DG solutions for the composition-describing scalars is introduced. The method based on the composition of subcell finite volume schemes and linear-scaling limiters leads to an overall positivity-preserving scheme in the inviscid limit, compatible with higher-order quadrature rules, and better preserving the subcell resolution compared to only using rescaling techniques.

Download or read book High order Hybridizable Discontinuous Galerkin Method for Viscous Compressible Flows written by Mostafa Javadzadeh Moghtader and published by . This book was released on 2017 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Fluid Dynamics (CFD) is an essential tool for engineering design and analysis, especially in applications like aerospace, automotive and energy industries. Nowadays most commercial codes are based on Finite Volume (FV) methods, which are second order accurate, and simulation of viscous compressible flow around complex geometries is still very expensive due to large number of low-order elements required. One the other hand, some sophisticated physical phenomena, like aeroacoustics, vortex dominated flows and turbulence, need very high resolution methods to obtain accurate results. High-order methods with their low spatial discretization errors, are a possible remedy for shortcomings of the current CFD solvers. Discontinuous Galerkin (DG) methods have emerged as a successful approach for non-linear hyperbolic problems and are widely regarded very promising for next generation CFD solvers. Their efficiency for high-order discretization makes them suitable for advanced physical models like DES and LES, while their stability in convection dominated regimes is also a merit of them. The compactness of DG methods, facilitate the parallelization and their element-by-element discontinuous nature is also helpful for adaptivity. This PhD thesis focuses on the development of an efficient and robust high-order Hybridizable Discontinuous Galerkin (HDG) Finite Element Method (FEM) for compressible viscous flow computations. HDG method is a new class of DG family which enjoys from merits of DG but has significantly less globally coupled unknowns compared to other DG methods. Its features makes HDG a possible candidate to be investigated as next generation high-order tools for CFD applications. The first part of this thesis recalls the basics of high-order HDG method. It is presented for the two-dimensional linear convection-diffusion equation, and its accuracy and features are investigated. Then, the method is used to solve compressible viscous flow problems modelled by non-linear compressible Navier-Stokes equations; and finally a new linearized HDG formulation is proposed and implemented for that problem, all using high-order approximations. The accuracy and efficiency of high-order HDG method to tackle viscous compressible flow problems is investigated, and both steady and unsteady solvers are developed for this purpose. The second part is the core of this thesis, proposing a novel shock-capturing method for HDG solution of viscous compressible flow problems, in the presence of shock waves. The main idea is to utilize the stabilization of numerical fluxes, via a discontinuous space of approximation inside the elements, to diminish or remove the oscillations in the vicinity of discontinuity. This discontinuous nodal basis functions, leads to a modified weak form of the HDG local problem in the stabilized elements. First, the method is applied to convection-diffusion problems with Bassi-Rebay and LDG fluxes inside the elements, and then, the strategy is extended to the compressible Navier-Stokes equations using LDG and Lax-Friedrichs fluxes. Various numerical examples, for both convection-diffusion and compressible Navier-Stokes equations, demonstrate the ability of the proposed method, to capture shocks in the solution, and its excellent performance in eliminating oscillations is the vicinity of shocks to obtain a spurious-free high-order solution.

Download or read book Development of the Discontinuous Galerkin Method for High resolution Large Scale CFD and Acoustics in Industrial Geometries written by Koen Hillewaert and published by Presses univ. de Louvain. This book was released on 2013-02-10 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this work is the practical development of the discontinuous Galerkin method, arguably the most mature high-order discretisation, for the scale resolving simulations of turbomachinery flows.

Download or read book A Discontinuous Galerkin Method for the Solution of Compressible Flows written by Cristian Biotto and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Parallel Implicit Reconstructed Discontinuous Galerkin Method for Compressible Flows on Hybrid Grids written by Yidong Xia and published by . This book was released on 2013 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Parallel Implicit Reconstructed Discontinuous Galerkin Method for Compressible Turbulent Flows on 3D Hybrid Grids written by Xiaodong Liu and published by . This book was released on 2016 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Optimal Modified Continuous Galerkin CFD written by A. J. Baker and published by John Wiley & Sons. This book was released on 2014-03-10 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the theory and applications of using weak form theory in incompressible fluid-thermal sciences Giving you a solid foundation on the Galerkin finite-element method (FEM), this book promotes the use of optimal modified continuous Galerkin weak form theory to generate discrete approximate solutions to incompressible-thermal Navier-Stokes equations. The book covers the topic comprehensively by introducing formulations, theory and implementation of FEM and various flow formulations. The author first introduces concepts, terminology and methodology related to the topic before covering topics including aerodynamics; the Navier-Stokes Equations; vector field theory implementations and large eddy simulation formulations. Introduces and addresses many different flow models (Navier-Stokes, full-potential, potential, compressible/incompressible) from a unified perspective Focuses on Galerkin methods for CFD beneficial for engineering graduate students and engineering professionals Accompanied by a website with sample applications of the algorithms and example problems and solutions This approach is useful for graduate students in various engineering fields and as well as professional engineers.

Download or read book Energy Stable High order Methods for Simulating Unsteady Viscous Compressible Flows on Unstructured Grids written by David Michael Williams and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: High-order methods have the potential to dramatically improve the accuracy and efficiency of flow simulations in the field of computational fluid dynamics (CFD). However, there remain questions regarding the stability and robustness of high-order methods for practical problems on unstructured triangular and tetrahedral grids. In this work, a new class of 'energy stable' high-order methods is identified. This class of schemes (referred to as the 'Energy Stable Flux Reconstruction' class of schemes) is proven to be stable for linear advection-diffusion problems, for all orders of accuracy on unstructured triangular grids in 2D and unstructured tetrahedral grids in 3D. Furthermore, this class of schemes is shown to be capable of recovering the well-known collocation-based nodal discontinuous Galerkin scheme, along with new schemes that possess explicit time-step limits which are (in some cases) more than 2x larger than those of the discontinuous Galerkin scheme. In addition, the stability of the Energy Stable Flux Reconstruction schemes is examined for nonlinear problems, and it is shown that stability depends on the degree of nonlinearity in the flux and on the placement of solution and flux points in each element. In particular, it is shown that choosing the solution and flux point locations to coincide with the locations of quadrature points promotes nonlinear stability by minimizing (or eliminating) nonlinear aliasing errors. A new class of symmetric quadrature points is identified on triangles and tetrahedra for this purpose. Finally, the Energy Stable Flux Reconstruction schemes and the new quadrature points are applied to several nonlinear problems with the aim of assessing how well the schemes perform in practice.

Download or read book An Unstructured Grid Generation and Adaptive Solution Technique for High Reynolds number Compressible Flows written by Gregory Allan Ashford and published by . This book was released on 1996 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Entropy stable Hybridized Discontinuous Galerkin Methods for Large eddy Simulation of Transitional and Turbulent Flows written by Pablo Fernández and published by . This book was released on 2019 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of computational fluid dynamics (CFD) in the aerospace industry is limited by the inability to accurately and reliably predict complex transitional and turbulent flows. This has become a major barrier to further reduce the costs, times and risks in the design process, further optimize designs, and further reduce fuel consumption and toxic emissions. Large-eddy simulation (LES) is currently the most promising simulation technique to accurately predict transitional and turbulent flows. LES, however, remains computationally expensive and often suffers from accuracy and robustness issues to the extent that it is still not practical for most applications of interest. In this thesis, we develop a series of methods and techniques to improve efficiency, accuracy and robustness of large-eddy simulations with the goal of making CFD a more powerful tool in the aerospace industry. First, we introduce a new class of high-order discretization schemes for the Euler and Navier-Stokes equations, referred to as the entropy-stable hybridized discontinuous Galerkin (DG) methods. As hybridized methods, they are amenable to static condensation and hence to more efficient implementations than standard DG methods. As entropy-stable methods, they are superior to conventional (non-entropy stable) methods for LES of compressible flows in terms of stability, robustness and accuracy. Second, we develop parallel iterative methods to efficiently and scalably solve the nonlinear system of equations arising from the discretization. The combination of hybridized DG methods with the proposed solution method provides excellent parallel scalability up to petascale and, for moderately high accuracy orders, leads to about one order of magnitude speedup with respect to standard DG methods. Third, we introduced a non-modal analysis theory that characterizes the numerical dissipation of high-order discretization schemes, including hybridized DG methods. Non-modal analysis provides critical guidelines on how to define the polynomial approximation space and the Riemann solver to improve accuracy and robustness in LES. Forth, we investigate how to best account for the effect of the subgrid scales (SGS) that, by definition, exist in LES. Numerical and theoretical results show the Riemann solver in the DG scheme plays the role of an implicit SGS model. More importantly, a change in the current best practices for SGS modeling is required in the context of high-order DG methods. And fifth, we present a physics-based shock capturing method for LES of high-Mach-number and high-Reynolds-number flows. The shock capturing method performs robustly from transonic to hypersonic regimes, provides sharp shock profiles, and has a small impact on the resolved turbulent structures. These are all critical ingredients to advance the state-of-the-art of high-order methods for LES, both in terms of methodology and understanding the relationship between the physics and the numerics.

Download or read book A Hybrid Reconstructed Discontinuous Galerkin and Continuous Galerkin Finite Element Method for Incompressible Flows on Unstructured Grids written by Aditya Kiran Pandare and published by . This book was released on 2015 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Robust and Accurate Shock capturing in Discontinuous Galerkin Discretizations written by Jae Hwan Choi and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Fluid Dynamics (CFD) has become a critical component in analyzing fluid flows and designing industrial products. Among various numerical methods in CFD, second-order numerical schemes have been widely used in both industry and academia. Second-order methods are robust enough to use on complex geometries and usually provide a sufficient amount of accuracy in flow simulations. However, second-order accurate solutions may not be sufficient for many aerodynamic applications such as vortex flows, Large Eddy Simulations (LES), and aeroacoustics problems. As a consequence, researchers have sought high-order numerical methods to simulate complex flows with low dissipation over the past few decades. Many approaches have been suggested including Finite Difference (FD), Finite Volume (FV), and Finite Element (FE) frameworks for CFD. In the group of high-order methods, discontinuous Galerkin (DG) methods have become popular in academia because of their distinctive benefits. For DG methods, high-order accuracy in flow solutions can be easily achieved by just adding more degrees of freedom in each element. Furthermore, DG methods are well suited to modern computer hardware, even on GPUs, due to high arithmetic intensity and the locality of operations. Despite their numerous benefits, DG methods are not widely adopted because of some remaining challenges, especially in industry. One of these difficulties is shock-capturing. Similarly to other numerical methods in CFD, DG methods also suffer from spurious oscillations if discontinuities arise during flow simulations. The accuracy of solutions will degrade significantly, or solutions may diverge unless these discontinuities are captured appropriately. Therefore, a shock-capturing capability becomes necessary for DG methods to simulate compressible flows with shocks. In this work, robust and accurate shock-capturing approaches for DG methods will be demonstrated. To precisely capture various strengths of shocks, a simple shock-detector is first proposed for DG discretizations, which only relies on local flow information. Additionally, filtering strengths are precalculated to avoid parameter tuning procedures and are optimized to achieve maximum accuracy while capturing shocks. The proposed methods are then applied to two- and three-dimensional canonical problems to demonstrate the shock-capturing capabilities of the proposed methods.