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A Parallel Implicit Reconstructed Discontinuous Galerkin Method For Compressible Flows On Hybrid Grids
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Book Synopsis A Parallel Implicit Reconstructed Discontinuous Galerkin Method for Compressible Flows on Hybrid Grids by : Yidong Xia
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:
Book Synopsis A Parallel Implicit Reconstructed Discontinuous Galerkin Method for Compressible Turbulent Flows on 3D Hybrid Grids by : Xiaodong Liu
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:
Book Synopsis A Set of Parallel, Implicit Methods for a Reconstructed Discontinuous Galerkin Method for Compressible Flows on 3D Hybrid Grids by :
Download or read book A Set of Parallel, Implicit Methods for a Reconstructed Discontinuous Galerkin Method for Compressible Flows on 3D Hybrid Grids written by and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A set of implicit methods are proposed for a third-order hierarchical WENO reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids. An attractive feature in these methods are the application of the Jacobian matrix based on the P1 element approximation, resulting in a huge reduction of memory requirement compared with DG (P2). Also, three approaches -- analytical derivation, divided differencing, and automatic differentiation (AD) are presented to construct the Jacobian matrix respectively, where the AD approach shows the best robustness. A variety of compressible flow problems are computed to demonstrate the fast convergence property of the implemented flow solver. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results on complex geometries indicate that this low-storage implicit method can provide a viable and attractive DG solution for complicated flows of practical importance.
Book Synopsis A Parallel Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Aritrary Grids by :
Download or read book A Parallel Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Aritrary Grids written by and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A reconstruction-based discontinuous Galerkin method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. In this method, an in-cell reconstruction is used to obtain a higher-order polynomial representation of the underlying discontinuous Galerkin polynomial solution and an inter-cell reconstruction is used to obtain a continuous polynomial solution on the union of two neighboring, interface-sharing cells. The in-cell reconstruction is designed to enhance the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. The inter-cell reconstruction is devised to remove an interface discontinuity of the solution and its derivatives and thus to provide a simple, accurate, consistent, and robust approximation to the viscous and heat fluxes in the Navier-Stokes equations. A parallel strategy is also devised for the resulting reconstruction discontinuous Galerkin method, which is based on domain partitioning and Single Program Multiple Data (SPMD) parallel programming model. The RDG method is used to compute a variety of compressible flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results demonstrate that this RDG method is third-order accurate at a cost slightly higher than its underlying second-order DG method, at the same time providing a better performance than the third order DG method, in terms of both computing costs and storage requirements.
Book Synopsis A Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Unstructured Tetrahedral Grids by :
Download or read book A Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Unstructured Tetrahedral Grids written by and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on unstructured tetrahedral grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on unstructured grids. The preliminary results indicate that this RDG method is stable on unstructured tetrahedral grids, and provides a viable and attractive alternative for the discretization of the viscous and heat fluxes in the Navier-Stokes equations.
Book Synopsis Discontinuous Galerkin Method by : Vít Dolejší
Download or read book Discontinuous Galerkin Method written by Vít Dolejší and published by Springer. This book was released on 2015-07-17 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of compressible flow. It deals with the theoretical as well as practical aspects of the DGM and treats the basic concepts and ideas of the DGM, as well as the latest significant findings and achievements in this area. The main benefit for readers and the book’s uniqueness lie in the fact that it is sufficiently detailed, extensive and mathematically precise, while at the same time providing a comprehensible guide through a wide spectrum of discontinuous Galerkin techniques and a survey of the latest efficient, accurate and robust discontinuous Galerkin schemes for the solution of compressible flow.
Book Synopsis The Proceedings of the 2018 Asia-Pacific International Symposium on Aerospace Technology (APISAT 2018) by : Xinguo Zhang
Download or read book The Proceedings of the 2018 Asia-Pacific International Symposium on Aerospace Technology (APISAT 2018) written by Xinguo Zhang and published by Springer. This book was released on 2019-06-08 with total page 3068 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a compilation of peer-reviewed papers from the 2018 Asia-Pacific International Symposium on Aerospace Technology (APISAT 2018). The symposium is a common endeavour between the four national aerospace societies in China, Australia, Korea and Japan, namely, the Chinese Society of Aeronautics and Astronautics (CSAA), Royal Aeronautical Society Australian Division (RAeS Australian Division), the Korean Society for Aeronautical and Space Sciences (KSAS) and the Japan Society for Aeronautical and Space Sciences (JSASS). APISAT is an annual event initiated in 2009 to provide an opportunity for researchers and engineers from Asia-Pacific countries to discuss current and future advanced topics in aeronautical and space engineering.
Book Synopsis A Hybrid Reconstructed Discontinuous Galerkin and Continuous Galerkin Finite Element Method for Incompressible Flows on Unstructured Grids by : Aditya Kiran Pandare
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:
Book Synopsis A CLASS OF RECONSTRUCTED DISCONTINUOUS GALERKIN METHODS IN COMPUTATIONAL FLUID DYNAMICS. by :
Download or read book A CLASS OF RECONSTRUCTED DISCONTINUOUS GALERKIN METHODS IN COMPUTATIONAL FLUID DYNAMICS. written by and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A class of reconstructed discontinuous Galerkin (DG) methods is presented to solve compressible flow problems on arbitrary grids. The idea is to combine the efficiency of the reconstruction methods in finite volume methods and the accuracy of the DG methods to obtain a better numerical algorithm in computational fluid dynamics. The beauty of the resulting reconstructed discontinuous Galerkin (RDG) methods is that they provide a unified formulation for both finite volume and DG methods, and contain both classical finite volume and standard DG methods as two special cases of the RDG methods, and thus allow for a direct efficiency comparison. Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are presented to obtain a quadratic polynomial representation of the underlying linear discontinuous Galerkin solution on each cell via a so-called in-cell reconstruction process. The devised in-cell reconstruction is aimed to augment the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. These three reconstructed discontinuous Galerkin methods are used to compute a variety of compressible flow problems on arbitrary meshes to assess their accuracy. The numerical experiments demonstrate that all three reconstructed discontinuous Galerkin methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstructed DG method provides the best performance in terms of both accuracy, efficiency, and robustness.
Book Synopsis A high-order discontinuous Galerkin method for unsteady compressible flows with immersed boundaries by : Stephan Krämer-Eis
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.
Book Synopsis A Comparative Study of Different Reconstruction Schemes for a Reconstructed Discontinuous Galerkin Method on Arbitrary Grids by :
Download or read book A Comparative Study of Different Reconstruction Schemes for a Reconstructed Discontinuous Galerkin Method on Arbitrary Grids written by and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A comparative study of different reconstruction schemes for a reconstruction-based discontinuous Galerkin, termed RDG(P1P2) method is performed for compressible flow problems on arbitrary grids. The RDG method is designed to enhance the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution via a reconstruction scheme commonly used in the finite volume method. Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are implemented to obtain a quadratic polynomial representation of the underlying discontinuous Galerkin linear polynomial solution on each cell. These three reconstruction/recovery methods are compared for a variety of compressible flow problems on arbitrary meshes to access their accuracy and robustness. The numerical results demonstrate that all three reconstruction methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstruction method provides the best performance in terms of both accuracy and robustness.
Book Synopsis A Hybrid Implicit-explicit Method for the Les of Compressible Flows on Unstructured Grids by : Mohammad Shoeybi
Download or read book A Hybrid Implicit-explicit Method for the Les of Compressible Flows on Unstructured Grids written by Mohammad Shoeybi and published by . This book was released on 2010 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Explicit Discontinuous Galerkin Method for Parallel Compressible Two-Phase Flow Simulations by : Malte Hoffmann
Download or read book An Explicit Discontinuous Galerkin Method for Parallel Compressible Two-Phase Flow Simulations written by Malte Hoffmann and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Hybrid, Explicit-implicit, Second-order TVD Method on Adaptive Unstructured Grids for Unsteady Compressible Flows by : Farhang Norouzi
Download or read book A Hybrid, Explicit-implicit, Second-order TVD Method on Adaptive Unstructured Grids for Unsteady Compressible Flows written by Farhang Norouzi and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: " This work is devoted to the development of a hybrid, explicit-implicit, scheme for simulation of unsteady compressible flows with shock waves. The proposed scheme is of the second-order accuracy in space and time for both explicit and implicit modes, while satisfying the TVD (Total Variation Diminishing) property. The scheme is designed for simulation of the compressible flows with temporal stiffness. In this situation,the numerical time step of explicit schemes is severely limited by particular conditions in a relatively small part of the computational domain, while the rest of the domain admits much higher time steps. The hybrid scheme is designed to operate in its implicit mode in the small areas causing temporal stiffness, thus allowing to proceed with higher time steps and reduce the computational time. In this study, a new hybridization approach is suggested. On its basis, the hybrid scheme is first introduced for hyperbolic conservation laws in one dimension. In order to satisfy the TVD property and obtain monotone solutions in the presence ofdiscontinuities, TVD limiters are applied to both spatial and temporal reconstructions. The second-order accuracy in time for the implicit mode, which is the main distinction of the proposed hybrid scheme in comparison with the existing methods, is achieved through a reconstruction of the solution in time. To make the reconstruction TVD preserving, a novel time limiter is derived. The stability condition and the relation to the hybridization factor of the new scheme are obtained. Moreover, the relationship of the proposed scheme with another existing hybrid method is revealed and analyzed. A set of one-dimensional test problems is used to demonstrate the accuracy and efficiency of the new hybrid scheme as well as to show its advantagesin comparison with the existing hybrid schemes. For two-dimensional problems, the hybrid scheme is generalized for the Euler and Navier-Stokes equations on unstructured grids. Similar to one-dimensional problems, reconstructions in space and time are applied with the corresponding TVD limiters. The newly proposed time limiter of the hybrid scheme is further generalized for unstructured grids. The non-linear system of discretized equations is solved using the Lower-Upper-Symmetric-Gauss-Seidel (LU-SGS) approximate factorization method for unstructured grids. In order to eliminate the factorization and linearization errors, internal iterations are introduced at each time step. The lower and upper matrices in the LU-SGS scheme are formed via reordering of grid nodes at each time step. In addition, local transient grid adaptation is applied near solution peculiarities, such as shock waves and contact surfaces. Viscous terms of the Navier-Stokes equations are also approximated with the second order of accuracy both in space and time in both explicit and implicit modes. The new hybrid scheme is applied to a number of demonstrative problems chosen to represent typical classes of gasdynamic problems with specific source of stiffness. The numerical results demonstrate the ability of the proposed hybrid scheme to produce the same accuracy as the purely explicit scheme (the well-known MUSCLHancock scheme), while reducing the computational time." --
Book Synopsis Parallel Implementation of the Discontinuous Galerkin Method by : Abdalkader Baggag
Download or read book Parallel Implementation of the Discontinuous Galerkin Method written by Abdalkader Baggag and published by . This book was released on 1999 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "This paper describes a parallel implementation of the discontinuous Galerkin method. Discontinuous Galerkin is a spatially compact method that retains its accuracy and robustness on non-smooth unstructured grids and is well suited for time dependent simulations. Several parallelization approaches are studied and evaluated. The most natural and symmetric of the approaches has been implemented in an object-oriented code used to simulate aeroacoustic scattering. The parallel implementation is MPI-based and has been tested on various parallel platforms such as the SGI Origin, IBM SP2, and clusters of SGI and Sun workstations. The scalability results presented for the SGI Origin show slightly superlinear speedup on a fixed-size problem due to cache effects."
Book Synopsis A Discontinuous Galerkin Method for the Solution of Compressible Flows by : Cristian Biotto
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:
Book Synopsis A Multi-resolution Discontinuous Galerkin Method for Unsteady Compressible Flows by : Andrew Brian Shelton
Download or read book A Multi-resolution Discontinuous Galerkin Method for Unsteady Compressible Flows written by Andrew Brian Shelton and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The issue of local scale and smoothness presents a crucial and daunting challenge for numerical simulation methods in fluid dynamics. Yet in the interests of both accuracy and economy, how can one devise a general technique that efficiently resolves flow features of consequence and discriminates against others which are either ``negligible' or amenable to ``universal' modeling? This is particularly difficult because geometries of engineering interest are complex and multi-dimensional, precluding a priori knowledge of the flowfield. To address this challenge, the current work employs wavelet theory for the local scale decomposition of functions, which provides a natural mechanism for the adaptive compression of data. The resulting technique is known as the Multi-Resolution Discontinuous Galerkin (MRDG) method.
