Stable Low-dissipation Schemes for Turbulent Compressible Flows PDF Download
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Author: Pramod Kumar V. Subbareddy
Publisher:
ISBN:
Category :
Languages : en
Pages : 214
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Author: Pramod Kumar V. Subbareddy
Publisher:
ISBN:
Category :
Languages : en
Pages : 214
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Author: Aleix Baez Vidal
Publisher:
ISBN:
Category :
Languages : en
Pages : 166
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The present thesis investigates how explicit filters can be useful in numerical simulations of turbulent, compressible flow with symmetry preserving discretizations. Such explicit filters provide stability to simulations with shocks, provide stability to low-dissipation schemes on smooth flows and are used as test filters in LES turbulence models such as the Variational Multi-Scale eddy viscosity model or regularization models. The present thesis is a step forward in four main aspects. First, a comparative study of the Symmetry Preserving schemes for compressible flow is conducted. It shows that Rozema's scheme is more stable and accurate than the other schemes compiled fromthe literature. A sligh tmodification on this scheme is presented and shown to be more stable and accurate in unstructured meshes, but lesser accurate and stable in uniform, structured meshes. Second, a theoretical analysis of the properties of filters for CFD and their consequences on the derivation of the LES equations is conducted. The analysis shows how the diffusive properties of filters are necessary for the consistency of the model. Third, a study of explicit filtering on discrete variables identifies the necessary constraints for the fulfillment of the discrete counterpart of the filter properties. It puts emphases on the different possibilities when requiring the filters to be diffusive. After it, a new family of filters has been derived and tested in newly developed tests that allow the independent study of each property. And last, an algorithm to couple adaptive filtering with time integration is reported and tested on the 2D Isentropic Vortex and on the Taylor-Green vortex problem. Filtering is shown to enhance stability at the cost of locally adding diffusion. This saves the simulations from being diffusive everywhere. The resulting methodology is also shown to be potentially useful for shock-capturing purposes with the simulation of a shock-tube in a fully unstructured mesh.
Author: Nima Tajallipour
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Roger Peyret
Publisher: Springer
ISBN: 3709125901
Category : Science
Languages : en
Pages : 320
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This book collects the lecture notes concerning the IUTAM School on Advanced Turbulent Flow Computations held at CISM in Udine September 7–11, 1998. The course was intended for scientists, engineers and post-graduate students interested in the application of advanced numerical techniques for simulating turbulent flows. The topic comprises two closely connected main subjects: modelling and computation, mesh pionts necessary to simulate complex turbulent flow.
Author: Riccardo Bonazza
Publisher: Springer
ISBN: 331916838X
Category : Science
Languages : en
Pages : 822
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This proceedings present the results of the 29th International Symposium on Shock Waves (ISSW29) which was held in Madison, Wisconsin, U.S.A., from July 14 to July 19, 2013. It was organized by the Wisconsin Shock Tube Laboratory, which is part of the College of Engineering of the University of Wisconsin-Madison. The ISSW29 focused on the following areas: Blast Waves, Chemically Reactive Flows, Detonation and Combustion, Facilities, Flow Visualization, Hypersonic Flow, Ignition, Impact and Compaction, Industrial Applications, Magnetohydrodynamics, Medical and Biological Applications, Nozzle Flow, Numerical Methods, Plasmas, Propulsion, Richtmyer-Meshkov Instability, Shock-Boundary Layer Interaction, Shock Propagation and Reflection, Shock Vortex Interaction, Shock Waves in Condensed Matter, Shock Waves in Multiphase Flow, as well as Shock Waves in Rarefield Flow. The two Volumes contain the papers presented at the symposium and serve as a reference for the participants of the ISSW 29 and individuals interested in these fields.
Author: D. Drikakis
Publisher: Springer Science & Business Media
ISBN: 354026454X
Category : Science
Languages : en
Pages : 623
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The study of incompressible ?ows is vital to many areas of science and te- nology. This includes most of the ?uid dynamics that one ?nds in everyday life from the ?ow of air in a room to most weather phenomena. Inundertakingthesimulationofincompressible?uid?ows,oneoftentakes many issues for granted. As these ?ows become more realistic, the problems encountered become more vexing from a computational point-of-view. These range from the benign to the profound. At once, one must contend with the basic character of incompressible ?ows where sound waves have been analytically removed from the ?ow. As a consequence vortical ?ows have been analytically “preconditioned,” but the ?ow has a certain non-physical character (sound waves of in?nite velocity). At low speeds the ?ow will be deterministic and ordered, i.e., laminar. Laminar ?ows are governed by a balance between the inertial and viscous forces in the ?ow that provides the stability. Flows are often characterized by a dimensionless number known as the Reynolds number, which is the ratio of inertial to viscous forces in a ?ow. Laminar ?ows correspond to smaller Reynolds numbers. Even though laminar ?ows are organized in an orderly manner, the ?ows may exhibit instabilities and bifurcation phenomena which may eventually lead to transition and turbulence. Numerical modelling of suchphenomenarequireshighaccuracyandmostimportantlytogaingreater insight into the relationship of the numerical methods with the ?ow physics.
Author: Pablo Fernández
Publisher:
ISBN:
Category :
Languages : en
Pages : 212
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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.
Author: Robert Moser
Publisher: Elsevier
ISBN: 032399833X
Category : Science
Languages : en
Pages : 568
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Numerical Methods in Turbulence Simulation provides detailed specifications of the numerical methods needed to solve important problems in turbulence simulation. Numerical simulation of turbulent fluid flows is challenging because of the range of space and time scales that must be represented. This book provides explanations of the numerical error and stability characteristics of numerical techniques, along with treatments of the additional numerical challenges that arise in large eddy simulations. Chapters are written as tutorials by experts in the field, covering specific both contexts and applications. Three classes of turbulent flow are addressed, including incompressible, compressible and reactive, with a wide range of the best numerical practices covered. A thorough introduction to the numerical methods is provided for those without a background in turbulence, as is everything needed for a thorough understanding of the fundamental equations. The small scales that must be resolved are generally not localized around some distinct small-scale feature, but instead are distributed throughout a volume. These characteristics put particular strain on the numerical methods used to simulate turbulent flows. Includes a detailed review of the numerical approximation issues that impact the simulation of turbulence Provides a range of examples of large eddy simulation techniques Discusses the challenges posed by boundary conditions in turbulence simulation and provides approaches to addressing them
Author: Zeyu Bai
Publisher:
ISBN:
Category :
Languages : en
Pages : 288
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Numerical simulations of multi-scale flow problems such as hypersonic boundary layer transition, turbulent flows, computational aeroacoustics and other flow problems with complex physics require high-order methods with high spectral resolutions. For instance, the receptivity mechanisms in the hypersonic boundary layer are the resonant interactions between forcing waves and boundary-layer waves, and the complex wave interactions are difficult to be accurately predicted by conventional low-order numerical methods. High-order methods, which are robust and accurate in resolving a wide range of time and length scales, are required. The objective of this dissertation is to develop and analyze new very high-order numerical methods with spectral-like resolution for flow simulations on structured grids, with focus on smooth flow problems involving multiple scales. These numerical methods include: the multi-layer compact (MLC) scheme, the directional multi-layer compact (DMLC) scheme, and the least square multi-layer compact (LSMLC) scheme. In the first place, a new upwind multi-layer compact (MLC) scheme up to seventh order is derived in a finite difference framework. By using the 'multi-layer' idea, which introduces first derivatives into the MLC schemes and approximates the second derivatives, the resolution of the MLC schemes can be significantly improved within a compact grid stencil. The auxiliary equations are introduced, and they are the only nontrivial equations. The original equation requires no approximation which contributes to good computational efficiency. In addition, the upwind MLC schemes are derived on centered stencils with adjustable parameters to control the dissipation. Fourier analysis is performed to show that the new MLC schemes have very small dissipation and dispersion in a wide range of wavenumbers in both one and two-dimensional cases, and the anisotropic error is much smaller than conventional finite difference methods in the two-dimensional case. Comparison with discontinuous-Galerkin methods is performed with Fourier analysis as well. Furthermore, stability analysis with matrix method shows that high-order boundary closure schemes are stable because of compactness of the stencils. The accuracies and rates of convergence of the new schemes are validated by numerical experiments of the linear advection equation, the nonlinear Euler equations, and the Navier-Stokes equations in both one and two-dimensional settings. The numerical results show that good computational efficiency, very high-order accuracies, and high spectral resolutions especially on coarse meshes can be attained with the MLC scheme. On the other hand, even though the MLC scheme is promising in most test cases, it shows weak numerical instabilities for a small range of wavenumbers when it is applied to multi-dimensional flows, which are mainly triggered by the inconsistency between its one and two-dimensional formulations. The instability could lead to divergence in long-time multi-dimensional simulations. Moreover, the cross-derivative approximation in the MLC scheme requires an ad-hoc selection of supporting grid points, and the cross-derivative approximation is relatively inefficient for very high-order cases. To address the remaining challenges of the MLC scheme and achieve better performance for multi-dimensional flow simulations, another two new schemes are developed - the directional multi-layer compact (DMLC) scheme, and the least square multi-layer compact (LSMLC) scheme. In the second place, a new upwind directional multi-layer compact (DMLC) scheme is developed for multi-dimensional simulations. The main idea of the DMLC scheme is to introduce auxiliary equation for cross derivative in multi-dimensional cases. Consequently, the spatial discretization can be fulfilled along each dimension independently. With this directional discretization technique, the one-dimensional formulation of the MLC scheme can be applied to all spatial derivatives in a multi-dimensional governing equation. Therefore, the DMLC scheme overcomes the inconsistency between one and two-dimensional formulations of the MLC scheme, and it also avoids the ad-hoc cross-derivative approximations. Two-dimensional Fourier analysis demonstrates that all modes of the DMLC scheme are stable in the full range of wavenumbers, and it has better spectral resolution and smaller anisotropic error than the MLC scheme. Stability analysis with matrix method indicates that stable boundary closure schemes are much easier to be obtained in the DMLC scheme. Numerical tests in the linear advection equation and the nonlinear Euler equations validate that the DMLC scheme are more accurate and require less CPU time than the MLC scheme on the same mesh. In particular, the long-time simulation results reveal that the DMLC scheme is always stable for both periodic and non-periodic boundary conditions in two-dimensional cases. In the third place, a new upwind least square multi-layer compact (LSMLC) scheme is developed for multi-dimensional simulations. The main idea of the LSMLC scheme is using the weighted least square approximation to redesign the two-dimensional formulation for cross derivatives. It avoids the ad-hoc selection of grid points in the MLC scheme. Meanwhile, the two-dimensional upwind scheme can be derived by introducing upwind correction into the weight function. The upwind factor can adjust the dissipation and stability of the LSMLC scheme. Lagrange multiplier is used to ensure that the LSMLC scheme satisfies both the consistency constraint at the base point and the one-dimensional constraint from the MLC scheme. The LSMLC scheme does not increase computational cost on structured meshes, and can be implemented in the same way as the MLC scheme. A parametric study based on two-dimensional Fourier analysis shows that the truncated Gaussian distribution (TGD) weight function leads to better LSMLC scheme among other weight functions because it removes the numerical instability and maintain small dissipations. The LSMLC scheme has larger dissipation than the MLC scheme, and shows similar spectral resolution. Stability analysis with matrix method indicates that a combination of an interior LSMLC scheme and MLC boundary closure schemes can improve the boundary stability while maintaining small dissipation. Numerical tests in the linear advection equation and the nonlinear Euler equations validate that the LSMLC scheme produces slightly larger errors compared with MLC scheme. The long-time simulation results reveal that the LSMLC scheme is always stable for both periodic and non-periodic boundary conditions in two-dimensional cases. Overall, the new very high-order multi-layer compact finite difference methods have the properties of simple formulations, high-order accuracies, spectral-like resolutions, and compact stencils, and they are suitable for accurate simulation of smooth multi-scale flows with complex physics. Among the three schemes developed in this dissertation, the DMLC scheme is always the best choice for multi-dimensional simulations because it shows comprehensive improvements from the MLC scheme with consistent stability, higher accuracy and spectral resolution, and better computational efficiency. The LSMLC scheme is also appropriate considering it has consistent stability and it is easy to be implemented.
Author: J. S. B. Gajjar
Publisher:
ISBN:
Category :
Languages : en
Pages : 42
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