Towards an Efficient and Robust High Order Accurate Flow Solver for Viscous Compressible Flows PDF Download
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Author: Sachin Premasuthan
Publisher:
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Category :
Languages : en
Pages :
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Book Description
Despite the advance in CFD over the past few decades, the field of high-order methods for unstructured grids has not yet reached the level of maturity required to solve real flow problems on complicated geometries. The present thesis work makes an effort towards the realization of a flow solver that is high-order accurate but also efficient, robust and geometrically flexible at the same time. The approach to high-order spatial discretization is based on the Spectral Difference (SD) method for unstructured quadrilateral meshes. High-order (quadratic and cubic) representation is used for curved boundary surfaces. Due to their slow convergence rates with standard explicit time-stepping schemes, the use of high order schemes becomes viable only when there is some kind of convergence acceleration technique used. Towards this end, the multi-order (p-multigrid) method and Implicit time-stepping are implemented, and significant convergence acceleration is achieved for both steady and unsteady flow problems. Another significant challenge with using high-order methods is their inability to handle flow discontinuities. An artificial viscosity based approach is designed and implemented to enable computation of flows with shocks. Adaptive mesh and order refinement have great potential in reducing the computational effort required to reach a specified level of accuracy, particularly in the context of high-order formulations. The capability for adaptive mesh and order refinement is enabled using mortar elements to handle non-conforming solution approximations at the cell interfaces. The flow solver is tested, validated and applied to a variety of flow problems. The current work also demonstrates the effectiveness of computational tools such as convergence acceleration, shock-capturing and adaptive refinement, for enhancing the efficiency and robustness of high order flow computations.
Author: Sachin Premasuthan
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Despite the advance in CFD over the past few decades, the field of high-order methods for unstructured grids has not yet reached the level of maturity required to solve real flow problems on complicated geometries. The present thesis work makes an effort towards the realization of a flow solver that is high-order accurate but also efficient, robust and geometrically flexible at the same time. The approach to high-order spatial discretization is based on the Spectral Difference (SD) method for unstructured quadrilateral meshes. High-order (quadratic and cubic) representation is used for curved boundary surfaces. Due to their slow convergence rates with standard explicit time-stepping schemes, the use of high order schemes becomes viable only when there is some kind of convergence acceleration technique used. Towards this end, the multi-order (p-multigrid) method and Implicit time-stepping are implemented, and significant convergence acceleration is achieved for both steady and unsteady flow problems. Another significant challenge with using high-order methods is their inability to handle flow discontinuities. An artificial viscosity based approach is designed and implemented to enable computation of flows with shocks. Adaptive mesh and order refinement have great potential in reducing the computational effort required to reach a specified level of accuracy, particularly in the context of high-order formulations. The capability for adaptive mesh and order refinement is enabled using mortar elements to handle non-conforming solution approximations at the cell interfaces. The flow solver is tested, validated and applied to a variety of flow problems. The current work also demonstrates the effectiveness of computational tools such as convergence acceleration, shock-capturing and adaptive refinement, for enhancing the efficiency and robustness of high order flow computations.
Author: Mostafa Javadzadeh Moghtader
Publisher:
ISBN:
Category :
Languages : en
Pages : 125
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Book Description
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.
Author: Zhi Jian Wang
Publisher: World Scientific
ISBN: 9814464694
Category : Science
Languages : en
Pages : 471
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Book Description
This book consists of important contributions by world-renowned experts on adaptive high-order methods in computational fluid dynamics (CFD). It covers several widely used, and still intensively researched methods, including the discontinuous Galerkin, residual distribution, finite volume, differential quadrature, spectral volume, spectral difference, PNPM, and correction procedure via reconstruction methods. The main focus is applications in aerospace engineering, but the book should also be useful in many other engineering disciplines including mechanical, chemical and electrical engineering. Since many of these methods are still evolving, the book will be an excellent reference for researchers and graduate students to gain an understanding of the state of the art and remaining challenges in high-order CFD methods.
Author:
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Category :
Languages : en
Pages :
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High-order accurate methods have the potential to dramatically reduce the computational time needed for aerodynamics simulations. This thesis studies the discretization and efficient convergence to steady state of the high-order accurate finite-volume method applied to the simplified problem of inviscid and laminar viscous two-dimensional flow equations. Each of the three manuscript chapters addresses a specific problem or limitation previously experienced with these schemes. The first manuscript addresses the absence of a method to maintain monotonicity of the solution at discontinuities while maintaining high-order accuracy in smooth regions. To resolve this, a slope limiter is carefully developed which meets these requirements while also maintaining the good convergence properties and computational efficiency of the least-squares reconstruction scheme. The second manuscript addresses the relatively poor convergence properties of Newton-GMRES methods applied to high-order accurate schemes. The globalization of the Newton method is improved through the use of an adaptive local timestep and of a line search algorithm. The poor convergence of the linear solver is improved through the efficient assembly of the exact flux Jacobian for use in preconditioning and to eliminate the additional residual evaluations needed by a matrix-free method. The third manuscript extends the discretization method to the viscous fluxes and boundary conditions. The discretization is demonstrated to achieve the expected order of accuracy. The fourth-order scheme is also shown to be more computationally efficient than the second-order scheme at achieving grid-converged values of drag for two-dimensional laminar flow over an airfoil.
Author: Suvanjan Bhattacharyya
Publisher: Springer Nature
ISBN: 9811962707
Category : Science
Languages : en
Pages : 628
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Book Description
This book presents the select proceedings of the 48th National Conference on Fluid Mechanics and Fluid Power (FMFP 2021) held at BITS Pilani in December 2021. It covers the topics such as fluid mechanics, measurement techniques in fluid flows, computational fluid dynamics, instability, transition and turbulence, fluid‐structure interaction, multiphase flows, micro- and nanoscale transport, bio-fluid mechanics, aerodynamics, turbomachinery, propulsion and power. The book will be useful for researchers and professionals interested in the broad field of mechanics.
Author: Marie Odile Bristeau
Publisher: Notes on Numerical Fluid Mechanics and Multidisciplinary Design
ISBN:
Category : Computers
Languages : en
Pages : 378
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Book Description
"Contributions to the GAMM Workshop on Numerical Simulation of Compressible Navier-Stokes Flows organized by INRIA in December 1985 [in Nice, France]"--P. 4 of cover.
Author: Timothy J. Barth
Publisher: Springer Science & Business Media
ISBN: 366203882X
Category : Mathematics
Languages : en
Pages : 594
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Book Description
The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining chal lenges facing the field of computational fluid dynamics. In structural me chanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the com putation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order ac curacy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence sug gests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Cen ter. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18,1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25,1998 at the NASA Ames Research Center in the United States.
Author: Gunilla Kreiss
Publisher: Springer Science & Business Media
ISBN: 3642117953
Category : Mathematics
Languages : en
Pages : 900
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Author: National Research Council
Publisher: National Academies Press
ISBN: 0309065372
Category : Science
Languages : en
Pages : 1039
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Book Description
The Twenty-Second Symposium on Naval Hydrodynamics was held in Washington, D.C., from August 9-14, 1998. It coincided with the 100th anniversary of the David Taylor Model Basin. This international symposium was organized jointly by the Office of Naval Research (Mechanics and Energy Conversion S&T Division), the National Research Council (Naval Studies Board), and the Naval Surface Warfare Center, Carderock Division (David Taylor Model Basin). This biennial symposium promotes the technical exchange of naval research developments of common interest to all the countries of the world. The forum encourages both formal and informal discussion of the presented papers, and the occasion provides an opportunity for direct communication between international peers.
Author: D. A. Caughey
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 664
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Book Description
Frontiers of Computational Fluid Dynamics 1994 Edited by D. A. Caughey Cornell University, Ithaca, New York, USA M. M. Hafez University of California, Davis, USA This book presents the current state of the art of Computational Fluid Dynamics (CFD). It is dedicated to Antony Jameson, in appreciation of his contributions to this field. Recent achievements in the various disciplines which contribute to CFD are discussed, including grid generation and adaptation, finite-volume and finite-element methods, multi-dimensional upwind schemes and multigrid convergence acceleration techniques. Simulations of inviscid and viscous flows are covered for both compressible and incompressible flows, with emphasis on flow control or optimal shape design in fluid mechanics. The book consists of 29 contributed chapters, which are grouped in six sections, covering: Design and Optimization of Aerodynamic Configurations Unstructured Grid Techniques Solution of the Euler Equations Solution of the Navier—Stokes Equations Applications in Aerodynamics Applications in Hydrodynamics Throughout the book, various approaches are critically examined, and new directions toward more efficient and robust tools of analysis and design, to meet the high expectations facing CFD, are emphasized.
