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High Order Numerical Methods For Unstructured Grids And Sliding Mesh
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Book Synopsis High-order Numerical Methods for Unstructured Grids and Sliding Mesh by : Gonzalo Sáez Mischlich
Download or read book High-order Numerical Methods for Unstructured Grids and Sliding Mesh written by Gonzalo Sáez Mischlich and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: High-order numerical methods have proven to be an essential tool to improve the accuracy of simulations involving turbulent flows through the solution of conservation laws. Such flows appear in a wide variety of industrial applications and its correct prediction is crucial to reduce the power consumption and improve the efficiency of these processes. The present study implements and analyzes different types of high-order spatial discretization schemes for unstructured grids to assess and quantify their accuracy in simulations of turbulent flows. In particular, high-order Finite Volume methods (FVM) based on least squares and fully constrained deconvolution operators are considered and their accuracy is evaluated in a variety of linear and non-linear test cases and throughanalytical analysis. Special emphasis is placed on the comparison of formally second-order and high-order FVM, showing that the former can over-perform the latter in terms of accuracy and computational performance in under-resolved configurations. High-order Spectral Element methods (SEM), including Spectral Difference (SD) and Flux Reconstruction (FR), are compared in different linear and non-linear configurations. Furthermore, a SD GPU-based solver (based on the open-source PyFR solver) is developed and its performance with respect to other state of the art CPU-based solvers will be discussed, showing that the developed GPU-based solver outperforms other state of the art CPU-based solvers in terms of performance-per-euro and performance-per-watt. The accuracy and behavior of SEM under aliasing are assessed in linear test cases using analytical tools. The use of grids with high-order cells, which allow to better describe the surfaces of interests of a given simulation, in combination with SEM is also analyzed. The latter analysis demonstrates that special care must be taken to ensure appropriate numerical accuracy when utilizing meshes with such elements. This document also presents the development and the analysis of the Spectral Difference Raviart-Thomas (SDRT) method for two and three-dimensional tensor product and simplex elements. This method is equivalent to the SD formulation for tensor product elements and it can be considered as a natural extension of the SD formulation for simplex elements. Additionally, a new family of FR methods, which is equivalent to the SDRT method under certain circumstances, is described. All these developments were implemented in the open-source PyFR solver and are compatible with CPU and GPU architectures. In the context of high-order simulations of turbulent flows found in rotor-stator interaction test cases, a sliding mesh method (which involves non-conformal grids and mesh motion) specifically tailored for massivelyparallel simulations is implemented within a CPU-based solver. The developed method is compatible with second-order and high-order FVM and SEM. Grid movement, needed to simulate rotor-stator test cases due to the relative movement of each domain zone, is treated using the Arbitrary-Lagrangian-Eulerian (ALE) formulation. The analysis of such formulation depicts its important influence on the numerical accuracy and stability of numerical simulations with mesh motion. Moreover, specific non-conformal discretization methodscompatible with second-order and high-order FVM and SEM are developed and their accuracy is assessed on different non-linear test cases. The parallel scalability of the method is assessed with up to 11000 cores, proving appropriate computational efficiency. The accuracy of the implementation is assessed through a set of linear and non-linear test cases. Preliminary results of the turbulent flow around a DGEN 380 fan stage in an under-resolved configuration are shown and compared to available experimental data.
Book Synopsis Very High-order Methods for 3D Arbitrary Unstructured Grids by : Panagiotis Tsoutsanis
Download or read book Very High-order Methods for 3D Arbitrary Unstructured Grids written by Panagiotis Tsoutsanis and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding the motion of fluids is crucial for the development and analysis of new designsand processes in science and engineering. Unstructured meshes are used in this contextsince they allow the analysis of the behaviour of complicated geometries and configurationsthat characterise the designs of engineering structures today. The existing numerical methodsdeveloped for unstructured meshes suffer from poor computational efficiency, and their applicabilityis not universal for any type of unstructured meshes. High-resolution high-orderaccurate numerical methods are required for obtaining a reasonable guarantee of physicallymeaningful results and to be able to accurately resolve complicated flow phenomena thatoccur in a number of processes, such as resolving turbulent flows, for direct numerical simulationof Navier-Stokes equations, acoustics etc. The aim of this research project is to establish and implement universal, high-resolution, veryhigh-order, non-oscillatory finite-volume methods for 3D unstructured meshes. A new classof linear and WENO schemes of very high-order of accuracy (5th) has been developed. Thekey element of this approach is a high-order reconstruction process that can be applied to anytype of meshes. The linear schemes which are suited for problems with smooth solutions, employ a single reconstruction polynomial obtained from a close spatial proximity. In theWENO schemes the reconstruction polynomials, arising from different topological regions, are non-linearly combined to provide high-order of accuracy and shock capturing features. The performance of the developed schemes in terms of accuracy, non-oscillatory behaviourand flexibility to handle any type of 3D unstructured meshes has been assessed in a series oftest problems. The linear and WENO schemes presented achieve very high-order of accuracy(5th). This is the first class of WENO schemes in the finite volume context that possess highorderof accuracy and robust non-oscillatory behaviour for any type of unstructured meshes. The schemes have been employed in a newly developed 3D unstructured solver (UCNS3D). UCNS3D utilises unstructured grids consisted of tetrahedrals, pyramids, prisms and hexahedralelements and has been parallelised using the MPI framework. The high parallel efficiencyachieved enables the large scale computations required for the analysis of new designs andprocesses in science and engineering.
Book Synopsis Efficient Implementation of High-Order Accurate Numerical Methods on Unstructured Grids by : Wanai Li
Download or read book Efficient Implementation of High-Order Accurate Numerical Methods on Unstructured Grids written by Wanai Li and published by . This book was released on 2014-06-30 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mesh Methods by : Viktor A. Rukavishnikov
Download or read book Mesh Methods written by Viktor A. Rukavishnikov and published by MDPI. This book was released on 2021-03-29 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models of various natural processes are described by differential equations, systems of partial differential equations and integral equations. In most cases, the exact solution to such problems cannot be determined; therefore, one has to use grid methods to calculate an approximate solution using high-performance computing systems. These methods include the finite element method, the finite difference method, the finite volume method and combined methods. In this Special Issue, we bring to your attention works on theoretical studies of grid methods for approximation, stability and convergence, as well as the results of numerical experiments confirming the effectiveness of the developed methods. Of particular interest are new methods for solving boundary value problems with singularities, the complex geometry of the domain boundary and nonlinear equations. A part of the articles is devoted to the analysis of numerical methods developed for calculating mathematical models in various fields of applied science and engineering applications. As a rule, the ideas of symmetry are present in the design schemes and make the process harmonious and efficient.
Book Synopsis Very High-order Methods for 3D Arbitrary Unstructured Grids by : Panagiotis Tsoutsanis
Download or read book Very High-order Methods for 3D Arbitrary Unstructured Grids written by Panagiotis Tsoutsanis and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding the motion of fluids is crucial for the development and analysis of new designsand processes in science and engineering. Unstructured meshes are used in this contextsince they allow the analysis of the behaviour of complicated geometries and configurationsthat characterise the designs of engineering structures today. The existing numerical methodsdeveloped for unstructured meshes suffer from poor computational efficiency, and their applicabilityis not universal for any type of unstructured meshes. High-resolution high-orderaccurate numerical methods are required for obtaining a reasonable guarantee of physicallymeaningful results and to be able to accurately resolve complicated flow phenomena thatoccur in a number of processes, such as resolving turbulent flows, for direct numerical simulationof Navier-Stokes equations, acoustics etc. The aim of this research project is to establish and implement universal, high-resolution, veryhigh-order, non-oscillatory finite-volume methods for 3D unstructured meshes. A new classof linear and WENO schemes of very high-order of accuracy (5th) has been developed. Thekey element of this approach is a high-order reconstruction process that can be applied to anytype of meshes. The linear schemes which are suited for problems with smooth solutions, employ a single reconstruction polynomial obtained from a close spatial proximity. In theWENO schemes the reconstruction polynomials, arising from different topological regions, are non-linearly combined to provide high-order of accuracy and shock capturing features. The performance of the developed schemes in terms of accuracy, non-oscillatory behaviourand flexibility to handle any type of 3D unstructured meshes has been assessed in a series oftest problems. The linear and WENO schemes presented achieve very high-order of accuracy(5th). This is the first class of WENO schemes in the finite volume context that possess highorderof accuracy and robust non-oscillatory behaviour for any type of unstructured meshes. The schemes have been employed in a newly developed 3D unstructured solver (UCNS3D). UCNS3D utilises unstructured grids consisted of tetrahedrals, pyramids, prisms and hexahedralelements and has been parallelised using the MPI framework. The high parallel efficiencyachieved enables the large scale computations required for the analysis of new designs andprocesses in science and engineering.
Book Synopsis Handbook of Grid Generation by : Joe F. Thompson
Download or read book Handbook of Grid Generation written by Joe F. Thompson and published by CRC Press. This book was released on 1998-12-29 with total page 1136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Grid Generation addresses the use of grids (meshes) in the numerical solutions of partial differential equations by finite elements, finite volume, finite differences, and boundary elements. Four parts divide the chapters: structured grids, unstructured girds, surface definition, and adaption/quality. An introduction to each section provides a roadmap through the material. This handbook covers: Fundamental concepts and approaches Grid generation process Essential mathematical elements from tensor analysis and differential geometry, particularly relevant to curves and surfaces Cells of any shape - Cartesian, structured curvilinear coordinates, unstructured tetrahedra, unstructured hexahedra, or various combinations Separate grids overlaid on one another, communicating data through interpolation Moving boundaries and internal interfaces in the field Resolving gradients and controlling solution error Grid generation codes, both commercial and freeware, as well as representative and illustrative grid configurations Handbook of Grid Generation contains 37 chapters as well as contributions from more than 100 experts from around the world, comprehensively evaluating this expanding field and providing a fundamental orientation for practitioners.
Book Synopsis Fluid Mechanics and Fluid Power (Vol. 3) by : Suvanjan Bhattacharyya
Download or read book Fluid Mechanics and Fluid Power (Vol. 3) written by Suvanjan Bhattacharyya and published by Springer Nature. This book was released on 2023-04-17 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis On Essentially Non-oscillatory Schemes on Unstructured Meshes: Analysis and Implementation by : Institute for Computer Applications in Science and Engineering
Download or read book On Essentially Non-oscillatory Schemes on Unstructured Meshes: Analysis and Implementation written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1992 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Optimization-based Method for High Order Gradient Calculation on Unstructured Meshes by :
Download or read book An Optimization-based Method for High Order Gradient Calculation on Unstructured Meshes written by and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A new implicit and compact optimization-based method is presented for high order derivative calculation for finite-volume numerical method on unstructured meshes. Highorder approaches to gradient calculation are often based on variants of the Least-Squares (L-S) method, an explicit method that requires a stencil large enough to accommodate the necessary variable information to calculate the derivatives. The new scheme proposed here is applicable for an arbitrary order of accuracy (demonstrated here up to 3rd order), and uses just the first level of face neighbors to compute all derivatives, thus reducing stencil size and avoiding stiffness in the calculation matrix. Preliminary results for a static variable field example and solution of a simple scalar transport (advection) equation show that the proposed method is able to deliver numerical accuracy equivalent to (or better than) the nominal order of accuracy for both 2nd and 3rd order schemes in the presence of a smoothly distributed variable field (i.e., in the absence of discontinuities). This new Optimization-based Gradient REconstruction (herein denoted OGRE) scheme produces, for the simple scalar transport test case, lower error and demands less computational time (for a given level of required precision) for a 3rd order scheme when compared to an equivalent L-S approach on a two-dimensional framework. For three-dimensional simulations, where the L-S scheme fails to obtain convergence without the help of limiters, the new scheme obtains stable convergence and also produces lower error solution when compared to a third order MUSCL scheme. Furthermore, spectral analysis of results from the advection equation shows that the new scheme is better able to accurately resolve high wave number modes, which demonstrates its potential to better solve problems presenting a wide spectrum of wavelengths, for example unsteady turbulent flow simulations.
Book Synopsis Recent Advances in CFD for Wind and Tidal Offshore Turbines by : Esteban Ferrer
Download or read book Recent Advances in CFD for Wind and Tidal Offshore Turbines written by Esteban Ferrer and published by Springer. This book was released on 2019-02-06 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents novel Computational Fluid Dynamics (CFD) techniques to compute offshore wind and tidal applications. The papers in this volume are based on a mini-symposium held at ECCOMAS 2018. Computational fluid dynamics (CFD) techniques are regarded as the main design tool to explore the new engineering challenges presented by offshore wind and tidal turbines for energy generation. The difficulty and costs of undertaking experimental tests in offshore environments have increased the interest in CFD which is used to design appropriate turbines and blades, understand fluid flow physical phenomena associated with offshore environments, predict power production or characterise offshore environments amongst other topics.
Book Synopsis Development of a High-Order Finite-Volume Method for Unstructured Meshes by : Sean McDonald
Download or read book Development of a High-Order Finite-Volume Method for Unstructured Meshes written by Sean McDonald and published by . This book was released on 2011 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of high-order solution methods remain a very active field of research in Computational Fluid Dynamics (CFD). These types of schemes have the potential to reduce the computational cost necessary to compute solutions to a desired level of accuracy. The goal of this thesis has been to develop a high-order Central Essentially Non Oscillatory (CENO) finite volume scheme for multi-block unstructured meshes. In particular, solutions to the compressible, inviscid Euler equations are considered. The CENO method achieves a high-order spatial reconstruction based on the k-exact method, combined with hybrid switching to limited piecewise linear reconstruction in non-smooth regions to maintain monotonicity. Additionally, fourth-order Runge-Kutta time marching is applied. The solver described has been validated through a combination of high-order function reconstructions, and solutions to the Euler equations. Cases have been selected to demonstrate high-orders of convergence, the application of the hybrid switching method, and the multi-block techniques which has been implemented.
Book Synopsis Efficient Numerical Methods and Information-Processing Techniques for Modeling Hydro- and Environmental Systems by : Reinhard Hinkelmann
Download or read book Efficient Numerical Methods and Information-Processing Techniques for Modeling Hydro- and Environmental Systems written by Reinhard Hinkelmann and published by Springer Science & Business Media. This book was released on 2006-08-10 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulation models have become indispensable in hydro- and environmental sciences and engineering. This monograph presents a general introduction to numerical simulation in environment water, based on the solution of the equations for groundwater flow and transport processes, for multiphase and multicomponent flow and transport processes in the subsurface as well as for flow and transport processes in surface waters. It displays in detail the state of the art of discretization and stabilization methods (e.g. finite-difference, finite-element, and finite-volume methods), parallel methods, and adaptive methods as well as fast solvers, with particular focus on explaining the interactions of the different methods. The book gives a brief overview of various information-processing techniques and demonstrates the interactions of the numerical methods with the information-processing techniques, in order to achieve efficient numerical simulations for a wide range of applications in environment water.
Book Synopsis Numerical methods for the Navier-Stokes equations by : Friedrich-Karl Hebeker
Download or read book Numerical methods for the Navier-Stokes equations written by Friedrich-Karl Hebeker and published by Vieweg+teubner Verlag. This book was released on 1994 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Sonderforschungsbereich "Reactive Flow, Diffusion and Transport" (SFB 359) at Heidelberg University and the IBM Scientific Center Heidelberg have jointly organized a workshop on "Numerical Methods for the Navier-Stokes Equations". This workshop took place from October 25-28, 1993, at the IBM Scientific Center and was attended by 113 scientists from 13 countries. The scientific program consisted of 12 invited and 34 contributed lectures which dealt with various aspects of the numerical solution of the Navier Stokes equations describing compressible as well as incompressible flows. The main topics were stable and higher-order discretization schemes, discretizations based on non-standard variational formulations, operator splitting methods, multilevel and domain decomposition techniques, a posteriori error control and adaptivity, and implementation issues on parallel computers. These proceedings contain 29 of the contributions to the workshop in alphabetical order. The editors thank the Deutsche Forschungsgemeinschaft (DFG) for its financial support through the SFB 359. They also like to express their gratitude to all persons involved in the organization of the workshop and the preparation of these proceedings. F. K. Hebeker April1994 R. Rannacher G. Wittum v CONTENTS Page M. BERZINS, J. M. WARE: Reliable Finite Volume Methods for Navier-Stokes Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . S. BIKKER, H. GREZA, W. KOSCHEL: Parallel Computing and Multigrid Solution on Adaptive Unstructured Meshes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 . . . . . . . . . . . . . . . . X.-C. CAl, W. D. GROPP, D. E. KEYES, M.D. TIDRIRI: Newton-Krylov-Schwarz Methods in CFD........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 . . . . . . . . . . . . . . . . . . . . H. DANIELS, A. PETERS: PASTIS-3D - A Parallel Finite Element Projection Code for the Time-Dependent Incompressible Navier-Stokes Equations. . . . . . . . . . 31 . . .
Book Synopsis Basic Structured Grid Generation by : M Farrashkhalvat
Download or read book Basic Structured Grid Generation written by M Farrashkhalvat and published by Elsevier. This book was released on 2003-02-11 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element, finite volume and finite difference methods use grids to solve the numerous differential equations that arise in the modelling of physical systems in engineering. Structured grid generation forms an integral part of the solution of these procedures. Basic Structured Grid Generation provides the necessary mathematical foundation required for the successful generation of boundary-conforming grids and will be an important resource for postgraduate and practising engineers.The treatment of structured grid generation starts with basic geometry and tensor analysis before moving on to identify the variety of approaches that can be employed in the generation of structured grids. The book then introduces unstructured grid generation by explaining the basics of Delaunay triangulation and advancing front techniques. A practical, straightforward approach to this complex subject for engineers and students. A key technique for modelling physical systems.
Book Synopsis Moving Mesh Methods for Moving Boundary Problems and Higher Order Partial Differential Equations by : Xiangmin Xu
Download or read book Moving Mesh Methods for Moving Boundary Problems and Higher Order Partial Differential Equations written by Xiangmin Xu and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis studies the moving mesh method and its applications in the numerical solution of moving boundary problems and higher order evolutionary partial differential equations. The concept of equidistribution has played a fundamental role in moving mesh methods. For a given adaptation function, de Boor's algorithm is commonly used for generating equidistributing meshes. The algorithm produces a sequence of meshes upon using piecewise constant interpolation for the adaptation function on the current mesh and generating a new mesh that exactly equidistributes the interpolant. Although the effectiveness of this algorithm was confirmed numerically long ago, the proof for the existence of the limit mesh and the convergence of this algorithm have thus far remained theoretically elusive. These theoretical issues are treated in Chapter 2 of this thesis. Numerical results are also given to illustrate the theoretical findings as well as stopping criteria necessary for the implementation of the algorithm. The use of moving meshes has become a popular technique for improving existing approximation schemes for moving boundary problems. In Chapter 3, we study the relative efficiency and accuracy of various numerical methods for moving boundary problems on moving meshes. A moving mesh front-tracking method based on equidistributing a specially designed adaptation function is proposed for moving boundary problems of implicit type. The resulting numerical method does not require any analytical knowledge of solutions, assumptions on solution profiles or interpolation/extrapolation which are common in other methods in the literature. Some preliminary work for moving mesh front-tracking methods in two dimensions is presented in Chapter 4. Finally, MOVCOL4, a moving mesh collocation code specifically designed for solving general fourth-order evolutionary partial differential equations, is analyzed in Chapter 5.
Book Synopsis Grid Generation Methods by : Vladimir D. Liseikin
Download or read book Grid Generation Methods written by Vladimir D. Liseikin and published by Springer. This book was released on 2017-06-12 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an introduction to methods of grid generation technology in scientific computing. Special attention is given to methods developed by the author for the treatment of singularly-perturbed equations, e.g. in modeling high Reynolds number flows. Functionals of conformality, orthogonality, energy and alignment are discussed.
Book Synopsis Discontinuous Galerkin Methods by : Bernardo Cockburn
Download or read book Discontinuous Galerkin Methods written by Bernardo Cockburn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.
