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.

Download or read book Efficient Implementation of High Order Accurate Numerical Methods on Unstructured Grids written by Wanai Li and published by Springer. This book was released on 2014-05-23 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis focuses on the development of high-order finite volume methods and discontinuous Galerkin methods, and presents possible solutions to a number of important and common problems encountered in high-order methods, such as the shock-capturing strategy and curved boundary treatment, then applies these methods to solve compressible flows.

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.

Download or read book A High Order Finite Volume Method for 3D Elastic Modelling on Unstructured Meshes written by Wensheng Zhang and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this chapter, a new efficient high-order finite volume method for 3D elastic modelling on unstructured meshes is developed. The stencil for the high-order polynomial reconstruction is generated by subdividing the relative coarse tetrahedrons. The reconstruction on the stencil is performed by using cell-averaged quantities represented by the hierarchical orthonormal basis functions. Unlike the traditional high-order finite volume method, the new method has a very local property like the discontinuous Galerkin method. Furthermore, it can be written as an inner-split computational scheme which is beneficial to reducing computational amount. The reconstruction matrix is invertible and remains unchanged for all tetrahedrons, and thus it can be pre-computed and stored before time evolution. These special advantages facilitate the parallelization and high-order computations. The high-order accuracy in time is obtained by the Runge-Kutta method. Numerical computations including a 3D real model with complex topography demonstrate the effectiveness and good adaptability to complex topography.

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.

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.

Download or read book The Finite Volume Method in Computational Fluid Dynamics written by F. Moukalled and published by Springer. This book was released on 2015-08-13 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explores both the theoretical foundation of the Finite Volume Method (FVM) and its applications in Computational Fluid Dynamics (CFD). Readers will discover a thorough explanation of the FVM numerics and algorithms used for the simulation of incompressible and compressible fluid flows, along with a detailed examination of the components needed for the development of a collocated unstructured pressure-based CFD solver. Two particular CFD codes are explored. The first is uFVM, a three-dimensional unstructured pressure-based finite volume academic CFD code, implemented within Matlab. The second is OpenFOAM®, an open source framework used in the development of a range of CFD programs for the simulation of industrial scale flow problems. With over 220 figures, numerous examples and more than one hundred exercise on FVM numerics, programming, and applications, this textbook is suitable for use in an introductory course on the FVM, in an advanced course on numerics, and as a reference for CFD programmers and researchers.

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 ADIGMA A European Initiative on the Development of Adaptive Higher Order Variational Methods for Aerospace Applications written by Norbert Kroll and published by Springer Science & Business Media. This book was released on 2010-09-18 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains results gained from the EU-funded 6th Framework project ADIGMA (Adaptive Higher-order Variational Methods for Aerodynamic Applications in Industry). The goal of ADIGMA was the development and utilization of innovative adaptive higher-order methods for the compressible flow equations enabling reliable, mesh independent numerical solutions for large-scale aerodynamic applications in aircraft industry. The ADIGMA consortium was comprised of 22 organizations which included the main European aircraft manufacturers, the major European research establishments and several universities, all with well proven expertise in Computational Fluid Dynamics (CFD). The book presents an introduction to the project, exhibits partners’ methods and approaches and provides a critical assessment of the newly developed methods for industrial aerodynamic applications. The best numerical strategies for integration as major building blocks for the next generation of industrial flow solvers are identified.

Download or read book Adaptive High order Methods in Computational Fluid Dynamics written by Z. J. Wang and published by World Scientific. This book was released on 2011 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book High Order Methods for Computational Physics written by Timothy J. Barth and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Download or read book Parallel Computational Fluid Dynamics written by Kenli Li and published by Springer. This book was released on 2014-03-08 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 25th International Conference on Parallel Computational Fluid Dynamics, ParCFD 2013, held in Changsha, China, in May 2013. The 35 revised full papers presented were carefully reviewed and selected from more than 240 submissions. The papers address issues such as parallel algorithms, developments in software tools and environments, unstructured adaptive mesh applications, industrial applications, atmospheric and oceanic global simulation, interdisciplinary applications and evaluation of computer architectures and software environments.

Download or read book Parallel Finite Volume Computation on General Meshes written by Yuri Vassilevski and published by Springer Nature. This book was released on 2020-06-26 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic methodology for the development of parallel multi-physics models and its implementation in geophysical and biomedical applications. The methodology includes conservative discretization methods for partial differential equations on general meshes, as well as data structures and algorithms for organizing parallel simulations on general meshes. The structures and algorithms form the core of the INMOST (Integrated Numerical Modelling Object-oriented Supercomputing Technologies) platform for the development of parallel models on general meshes. The authors consider applications for addressing specific geophysical and biomedical challenges, including radioactive contaminant propagation with subsurface waters, reservoir simulation, and clot formation in blood flows. The book gathers all the components of this methodology, from algorithms and numerical methods to the open-source software, as well as examples of practical applications, in a single source, making it a valuable asset for applied mathematicians, computer scientists, and engineers alike.

Download or read book High order Methods on Mixed element Unstructured Meshes for Aeronautical Applications written by Antonios Foivos Antoniadis and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Higher resolution and reliability are the desiderata for Computational Fluid Dynamics and main drivers for the development, implementation and validation of highorder accurate methods. Complex fluid dynamic phenomena such as shock-wave boundary-layer interactions, turbulent separated flows and fluid problems involving multiple scales are adequately resolved with high-order schemes. The spatial representation of the flow field by an unstructured mesh provides flexibility, automation, fast and effortless grid generation and exceptional load balance on multiple processor computers. This plethora of advantages is mirrored by the unprecedented popularity of unstructured-based schemes. The objective of this PhD project is the implementation of two high-order schemes for the compressible Navier-Stokes equations in the context of the finite volume "kexact" framework: the MUSCL-TVD and WENO. The schemes are formulated in two and three space dimensions for mixed-element unstructured meshes; in addition, the Spalart-Allmaras turbulence model is implemented into the developed numerical framework. A wide range of applications are considered spanning from low-speed flows (M = 0.08) to supersonic conditions (M = 5.0); inviscid and viscous simulations in a broad spectrum of Reynolds numbers ranging from Re = 500 up to Re = 37×106. The applications include: the Taylor-Green vortex, the ONERA-M6 wing, flat plate, the NACA-0012 and the MD 30P-30N aerofoils, and a shock-wave boundary-layer interaction. For the examined cases, WENO schemes demonstrate superior accuracy, numerical dissipation and non-oscillatory behaviour over the MUSCL-TVD. High-order schemes inherit low numerical dissipation properties while turbulence models induce dissipation, this disequilibrium has adverse effects on the stability, convergence and accuracy of the simulation; therefore, turbulence model re-calibration would be required in order to accommodate high-order discretisation methods.

Download or read book Coastal Engineering 2006 written by Jane McKee Smith and published by . This book was released on 2007 with total page 1128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Proceedings contains 445 papers presented at the 30th International Conference on Coastal Engineering, which was held in San Diego, California, USA, 3-8 September 2006. The Proceedings is divided into five parts: Waves; Swash, Nearshore Currents, and Long Waves; Coastal Management, Risk, and Ecosystem Restoration; Sediment Transport and Morphology; and Coastal Structures. The individual papers cover a broad range of topics including theory, numerical and physical modeling, field measurements, case studies, design, and management. These papers provide engineers, scientists, and planners state-of-the-art information on coastal engineering and coastal processes.

Download or read book Study of Unstructured Finite Volume Methods for the Solution of the Euler Equations written by Ivan Padilla Montero and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This work deals with the numerical solution of inviscid compressible flows by means of the Euler equations. It focuses on the description of an unstructured finite volume method for these equations and its numerical application to solve external, two-dimensional steady problems. On first place, the standard formulation of the Euler equations is presented, reviewing the most important properties that characterize their mathematical behavior. The hyperbolic nature of the system is discussed, emphasizing the fundamental importance of taking into account the propagation of information in the flow field in order to obtain physically meaningful solutions, which also leads to a description of how the boundary conditions should be treated to avoid undesirable behaviors. To complete this presentation, a dimensionless form of the equations is derived, which provides substantial advantages to the numerical solution. The attention is then focused on the unstructured finite volume formulation, which is based on a central approximation of the fluxes at the volume interfaces. According to the need of properly accounting for the propagation of characteristic variables, the requirement to add artificial dissipation terms to the central discretization is justified. Then, two classical forms of artificial dissipation are defined, namely, the first-order upwind scheme and the Jameson-Schmidt-Turkel high-order model, detailing how to adapt the formulation of the dissipation terms to an unstructured mesh. Eventually, the time integration of the spatially discretized equations is assessed. With the objective of performing a practical implementation of the theoretical concepts studied, the development of a numerical solver is presented next, briefly describing the program structure and characteristics. After that, five different test cases are solved with the purpose of validating the code, consisting on two transonic flows around a NACA0012 airfoil and three supersonic examples, respectively around a NACA0012 airfoil, a double wedge airfoil and circular cylinder. The results obtained for each case are then analyzed and compared against reference solutions, showing an overall satisfactory performance of the solver developed.