Download or read book An Anisotropic Adaptive Method for the Solution of 3 D Inviscid and Viscous Compressible Flows written by Anna Tam and published by . This book was released on 1998 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The solution of complex three-dimensional computational fluid dynamics (CFD) problems in general necessitates the use of a large number of mesh points to approximate directional flow features such as shocks, boundary layers, vortices and wakes. Such large grid sizes have motivated researchers to investigate methods of introducing very high aspect ratio elements to capture these features. In this Thesis, an anisotropic adaptive grid method has been developed for the solution of three-dimensional inviscid and viscous flows by the finite element method. An edge-based error estimate drives a mesh movement strategy that allows directional stretching and re-orientation of the grid with more mesh points introduced along those directions with rapidly changing gradients. The error estimate is built from a modified positive-definite form of the Hessian tensor of a selected solution variable or combination of variables. The resulting metric tensor controls the magnitude as well as, the direction of the grid stretching. The desired directionally adapted anisotropic mesh is constructed in physical space by a coordinate transformation based on this tensor. This research thus seeks a near-isotropic mesh in the transformed metric space and an equidistribution of the error over the mesh edges. The adaptive strategy can be considered to be the first 3-D implementation of an improved spring analogy-based algorithm originally applied on quadrilateral meshes. The adaptive methodology has been validated on various benchmark cases on both hexahedral and tetrahedral meshes. The numerical results obtained span inviscid and viscous flows, as well as internal and external aerodynamics. The effectiveness of the adaptive scheme to equidistribute the interpolation error over the edges of tetrahedral and hexahedral meshes has been gauged on analytical test cases where near-Gaussian distributions of the error were obtained. It was further demonstrated that the error estimate closely follows the true solution error. In analyzing the solution error of different sized non-adapted and adapted grids, one could not only achieve the same level of solution error by adapting and solving on a much coarser grid, but a significant reduction in solution time as well. All test cases revealed that the flow solver required lower amounts of artificial dissipation for solution on the final adapted grids. The current work should convincingly pave the way for its logical extension to unstructured grids, taking further advantage of refinement, coarsening and edge-swapping operations. It is strongly anticipated that this approach will shortly result in "optimal" grids.
Download or read book An Upwind Method for the Solution of the 3D Euler and Navier Stokes Equations on Adaptively Meshes written by Michael J. Aftosmis and published by . This book was released on 1992 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new node based upwind scheme for the solution of the 3D Navier- Stokes equations on adaptively refined meshes is presented. The method uses a second-order upwind TVD scheme to integrate the convective terms, and discretizes the viscous terms with a new compact central difference technique. Grid adaptation is achieved through directional division of hexahedral cells in response to evolving features as the solution converges. The method is advanced in time with a multistage Runge-Kutta time stepping scheme. Two- and three- dimensional examples establish the accuracy of the inviscid and viscous discretization. These investigations highlight the ability of the method to produce crisp shocks, while accurately and economically resolving viscous layers. The representation of these and other structures is shown to be comparable to that obtained by structured methods. Further 3D examples demonstrate the ability of the adaptive algorithm to effectively locate and resolve multiple scale features in complex 3D flows with many interacting, viscous, and inviscid structures.
Download or read book An Upwind Method for the Solution of the 3D Euler and Navier Stokes Equations on Adaptively Meshes written by and published by . This book was released on 1992 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new node based upwind scheme for the solution of the 3D Navier- Stokes equations on adaptively refined meshes is presented. The method uses a second-order upwind TVD scheme to integrate the convective terms, and discretizes the viscous terms with a new compact central difference technique. Grid adaptation is achieved through directional division of hexahedral cells in response to evolving features as the solution converges. The method is advanced in time with a multistage Runge-Kutta time stepping scheme. Two- and three- dimensional examples establish the accuracy of the inviscid and viscous discretization. These investigations highlight the ability of the method to produce crisp shocks, while accurately and economically resolving viscous layers. The representation of these and other structures is shown to be comparable to that obtained by structured methods. Further 3D examples demonstrate the ability of the adaptive algorithm to effectively locate and resolve multiple scale features in complex 3D flows with many interacting, viscous, and inviscid structures.
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2000 with total page 992 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Efficient High order Accurate Unstructured Finite volume Algorithms for Viscous and Inviscid Compressible Flows written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book American Doctoral Dissertations written by and published by . This book was released on 1999 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book International Aerospace Abstracts written by and published by . This book was released on 1999 with total page 1048 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computational Fluid Dynamics 2010 written by Alexander Kuzmin and published by Springer Science & Business Media. This book was released on 2011-05-03 with total page 902 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Conference on Computational Fluid Dynamics is held every two years and brings together physicists, mathematicians and engineers to review and share recent advances in mathematical and computational techniques for modeling fluid flow. The proceedings of the 2010 conference (ICCFD6) held in St Petersburg, Russia, contain a selection of refereed contributions and are meant to serve as a source of reference for all those interested in the state of the art in computational fluid dynamics.
Download or read book The Finite Element Method Set written by O. C. Zienkiewicz and published by Elsevier. This book was released on 2005-11-25 with total page 1863 pages. Available in PDF, EPUB and Kindle. Book excerpt: The sixth editions of these seminal books deliver the most up to date and comprehensive reference yet on the finite element method for all engineers and mathematicians. Renowned for their scope, range and authority, the new editions have been significantly developed in terms of both contents and scope. Each book is now complete in its own right and provides self-contained reference; used together they provide a formidable resource covering the theory and the application of the universally used FEM. Written by the leading professors in their fields, the three books cover the basis of the method, its application to solid mechanics and to fluid dynamics.* This is THE classic finite element method set, by two the subject's leading authors * FEM is a constantly developing subject, and any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in these books * Fully up-to-date; ideal for teaching and reference
Download or read book Applied mechanics reviews written by and published by . This book was released on 1948 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Discontinuous Galerkin Method for the Solution of Compressible Flows written by Cristian Biotto and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Journal of Fluids Engineering written by and published by . This book was released on 1999 with total page 964 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Finite Element Method for Fluid Dynamics written by O. C. Zienkiewicz and published by Butterworth-Heinemann. This book was released on 2013-11-21 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Finite Element Method for Fluid Dynamics offers a complete introduction the application of the finite element method to fluid mechanics. The book begins with a useful summary of all relevant partial differential equations before moving on to discuss convection stabilization procedures, steady and transient state equations, and numerical solution of fluid dynamic equations. The character-based split (CBS) scheme is introduced and discussed in detail, followed by thorough coverage of incompressible and compressible fluid dynamics, flow through porous media, shallow water flow, and the numerical treatment of long and short waves. Updated throughout, this new edition includes new chapters on: - Fluid-structure interaction, including discussion of one-dimensional and multidimensional problems - Biofluid dynamics, covering flow throughout the human arterial system Focusing on the core knowledge, mathematical and analytical tools needed for successful computational fluid dynamics (CFD), The Finite Element Method for Fluid Dynamics is the authoritative introduction of choice for graduate level students, researchers and professional engineers. - A proven keystone reference in the library of any engineer needing to understand and apply the finite element method to fluid mechanics - Founded by an influential pioneer in the field and updated in this seventh edition by leading academics who worked closely with Olgierd C. Zienkiewicz - Features new chapters on fluid-structure interaction and biofluid dynamics, including coverage of one-dimensional flow in flexible pipes and challenges in modeling systemic arterial circulation
Download or read book Anisotropic hp Mesh Adaptation Methods written by Vít Dolejší and published by Springer Nature. This book was released on 2022-06-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mesh adaptation methods can have a profound impact on the numerical solution of partial differential equations. If devised and implemented properly, adaptation significantly reduces the size of the algebraic systems resulting from the discretization, while ensuring that applicable error tolerances are met. In this monograph, drawing from many years of experience, the authors give a comprehensive presentation of metric-based anisotropic hp-mesh adaptation methods. A large part of this monograph is devoted to the derivation of computable interpolation error estimates on simplicial meshes, which take into account the geometry of mesh elements as well as the anisotropic features of the interpolated function. These estimates are then used for the optimization of corresponding finite element spaces in a variety of settings. Both steady and time dependent problems are treated, as well as goal-oriented adaptation. Practical aspects of implementation are also explored, including several algorithms. Many numerical experiments using the discontinuous Galerkin method are presented to illustrate the performance of the adaptive techniques. This monograph is intended for scientists and researchers, including doctoral and master-level students. Portions of the text can also be used as study material for advanced university lectures concerning a posteriori error analysis and mesh adaptation.
Download or read book Aeronautical Engineering written by and published by . This book was released on 1991 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Mathematics and Advanced Applications written by F. Brezzi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 981 pages. Available in PDF, EPUB and Kindle. Book excerpt: An invaluable instrument for gaining a wide-ranging perspective on the latest developments in mathematical aspects of scientific computing, discovering new applications and the most recent developments in long-standing applications. Provides an insight into the state of the art of Numerical Mathematics and, more generally, into the field of Advanced Applications.
