Download or read book Four dimensional Anisotropic Mesh Adaptation for Spacetime Numerical Simulations written by Philip Claude Delhaye Caplan and published by . This book was released on 2019 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineers and scientists are increasingly relying on high-fidelity numerical simulations. Within these simulations, mesh adaptation is useful for obtaining accurate predictions of an output of interest subject to a computational cost constraint. In the quest for accurately predicting outputs in problems with time-dependent solution features, a fully unstructured coupled spacetime approach has been shown to be useful in reducing the cost of the overall simulation. However, for the simulation of unsteady three-dimensional partial differential equations (PDEs), a four-dimensional mesh adaptation tool is needed. This work develops the first anisotropic metric-conforming four-dimensional mesh adaptation tool for performing adaptive numerical simulations of unsteady PDEs in three dimensions. The theory and implementation details behind our algorithm are first developed alongside an algorithm for constructing four-dimensional geometry representations. We then demonstrate our algorithm on three-dimensional benchmark cases and it appears to outperform existing implementations, both in metric-conformity and expected tetrahedra counts. We study the utility of the mesh adaptation components to justify the design of our algorithm. We then develop four-dimensional benchmark cases and demonstrate that metric-conformity and expected pentatope counts are also achieved. This is the first time anisotropic four-dimensional meshes have been presented in the literature. Next, the entire mesh adaptation framework, Mesh Optimization via Error Sampling and Synthesis (MOESS), is extended to the context of finding the optimal mesh to represent a function of four variables. The mesh size and aspect ratio distributions of the optimized meshes match the analytic ones, thus verifying our framework. Finally, we apply MOESS in conjunction with the mesh adaptation tool to perform the first four-dimensional anisotropic mesh adaptation for the solution of the advection-diffusion equation. The optimized meshes effectively refine the solution features corresponding to both a boundary layer solution as well as an expanding spherical wave.

Download or read book Two dimensional Three dimensional and Four dimensional Anisotropic Mesh Adaptation for the Time continuous Space time Finite Element Method with Applications to the Incompressible Navier Stokes Equations written by Pascal Tremblay and published by . This book was released on 2007 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Meshing Geometric Modeling and Numerical Simulation Volume 2 written by Paul Louis George and published by John Wiley & Sons. This book was released on 2019-01-25 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Triangulations, and more precisely meshes, are at the heart of many problems relating to a wide variety of scientific disciplines, and in particular numerical simulations of all kinds of physical phenomena. In numerical simulations, the functional spaces of approximation used to search for solutions are defined from meshes, and in this sense these meshes play a fundamental role. This strong link between meshes and functional spaces leads us to consider advanced simulation methods in which the meshes are adapted to the behaviors of the underlying physical phenomena. This book presents the basic elements of this vision of meshing. These mesh adaptations are generally governed by a posteriori error estimators representing an increase of the error with respect to a size or metric. Independently of this metric of calculation, compliance with a geometry can also be calculated using a so-called geometric metric. The notion of mesh thus finds its meaning in the metric of its elements.

Download or read book Time accurate Anisotropic Mesh Adaptation for Three dimensional Moving Mesh Problems written by Nicolas Barral and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time dependent simulations are still a challenge for industry, notably due to problems raised by moving boundaries, both in terms of CPU cost and accuracy. This thesis presents contributions to several aspects of simulations with moving meshes. A moving-mesh algorithm based on a large deformation time step and connectivity changes (swaps) is studied. An elasticity method and an Inverse Distance Weighted interpolation method are compared on many 3D examples, demonstrating the efficiency of the algorithm in handling large geometry displacement without remeshing. This algorithm is coupled with an Arbitrary-Lagrangian-Eulerian (ALE) solver, whose schemes and implementation in 3D are described in details. A linear interpolation scheme is used to handle swaps. Validation test cases showed that the use of swaps does not impact notably the accuracy of the solution, while several other complex 3D examples demonstrate the capabilities of the approach both with imposed motion and Fluid-Structure Interaction problems. Metric-based mesh adaptation has proved its efficiency in improving the accuracy of steady simulation at a reasonable cost. We consider the extension of these methods to unsteady problems, updating the previous fixed-point algorithm thanks to a new space-time error analysis based on the continuous mesh model. An efficient p-thread parallelization enables running 3D unsteady adaptative simulations with a new level of accuracy. This algorithm is extended to moving mesh problems, notably by correcting the optimal unsteady metric. Finally several 3D examples of adaptative moving mesh simulations are exhibited, that prove our concept by improving notably the accuracy of the solution for a reasonable time cost.

Download or read book Mesh Adaptation for Computational Fluid Dynamics Volume 1 written by Alain Dervieux and published by John Wiley & Sons. This book was released on 2022-09-21 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simulation technology, and computational fluid dynamics (CFD) in particular, is essential in the search for solutions to the modern challenges faced by humanity. Revolutions in CFD over the last decade include the use of unstructured meshes, permitting the modeling of any 3D geometry. New frontiers point to mesh adaptation, allowing not only seamless meshing (for the engineer) but also simulation certification for safer products and risk prediction. Mesh Adaptation for Computational Dynamics 1 is the first of two volumes and introduces basic methods such as feature-based and multiscale adaptation for steady models. Also covered is the continuous Riemannian metrics formulation which models the optimally adapted mesh problem into a pure partial differential statement. A number of mesh adaptative methods are defined based on a particular feature of the simulation solution. This book will be useful to anybody interested in mesh adaptation pertaining to CFD, especially researchers, teachers and students.

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 Adaptive Mesh Refinement Theory and Applications written by Tomasz Plewa and published by Springer Science & Business Media. This book was released on 2004-12-08 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced numerical simulations that use adaptive mesh refinement (AMR) methods have now become routine in engineering and science. Originally developed for computational fluid dynamics applications these methods have propagated to fields as diverse as astrophysics, climate modeling, combustion, biophysics and many others. The underlying physical models and equations used in these disciplines are rather different, yet algorithmic and implementation issues facing practitioners are often remarkably similar. Unfortunately, there has been little effort to review the advances and outstanding issues of adaptive mesh refinement methods across such a variety of fields. This book attempts to bridge this gap. The book presents a collection of papers by experts in the field of AMR who analyze past advances in the field and evaluate the current state of adaptive mesh refinement methods in scientific computing.

Download or read book 3D Anisotropic Mesh Adaptation for Reynolds Averaged Navier Stokes Simulations written by Loïc Frazza and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fast and reliable simulation of turbulent flow using Reynolds Averaged Navier Stokes (RANS) models is a major financial issue for many industries. With the increasing complexity of geometries and simulated flows, as well as requirements in terms of fidelity, the generation of appropriate meshes has become a key link in the chain of computation. We show in this thesis the ability of modern numerical schemes to simulate turbulent flows on fully unstructured meshes generated automatically using mesh adaptation methods. We present the implementation of different versions of the Spalart-Allmaras model as well as the numerical choices guaranteeing a sufficient robustness of the solver in order to not require a structured boundary layer. We then introduce the error analysis necessary to propose different error estimators for mesh optimization. This methodology is tested on various external aerodynamic and turbomachinery test cases and compared to traditional mesh generation methods. We show the ability of mesh adaptation methods to automatically generate optimal mesh sizes for RANS simulations on realistic and complex geometries.

Download or read book Numerical Methods and Mesh Adaptation for Reliable Rans Simulations written by Victorien Menier and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis deals with the high-fidelity prediction of viscous turbulent flows modelized by the Reynolds-Averaged Navier-Stokes (RANS) equations. If mesh adaptation has been successfully applied to inviscid simulations like the sonic boom prediction or the blast propagation, demonstrating that these methods are also well-suited for 3D RANS simulations remains a challenge. This thesis addresses research issues that arise in this context, which are related to both numerical methods (flow solver) and mesh adaptation strategies. For the numerical methods, we have implemented a turbulence model in our in-house flow solver and carried out its verification & validation study. Accurate results were obtained for a representative set of test cases, including the drag prediction workshop. Additional developments have been done to improve the robustness and the convergence speed of the flow solver. They include the implementation of an implicit time integration and of a multigrid acceleration procedure. As regards mesh adaptation, we have coupled the adaptive process to multigrid in order to benefit from its convergence properties and thus improve the robustness while preventing losses of computational effort. We also have devised a parallel mesh generation algorithm. We are able to generate anisotropic adapted meshes containing around one billion elements in less than 20min on 120 cores. Finally, we introduced a procedure to automatically generate anisotropic adapted quasi-structured meshes in boundary layer regions.

Download or read book An Adaptive Framework for High order Mixed element Numerical Simulations written by Philip Claude Delhaye Caplan and published by . This book was released on 2014 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work builds upon an adaptive simulation framework to allow for mixed-element meshes in two dimensions. Contributions are focused in the area of mesh generation which employs the Lk norm to produce various mesh types. Mixed-element meshes are obtained by first using the L[alpha] norm to create a right-triangulation which is then combined to form quadrilaterals through a graph-matching approach. The resulting straight-sided mesh is then curved using a nonlinear elasticity analogy. Since the element sizes and orientations are prescribed to the mesh generator through a field of Riemannian metric tensors, the adaptation algorithm used to compute this field is also discussed. The algorithm is first tested through the L2 error control of isotropic and anisotropic problems and shows that optimal mesh gradings can be obtained. Problems drawn from aerodynamics are then used to demonstrate the ability of the algorithm in practical applications. With mixed element meshes, the adaptation algorithm works well in practice, however, improvements can be made in the cost and error models. In fact, using the L[alpha]-generated meshes inherits the same properties of traditional triangulations while adding structure to the mesh. The use of the L[alpha]-norm in generating tetrahedral meshes is worth pursuing in the future.

Download or read book Two Dimensional Anisotropic Cartesian Mesh Adaptation for the Compressible Euler Equations electronic Resource written by Keats, William A and published by University of Waterloo. This book was released on 2004 with total page 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.

Download or read book Residual based Isotropic and Anisotropic Mesh Adaptation for Computational Fluid Dynamics written by Amir R. Baserinia and published by . This book was released on 2008 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The accuracy of a fluid flow simulation depends not only on the numerical method used for discretizing the governing equations, but also on the distribution and topology of the mesh elements. Mesh adaptation is a technique for automatically modifying the mesh in order to improve the simulation accuracy in an attempt to reduce the manual work required for mesh generation. The conventional approach to mesh adaptation is based on a feature-based criterion that identifies the distinctive features in the flow field such as shock waves and boundary layers. Although this approach has proved to be simple and effective in many CFD applications, its implementation may require a lot of trial and error for determining the appropriate criterion in certain applications. An alternative approach to mesh adaptation is the residual-based approach in which the discretization error of the fluid flow quantities across the mesh faces is used to construct an adaptation criterion. Although this approach provides a general framework for developing robust mesh adaptation criteria, its incorporation leads to significant computational overhead. The main objective of the thesis is to present a methodology for developing an appropriate mesh adaptation criterion for fluid flow problems that offers the simplicity of a feature-based criterion and the robustness of a residual-based criterion. This methodology is demonstrated in the context of a second-order accurate cell-centred finite volume method for simulating laminar steady incompressible flows of constant property fluids. In this methodology, the error of mass and momentum flows across the faces of each control volume are estimated with a Taylor series analysis. Then these face flow errors are used to construct the desired adaptation criteria for triangular isotropic meshes and quadrilateral anisotropic meshes. The adaptation results for the lid-driven cavity flow show that the solution error on the resulting adapted meshes is 80 to 90 percent lower than that of a uniform mesh with the same number of control volumes. The advantage of the proposed mesh adaptation method is the capability to produce meshes that lead to more accurate solutions compared to those of the conventional methods with approximately the same amount of computational effort.

Download or read book Two dimensional Anisotropic Cartesian Mesh Adaption for the Compressible Euler Equations written by W. Andrew Keats and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Simulating transient compressible flows involving shock waves presents challenges to the CFD practitioner in terms of the mesh quality required to resolve discontinuities and prevent smearing. This document discusses a novel two-dimensional Cartesian anisotropic mesh adaptation technique implemented for transient compressible flow. This technique, originally developed for laminar incompressible flow, is efficient because it refines and coarsens cells using criteria that consider the solution in each of the cardinal directions separately. In this document the method will be applied to compressible flow. The procedure shows promise in its ability to deliver good quality solutions while achieving computational savings. Transient shock wave diffraction over a backward step and shock reflection over a forward step are considered as test cases because they demonstrate that the quality of the solution can be maintained as the mesh is refined and coarsened in time. The data structure is explained in relation to the computational mesh, and the object-oriented design and implementation of the code is presented. Refinement and coarsening algorithms are outlined. Computational savings over uniform and isotropic mesh approaches are shown to be significant.

Download or read book Anisotropic Finite Element Mesh Adaptation Via Higher Dimensional Embedding written by Franco Dassi and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Advances in Biomechanics and Tissue Regeneration written by Mohamed H. Doweidar and published by Academic Press. This book was released on 2019-08-13 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Biomechanics and Tissue Regeneration covers a wide range of recent development and advances in the fields of biomechanics and tissue regeneration. It includes computational simulation, soft tissues, microfluidics, the cardiovascular system, experimental methods in biomechanics, mechanobiology and tissue regeneration. The state-of-the-art, theories and application are presented, making this book ideal for anyone who is deciding which direction to take their future research in this field. In addition, it is ideal for everyone who is exploring new fields or currently working on an interdisciplinary project in tissue biomechanics. - Combines new trends in biomechanical modelling and tissue regeneration - Offers a broad scope, covering the entire field of tissue biomechanics - Contains perspectives from engineering, medicine and biology, thus giving a holistic view of the field

Download or read book International Aerospace Abstracts written by and published by . This book was released on 1999 with total page 974 pages. Available in PDF, EPUB and Kindle. Book excerpt: