On the Stability of Fully Adaptive Multiscale Schemes for Conservation Laws Using Approximate Flux and Source Reconstruction Strategies PDF Download

Author: Nune Hovhannisyan
Publisher:
ISBN:
Category :
Languages : en
Pages : 44

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Author: Wolfgang Schröder
Publisher: Springer Science & Business Media
ISBN: 3642040888
Category : Technology & Engineering
Languages : en
Pages : 434

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The Collaborative Research Center SFB 401: Flow Modulation and Fluid-Structure Interaction at Airplane Wings investigates numerically and experimentally fundamental problems of very high capacity aircraft having large elastic wings. This issue summarizes the findings of the 12-year research program at RWTH Aachen University which was funded by the Deutsche Forschungsgemeinschaft (DFG) from 1997 through 2008. The research program covered the following three main topics of large transport aircraft: (i) Model flow, wakes, and vortices of airplanes in high-lift-configuration, (ii) Numerical tools for large scale adaptive flow simulation based on multiscale analysis and a parametric mapping concept for grid generation, and (iii) Validated computational design tools based on direct aeroelastic simulation with reduced structural models.

Author: Birgit Gottschlich-Müller
Publisher:
ISBN: 9783826540554
Category :
Languages : en
Pages : 195

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Author: Die deutsche Nationalbibliothek
Publisher:
ISBN:
Category :
Languages : de
Pages : 914

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Author: Dietmar Kröner
Publisher: John Wiley & Sons
ISBN:
Category : Conservation laws (Mathematics)
Languages : en
Pages : 528

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Author: Jan S. Hesthaven
Publisher: SIAM
ISBN: 1611975107
Category : Science
Languages : en
Pages : 571

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Book Description
Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains a challenge and many questions are left open; thus it is an active and fruitful area of research. Numerical Methods for Conservation Laws: From Analysis to Algorithms offers the first comprehensive introduction to modern computational methods and their analysis for hyperbolic conservation laws, building on intense research activities for more than four decades of development; discusses classic results on monotone and finite difference/finite volume schemes, but emphasizes the successful development of high-order accurate methods for hyperbolic conservation laws; addresses modern concepts of TVD and entropy stability, strongly stable Runge-Kutta schemes, and limiter-based methods before discussing essentially nonoscillatory schemes, discontinuous Galerkin methods, and spectral methods; explores algorithmic aspects of these methods, emphasizing one- and two-dimensional problems and the development and analysis of an extensive range of methods; includes MATLAB software with which all main methods and computational results in the book can be reproduced; and demonstrates the performance of many methods on a set of benchmark problems to allow direct comparisons. Code and other supplemental material will be available online at publication.

Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781719396943
Category :
Languages : en
Pages : 34

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A formulation for the discontinuous Galerkin (DG) method that leads to solutions using the differential form of the equation (as opposed to the standard integral form) is presented. The formulation includes (a) a derivative calculation that involves only data within each cell with no data interaction among cells, and (b) for each cell, corrections to this derivative that deal with the jumps in fluxes at the cell boundaries and allow data across cells to interact. The derivative with no interaction is obtained by a projection, but for nodal-type methods, evaluating this derivative by interpolation at the nodal points is more economical. The corrections are derived using the approximate (Dirac) delta functions. The formulation results in a family of schemes: different approximate delta functions give rise to different methods. It is shown that the current formulation is essentially equivalent to the flux reconstruction (FR) formulation. Due to the use of approximate delta functions, an energy stability proof simpler than that of Vincent, Castonguay, and Jameson (2011) for a family of schemes is derived. Accuracy and stability of resulting schemes are discussed via Fourier analyses. Similar to FR, the current formulation provides a unifying framework for high-order methods by recovering the DG, spectral difference (SD), and spectral volume (SV) schemes. It also yields stable, accurate, and economical methods. Huynh, H. T. Glenn Research Center COMPUTATIONAL FLUID DYNAMICS; CONSERVATION LAWS; DIFFERENTIAL EQUATIONS; DERIVATION; DELTA FUNCTION; GALERKIN METHOD; FOURIER ANALYSIS; FLUX DENSITY; NUMERICAL ANALYSIS; SPECTRAL METHODS; NAVIER-STOKES EQUATION; UNSTRUCTURED GRIDS (MATHEMATICS); STABILITY; COSTS; PROVING

Author: Folkmar A. Bornemann
Publisher:
ISBN:
Category : Differential equations, Hyperbolic
Languages : en
Pages : 16

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Abstract: "A new adaptive approach for one-dimensional scalar conservation laws with convex flux is proposed. The initial data are approximated on an adaptive grid by a problem dependent, monotone interpolation procedure in such a way, that the multivalued problem of characteristic transport can be easily and explicitly solved. The unique entropy solution is chosen by means of a selection criterion due to LAX. For arbitrary times, the solution is represented by an adaptive monotone spline interpolation. The spatial approximation is controlled by local L-1 error estimates. As a distinctive feature of the approach, there is no discretization in time. The method is monotone on fixed grids. Numerical examples are included, to demonstrate the predicted behavior."

Author: Paul Anthony Burton
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author: Bernardo Cockburn
Publisher: Springer Science & Business Media
ISBN: 3642597211
Category : Mathematics
Languages : en
Pages : 468

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Book Description
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.