Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects
| Author | : Andrea Donato |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 623 |
| Release | : 2013-03-08 |
| Genre | : Technology & Engineering |
| ISBN | : 3322878716 |
Nonlinear Hyperbolic Problems Theoretical Applied And Computational Aspects
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Numerical Approximation of Hyperbolic Systems of Conservation Laws
| Author | : Edwige Godlewski |
| Publisher | : Springer Nature |
| Total Pages | : 846 |
| Release | : 2021-08-28 |
| Genre | : Mathematics |
| ISBN | : 1071613448 |
This monograph is devoted to the theory and approximation by finite volume methods of nonlinear hyperbolic systems of conservation laws in one or two space variables. It follows directly a previous publication on hyperbolic systems of conservation laws by the same authors. Since the earlier work concentrated on the mathematical theory of multidimensional scalar conservation laws, this book will focus on systems and the theoretical aspects which are needed in the applications, such as the solution of the Riemann problem and further insights into more sophisticated problems, with special attention to the system of gas dynamics. This new edition includes more examples such as MHD and shallow water, with an insight on multiphase flows. Additionally, the text includes source terms and well-balanced/asymptotic preserving schemes, introducing relaxation schemes and addressing problems related to resonance and discontinuous fluxes while adding details on the low Mach number situation.
Theory, Numerics and Applications of Hyperbolic Problems II
| Author | : Christian Klingenberg |
| Publisher | : Springer |
| Total Pages | : 714 |
| Release | : 2018-08-01 |
| Genre | : Mathematics |
| ISBN | : 9783319915470 |
The second of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016. It focuses on the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models (PDEs of mixed type, kinetic equations, nonlocal or/and discrete models) found in the field of applied sciences.
Error Estimates for Well-Balanced Schemes on Simple Balance Laws
| Author | : Debora Amadori |
| Publisher | : Springer |
| Total Pages | : 119 |
| Release | : 2015-10-23 |
| Genre | : Mathematics |
| ISBN | : 3319247859 |
This monograph presents, in an attractive and self-contained form, techniques based on the L1 stability theory derived at the end of the 1990s by A. Bressan, T.-P. Liu and T. Yang that yield original error estimates for so-called well-balanced numerical schemes solving 1D hyperbolic systems of balance laws. Rigorous error estimates are presented for both scalar balance laws and a position-dependent relaxation system, in inertial approximation. Such estimates shed light on why those algorithms based on source terms handled like "local scatterers" can outperform other, more standard, numerical schemes. Two-dimensional Riemann problems for the linear wave equation are also solved, with discussion of the issues raised relating to the treatment of 2D balance laws. All of the material provided in this book is highly relevant for the understanding of well-balanced schemes and will contribute to future improvements.
Hyperbolic Problems: Theory, Numerics, Applications - Proceedings Of The Fifth International Conference
| Author | : James Glimm |
| Publisher | : World Scientific |
| Total Pages | : 510 |
| Release | : 1996-03-14 |
| Genre | : |
| ISBN | : 9814548588 |
The intellectual center of this proceedings volume is the subject of conservation laws. Conservation laws are the most basic model of many continuum processes, and for this reason they govern the motion of fluids, solids, and plasma. They are basic to the understanding of more complex modeling issues, such as multiphase flow, chemically reacting flow, and non-equilibrium thermodynamics. Equations of this type also arise in novel and unexpected areas, such as the pattern recognition and image processing problem of edge enhancement and detection. The articles in this volume address the entire range of the study of conservation laws, including the fundamental mathematical theory, familiar and novel applications, and the numerical problem of finding effective computational algorithms for the solution of these problems.
Applied Computational Electromagnetics
| Author | : Nikolaos K. Uzunoglu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 533 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 3642596290 |
@EOI: AEI rEOMETPEI Epigram of the Academy of Plato in Athens Electromagnetism, the science of forces arising from Amber (HAEKTPON) and the stone of Magnesia (MArNHLIA), has been the fOWldation of major scientific breakthroughs, such as Quantum Mechanics and Theory of Relativity, as well as most leading edge technologies of the twentieth century. The accuracy of electromagnetic fields computations for engineering purposes has been significantly improved during the last decades, due to the deVelopment of efficient computational techniques and the availability of high performance computing. The present book is based on the contributions and discussions developed during the NATO Advanced Study Institute on Applied Computational Electromagnetics: State of the Art and Future Trends, which has taken place in Hellas, on the island of Samos, very close to the birthplace of Electromagnetism. The book covers the fundamental concepts, recent developments and advanced applications of Integral Equation and Metliod of Moments Techniques, Finite Element and BOWldary Element Methods, Finite Difference Time Domain and Transmission Line Methods. Furthermore, topics related to Computational Electromagnetics, such as Inverse Scattering, Semi-Analytical Methods and Parallel Processing Techniques are included. The collective presentation of the principal computational electromagnetics techniques, developed to handle diverse challenging leading edge technology problems, is expected to be useful to researchers and postgraduate students working in various topics of electromagnetic technologies.
Boundary Elements: Implementation and Analysis of Advanced Algorithms
| Author | : Wolfgang Hackbusch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 281 |
| Release | : 2013-04-17 |
| Genre | : Technology & Engineering |
| ISBN | : 3322899411 |
Englischer Text: The volume contains 21 contributions to the 12th GAMM-Seminar (Kiel, January 1996), which was devoted to advanced algorithms in the field of boundary element methods. The topics were e. g. cubature techniques, multiscale methods, hp-discretisation, error estimation, domain decomposition, and programm design. Deutscher Text: Der Band enthält die 21 Beiträge zum 12. GAMM-Seminar (Kiel, Jaunuar 1996), welches sich mit fortgeschrittenen Algorithmen auf dem Gebiet der Randwertprobleme befaßte.
Advances in the Theory of Shock Waves
| Author | : Heinrich Freistühler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 527 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461201934 |
In the field known as "the mathematical theory of shock waves," very exciting and unexpected developments have occurred in the last few years. Joel Smoller and Blake Temple have established classes of shock wave solutions to the Einstein Euler equations of general relativity; indeed, the mathematical and physical con sequences of these examples constitute a whole new area of research. The stability theory of "viscous" shock waves has received a new, geometric perspective due to the work of Kevin Zumbrun and collaborators, which offers a spectral approach to systems. Due to the intersection of point and essential spectrum, such an ap proach had for a long time seemed out of reach. The stability problem for "in viscid" shock waves has been given a novel, clear and concise treatment by Guy Metivier and coworkers through the use of paradifferential calculus. The L 1 semi group theory for systems of conservation laws, itself still a recent development, has been considerably condensed by the introduction of new distance functionals through Tai-Ping Liu and collaborators; these functionals compare solutions to different data by direct reference to their wave structure. The fundamental prop erties of systems with relaxation have found a systematic description through the papers of Wen-An Yong; for shock waves, this means a first general theorem on the existence of corresponding profiles. The five articles of this book reflect the above developments.
Computational Fluid Dynamics on Parallel Systems
| Author | : Siegfried Wagner |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 205 |
| Release | : 2013-06-29 |
| Genre | : Science |
| ISBN | : 3322894541 |
Within the DFG -Schwerpunktprogramm "Stromungssimulation mit Hochleistungsrechnern" and within the activities of the French-German cooperation of CNRS and DFG a DFG symposium on "Computational Fluid Dynamics (CFD) on Parallel Systems" was organized at the Institut fur Aerodynamik and Gasdynamik of the Stuttgart University, 9-10 December 1993. This symposium was attended by 37 scientists. The scientific program consisted of 18 papers that considered finite element, finite volume and a two step Taylor Galerkin algorithm for the numerical solution of the Euler and Navier-Stokes equations on massively parallel computers with MIMD and SIMD architecture and on work station clusters. Incompressible and compressible, steady and unsteady flows were considered including turbu lent combustion with complex chemistry. Structured and unstructured grids were used. High numerical efficiency was demonstrated by multiplicative, additive and multigrid methods. Shared memory, virtual shared memory and distributed memory systems were investigated, in some cases based on an automatic grid partitioning technique. Various methods for domain decomposition were investigated. The key point of these methods is the resolution of the inter face problem because the matrix involved can be block dense. Multilevel decomposition can be very efficient using multifrontal algorithm. The numerical methods include explicit and implicit schemes. In the latter case the system of equations is often solved by a Gauss -Seidel line re laxation technique.
Adaptive Methods — Algorithms, Theory and Applications
| Author | : W. Hackbusch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 281 |
| Release | : 2013-11-21 |
| Genre | : Computers |
| ISBN | : 3663142469 |
The GAMM Committee for "Efficient Numerical Methods for Partial Differential Equations" organizes workshops on subjects concerning the algorithmical treat ment of partial differential equations. The topics are discretization methods like the finite element and finite volume method for various types of applications in structural and fluid mechanics. Particular attention is devoted to advanced solu tion techniques. th The series of such workshops was continued in 1993, January 22-24, with the 9 Kiel-Seminar on the special topic "Adaptive Methods Algorithms, Theory and Applications" at the Christian-Albrechts-University of Kiel. The seminar was attended by 76 scientists from 7 countries and 23 lectures were given. The list of topics contained general lectures on adaptivity, special discretization schemes, error estimators, space-time adaptivity, adaptive solvers, multi-grid me thods, wavelets, and parallelization. Special thanks are due to Michael Heisig, who carefully compiled the contribu tions to this volume. November 1993 Wolfgang Hackbusch Gabriel Wittum v Contents Page A. AUGE, G. LUBE, D. WEISS: Galerkin/Least-Squares-FEM and Ani- tropic Mesh Refinement. 1 P. BASTIAN, G. WmUM : Adaptive Multigrid Methods: The UG Concept. 17 R. BEINERT, D. KRONER: Finite Volume Methods with Local Mesh Alignment in 2-D. 38 T. BONK: A New Algorithm for Multi-Dimensional Adaptive Nume- cal Quadrature. 54 F.A. BORNEMANN: Adaptive Solution of One-Dimensional Scalar Conservation Laws with Convex Flux. 69 J. CANU, H. RITZDORF : Adaptive, Block-Structured Multigrid on Local Memory Machines. 84 S. DAHLKE, A. KUNaTH: Biorthogonal Wavelets and Multigrid. 99 B. ERDMANN, R.H.W. HOPPE, R.
