Format:
Online-Ressource (XVIII, 518 p. 163 illus., 80 illus. in color, online resource)
ISBN:
9783319055916
Series Statement:
Springer Proceedings in Mathematics & Statistics 78
Content:
The methods considered in the 7th conference on "Finite Volumes for Complex Applications" (Berlin, June 2014) have properties which offer distinct advantages for a number of applications. The second volume of the proceedings covers reviewed contributions reporting successful applications in the fields of fluid dynamics, magnetohydrodynamics, structural analysis, nuclear physics, semiconductor theory and other topics. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. Researchers, PhD and masters level students in numerical analysis, scientific computing and related fields such as partial differential equations will find this volume useful, as will engineers working in numerical modeling and simulations
Note:
Description based upon print version of record
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Preface; Organization Committees; Contents; Part IIIElliptic and Parabolic Problems; 46 Asymptotic-Preserving Methods for an Anisotropic Model of Electrical Potential in a Tokamak; 1 Introduction; 2 Anisotropic Model of the Electrical Potential; 3 The Micro-Macro Asymptotic-Preserving Method; 4 Numerical Experiments; 5 Conclusion; References; 47 Semi-implicit Second Order Accurate Finite Volume Method for Advection-Diffusion Level Set Equation; 1 Introduction; 2 Mathematical Model; 3 Finite Volume Method; 4 Solution of Algebraic Equations; 5 Numerical Experiments; 6 Conclusions
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References48 Adaptive Time Discretization and Linearization Based on a Posteriori Estimates for the Richards Equation; 1 Introduction; 2 A Posteriori Error Estimate; 3 Application to the DDFV Scheme; 4 Results; 5 Conclusions; References; 49 Monotone Combined Finite Volume-Finite Element Scheme for a Bone Healing Model; 1 Introduction; 2 The Combined FV-FE Scheme; 3 Monotone Correction; 4 Numerical Experiments; References; 50 Vertex Approximate Gradient Scheme for Hybrid Dimensional Two-Phase Darcy Flows in Fractured Porous Media
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1 Hybrid Dimensional Two-Phase Darcy Flow Model in Fractured Porous Media2 Vertex Approximate Gradient Discretization; 3 Numerical Experiments; References; 51 Coupling of a Two Phase Gas Liquid Compositional 3D Darcy Flow with a 1D Compositional Free Gas Flow; 1 Model; 2 Numerical Test; 3 Convergence Analysis of a Simplified Model; References; 52 Gradient Discretization of Hybrid Dimensional Darcy Flows in Fractured Porous Media; 1 Hybrid Dimensional Darcy Flow in Fractured Porous Media; 2 Gradient Discretization; 3 Two Examples of Gradient Discretizations of Hybrid Dimensional Models
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4 Numerical ExperimentsReferences; 53 A Gradient Scheme for the Discretization of Richards Equation; 1 Richards Equation; 2 Gradient Discretization; 3 Numerical Tests; 3.1 The Hornung-Messing Problem; 3.2 The Haverkamp Problem; References; 54 Convergence of a Finite Volume Scheme for a Corrosion Model; 1 General Framework; 2 Presentation of the Model and of the Hypotheses; 3 Numerical Scheme; 4 Main Results; 5 A Priori Estimates; 6 Conclusion; References; 55 High Performance Computing Linear Algorithms for Two-Phase Flow in Porous Media; 1 Introduction
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2 Discretization and Parallel Implementation3 Fix-Point Methods; 4 Numerical Results; References; 56 Numerical Solution of Fluid-Structure Interaction by the Space-Time Discontinuous Galerkin Method; 1 Formulation of the Problem; 1.1 Flow Problem; 1.2 Elasticity Problem; 2 Discrete Problem; 2.1 Discretization of the Flow Problem; 2.2 Discretization of the Elasticity Problem; 3 Numerical Results; References; 57 An Anisotropic Diffusion Finite Volume Algorithm Using a Small Stencil; 1 Introduction; 2 Space Discretization of the Anisotropic Heterogeneous Diffusion Equation
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2.1 Space Discretization
Additional Edition:
ISBN 9783319055909
Additional Edition:
Erscheint auch als Druck-Ausgabe FVCA (7 : 2014 : Berlin) Finite volumes for complex applications VII Cham : Springer, 2014 ISBN 9783319055909
Language:
English
DOI:
10.1007/978-3-319-05591-6
URL:
Volltext
(lizenzpflichtig)
Author information:
Ohlberger, Mario
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