| Description |
1 online resource |
| Series |
Lecture notes in computational science and engineering ; 99 |
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Lecture notes in computational science and engineering ; 99.
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| Contents |
880-01 High-order Asymptotic-Preserving methods for nonlinear relaxation from hyperbolic systems to convection-diffusion equations -- A hybrid finite difference-WENO scheme for large eddy simulation of compressible flows -- Finite volume formulation of a third-order residual-based compact scheme for unsteady flow computations -- Parallel implementation of k-exact Finite Volume Reconstruction on Unstructured Grids -- 3D Application of Higher Order Multigrid Algorithms for a RANS-kw DG-Solver -- Taylor expansion method for linear lattice Boltzmann schemes with an external force. Application to boundary conditions -- High order SFV and mixed SDG/FV methods for the uncertainty quantification in multidimensional conservation laws -- High-order Discontinuous Galerkin solution of unsteady flows by using an advanced implicit method -- Detecting edges in high order methods for hyperbolic conservation laws -- A comparison of analytical solutions of a high-order RBC scheme and its equivalent differential equation for a steady shock problem -- Discontinuous Galerkin method and applications to fluid-structure interaction problems |
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880-01/(S Machine generated contents note: 1. High--Order Asymptotic--Preserving Methods for Nonlinear Relaxation from Hyperbolic Systems to Convection-Diffusion Equations / Giovanni Russo -- 1.1. Introduction -- 1.2. Implicit--Explicit (IMEX) Runge-Kutta (R-K) Schemes -- 1.3. Computation of the Limit Solution -- 1.4. Penalization Techinique -- 1.5. Numerical Test -- References -- 2. Hybrid Finite Difference-WENO Scheme for Large Eddy Simulation of Compressible Flows / Anne Burbeau-Augoula -- 2.1. Introduction -- 2.2. Finite-Difference Scheme for Smooth Solutions -- 2.2.1. On the Problem of Numerical Instability -- 2.2.2. Skew-Symmetric Form for the Convective Terms -- 2.2.3. Finite-Difference Approximation of the Skew-Symmetric Form -- 2.3. WENO Scheme for Shock Waves -- 2.4. Hybrid Approach -- 2.4.1. Shock Detecting Sensor -- 2.4.2. Hybrid Flux -- 2.4.3. Multidimensional Case -- 2.5. Numerical Results -- 2.5.1. Taylor-Green Vortex Flow -- 2.5.2. Shu-Osher Test Case -- 2.5.3. Compressible Isotropic Turbulence -- 2.6. Concluding Remarks -- References -- 3. Finite Volume Formulation of a Third-Order Residual-Based Compact Scheme for Unsteady Flow Computations / Alain Lerat -- 3.1. Introduction -- 3.2. Finite Volume Framework -- 3.3. Finite Volume RBC Schemes -- 3.4. Direct FV Extension of RBC Schemes -- 3.4.1. Approximation of the Main Residual -- 3.4.2. Residual-Based Dissipation Operator -- 3.5. Finite Volume Third-Order RBC Scheme -- 3.5.1. Approximation of the Main Residual -- 3.5.2. Approximation of the Mid-point Residuals -- 3.6. Stability Properties of RBCi -- 3.6.1. Dissipation Properties of RBCi -- 3.6.2. Cauchy Stability of RBCi -- 3.7. Numerical Applications -- 3.7.1. Advection of an Inviscid Vortex -- 3.7.2. Laminar Flow Past a Cylinder -- 3.7.3. VKI LS-59 Turbine Cascade -- 3.8. Conclusions -- References -- 4. Parallel Implementation of k-Exact Finite Volume Reconstruction on Unstructured Grids / Jean-Pierre Croisille -- 4.1. Introduction -- 4.2. Notation -- 4.2.1. Finite-Volume Notation -- 4.2.2. Tensor Notation -- 4.3. Algebra of k -- Exact Reconstruction for Derivatives -- 4.4. Implementing k-Exact Reconstructions -- 4.4.1. Efficient Reconstruction Algorithm -- 4.4.2. Practical Implementation -- 4.5. Numerical Convergence of k-Exact Reconstructions -- 4.6. Isothermal Vortex Test-Case -- 4.7. Conclusion -- References -- 5. 3D Application of Higher Order Multigrid Algorithms for a RANS-kω DG-Solver / Tobias Leicht -- 5.1. Introduction -- 5.2. Discretization -- 5.3. Multigrid Algorithms -- 5.4. Numerical Results -- 5.5. Summary and Outlook -- References -- 6. Taylor Expansion Method for Linear Lattice Boltzmann Schemes with an External Force: Application to Boundary Conditions / Mohamed Mahdi Tekitek -- 6.1. Introduction -- 6.2. Lattice Boltzmann Scheme with a Forcing Drift -- 6.3. Taylor Expansion Method for the Equivalent Equations -- 6.4. Boundary Conditions for D1Q3 Thermal Problems -- 6.5. D2Q9 for a Linear Acoustic Type Fluid -- 6.6. D2Q13 for a Linearized Fluid -- 6.7. Conclusion -- References -- 7. High Order SFV and Mixed SDG/FV Methods for the Uncertainty Quantification in Multidimensional Conservation Laws / Siddhartha Mishra -- 7.1. Introduction -- 7.2. Conservation Laws with Random Flux and Initial Data -- 7.3. Stochastic FVM -- 7.4. Convergence and Efficiency Analysis for SFVM -- 7.4.1. Convergence of Statistical Moments in L1-Norm -- 7.4.2. Efficiency Estimates -- 7.4.3. Numerical Convergence Analysis -- 7.4.4. Numerical Results -- 7.5. Stochastic DG/FVM -- 7.5.1. Stochastic DG/FV Method -- 7.5.2. Numerical Results -- 7.6. Stochastic Mesh Adaptation -- 7.6.1. Stochastic Mesh Adaptation Based on Karhunen-Loeve Expansion -- 7.6.2. Numerical Results -- 7.7. Conclusions -- References -- 8. High-Order Discontinuous Galerkin Solution of Unsteady Flows by Using an Advanced Implicit Method / Antonio Ghidoni -- 8.1. Introduction -- 8.2. Governing Equations -- 8.3. DG Space Discretization -- 8.4. TIAS Time Discretization -- 8.5. Numerical Results -- 8.5.1. Convection of an Isentropic Vortex -- 8.5.2. Unsteady Vortex Shedding Behind a Circular Cylinder -- 8.6. Conclusions -- References -- 9. Detecting Edges in High Order Methods for Hyperbolic Conservation Laws / Martina Wirz -- 9.1. Introduction -- 9.2. Conjugated Fourier Partial Sums -- 9.3. Generalized Twodimensional Case -- 9.4. Application to Local Methods -- 9.4.1. Spectral Difference Method with Modal Filtering -- 9.4.2. Application to the Spectral Difference Method -- 9.5. Conclusion and Outlook -- References -- 10. Comparison of Analytical Solutions of a High-Order RBC Scheme and Its Equivalent Differential Equation for a Steady Shock Problem / Alain Lerat -- 10.1. Introduction -- 10.2. Residual-Based Compact Schemes -- 10.3. Steady Discrete Shocks -- 10.4. Steady Shock Profiles of the Equivalent Differential Equation -- 10.5. Conclusions -- References -- 11. Discontinuous Galerkin Method and Applications to Fluid-Structure Interaction Problems / Adam Kosfic -- 11.1. Introduction -- 11.2. Continuous Problem -- 11.2.1. Flow Problem -- 11.2.2. Dynamical Elasticity Problem -- 11.2.3. Interaction of the Compressible Flow and Dynamical Elasticity Problem -- 11.3. Discrete Problem -- 11.3.1. Space Discretization of the Flow Problem by the Discontinuous Galerkin Method -- 11.3.3. Discretization of the Structural Problem -- 11.3.4. Coupling Procedure -- 11.3.5. Numerical Results -- 11.4. Conclusion |
| Summary |
This book collects papers presented during the European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs (HONOM 2013) that was held at INRIA Bordeaux Sud-Ouest, Talence, France in March, 2013. The central topic is high order methods for compressible fluid dynamics. In the workshop, and in this proceedings, greater emphasis is placed on the numerical than the theoretical aspects of this scientific field. The range of topics is broad, extending through algorithm design, accuracy, large scale computing, complex geometries, discontinuous Galerkin, finite element methods, Lagrangian hydrodynamics, finite difference methods and applications and uncertainty quantification. These techniques find practical applications in such fields as fluid mechanics, magnetohydrodynamics, nonlinear solid mechanics, and others for which genuinely nonlinear methods are needed |
| Analysis |
wiskunde |
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mathematics |
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partial differential equations |
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computerwiskunde |
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computational mathematics |
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numerieke wiskunde |
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numerical mathematics |
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wiskundige modellen |
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mathematical models |
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toegepaste wiskunde |
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applied mathematics |
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Mathematics (General) |
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Wiskunde (algemeen) |
| Bibliography |
Includes bibliographical references |
| Notes |
Print version record |
| Subject |
Differential equations, Partial.
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Evolution equations.
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Computer science.
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Electronic Data Processing
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Computer science
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Differential equations, Partial
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Evolution equations
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| Genre/Form |
proceedings (reports)
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Conference papers and proceedings
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Conference papers and proceedings.
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Actes de congrès.
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| Form |
Electronic book
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| Author |
Abgrall, Rémi, editor.
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| ISBN |
9783319054551 |
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3319054554 |
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9783319054568 |
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3319054562 |
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9783319381725 |
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3319381725 |
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