Wang, Zhi Jian.
Adaptive High-Order Methods in Computational Fluid Dynamics. - 1 online resource (471 pages) - Advances in Computational Fluid Dynamics Ser. ; v.2 . - Advances in Computational Fluid Dynamics Ser. .
Intro -- CONTENTS -- Preface -- Chapter 1: Discontinuous Galerkin for Turbulent Flows Francesco Bassi, Lorenzo Botti, Alessandro Colombo, Antonio Ghidoni And Stefano Rebay -- 1. Introduction -- 2. DG Solution of the RANS and k-! Equations -- 2.1. Governing equations -- 2.1.1. Surface boundary condition for -- 2.2. DG space discretization -- 2.2.1. Orthonormal and hierarchical basis functions -- 2.3. Time integration -- 2.3.1. Linearly implicit Runge-Kutta schemes -- 2.4. Shock-capturing approach -- 3. Numerical Results -- 3.1. L1T2 3-element airfoil -- 3.2. ONERA M6 wing -- 3.3. DPWIII W1 wing -- 3.4. DLR-F6 wing-body configuration -- 3.5. NASA 65 sweep delta wing -- 4. Final Remarks -- Acknowledgments -- References -- Chapter 2: Massively Parallel Solution Techniques for Higher-Order Finite-Element Discretizations in CFD Laslo T. Diosady and David L. Darmofal -- 1. Introduction -- 2. Schwarz Methods -- 2.1. The case of two subdomains -- 2.2. The case of many subdomains -- 2.3. Large scale CFD applications -- 3. Schur Complement Methods -- 3.1. An interface problem -- 3.2. Classical substructuring methods -- 3.3. Approximate factorizations -- 4. Neumann-Neumann Methods -- 4.1. BDDC and FETI-DP -- 5. Numerical Results -- References -- Chapter 3: Error Estimation and hp-Adaptive Mesh Refinement for Discontinuous Galerkin Methods Tobias Leicht and Ralf Hartmann -- 1. Introduction -- 2. Flow Problem and Its Discretization -- 3. Error Estimation and Local Error Indicators -- 3.1. Single target quantities -- 3.2. Multiple target quantities -- 4. Adaptation Strategies -- 4.1. Comparison of h- and p-type mesh refinement -- 4.2. Combined hp-refinement -- 4.3. hp-indicator in 1D -- 4.4. hp-indicator in multiple dimensions and for systems of equations -- 4.5. Anisotropic h-subdivision -- 5. Adaptive Refinement Algorithm -- 6. Numerical Results. 6.1. Laminar subsonic flow around an airfoil -- 6.2. Transonic flow around an airfoil -- 6.3. Laminar flow around a delta wing -- 6.4. L1T2 three element high lift configuration -- 6.5. Subsonic turbulent flow around the DLR-F6 wing-body configuration -- 7. Conclusion and Outlook -- Acknowledgments -- References -- Chapter 4: A Runge-Kutta based Discontinuous Galerkin Method with Time Accurate Local Time Stepping Gregor J. Gassner, Florian Hindenlang and Claus-Dieter Munz -- 1. Introduction -- 2. General Formulation -- 2.1. The semi discrete form -- 2.2. The fully discrete form -- 2.3. The predictor-corrector formulation -- 3. Beyond the Global Time Integration Paradigm -- 3.1. Time-accurate local time stepping -- 4. Results -- 4.1. Time accuracy -- 4.2. Accuracy for non-linear problems -- 4.3. Application -- 5. Conclusion -- Acknowledgments -- References -- Chapter 5: High-Order Discontinuous Galerkin Methods for CFD Jaime Peraire and Per-Olof Persson -- 1. Introduction -- 2. Governing Equations -- 2.1. The compressible Navier-Stokes equations -- 2.2. Turbulence modeling -- 2.3. Mapping-based ALE formulation for deformable domains -- 2.3.1. The mapping -- 2.3.2. Transformed equations -- 2.3.3. Geometric conservation law -- 3. Numerical Methods -- 3.1. The compact Discontinuous Galerkin method -- 3.2. Stabilization by artificial diffusion -- 3.2.1. Artificial viscosity models -- 3.2.2. Discontinuity sensor -- 3.3. Parallel preconditioned Newton-Krylov solvers -- 3.3.1. Jacobian sparsity pattern -- 3.3.2. Incomplete LU preconditioning -- 3.3.3. Minimum discarded fill element ordering -- 3.3.4. Coarse scale corrections and the ILU/Coarse scale preconditioner -- 3.3.5. Parallelization -- 4. Applications -- 4.1. Aeroacoustics and Kelvin-Helmholtz instability -- 4.2. Implicit large Eddy simulations of flow past airfoil -- 4.3. Transonic turbulent flows. 4.4. Flapping elliptic wings -- 5. Acknowledgements -- References -- Chapter 6: Weighted Non-Oscillatory Limiters for Runge-Kutta Discontinuous Galerkin Methods Jianxian Qiu -- 1. Introduction -- 2. Description of Troubled-Cell Indicators -- 3. WENO Reconstruction as a Limiter for the RKDG Method -- 3.1. WENO reconstruction in one dimensional case -- 3.2. WENO reconstruction in two dimensional case -- 4. HWENO Reconstruction as a Limiter for the RKDG Method -- 4.1. HWENO reconstruction in one dimensional case -- 4.2. HWENO reconstruction in two dimensional case -- 5. Numerical Results -- 6. Concluding Remarks -- References -- Chapter 7: A Venerable Family of Discontinuous Galerkin Schemes for Diffusion Revisited Bram van Leer, Marcus Lo, Rita Gitik and Shohei Nomura -- 1. Introduction -- 2. The ( ,µ)-family -- 3. Operator Form and Fourier Transform -- 4. The ( , µ) Playing Field -- 4.1. The line + µ = 0 -- 4.2. The line + µ = 5 2 -- 4.3. The line - µ = -2 -- 5. Stability Range -- 6. Two Newer Schemes -- 6.1. Recovery scheme ( 1 4, 9 4) -- 6.2. Second Bassi-Rebay scheme (-1,3) -- 7. Schemes Outside the Family -- 7.1. RDG-2x -- 7.2. Poor Man's Recovery scheme -- 7.3. LDG -- 8. Numerical Test -- 9. Conclusion -- References -- Chapter 8: PNPM Schemes on Unstructured Meshes for Time-Dependent Partial Differential Equations Michael Dumbser -- 1. Introduction -- 1.1. Historic background -- 1.2. Governing PDE -- 2. The Unified PNPM Reconstruction Operator on General Unstructured Meshes -- 3. An Approach for High-Order One-Step Time- Discretization of PDE Systems with Stiff Source Terms -- 4. The Fully Discrete PNPM Method -- 4.1. Algorithm summary -- 5. Applications -- 5.1. Compressible Navier-Stokes equations -- 5.1.1. Governing PDE -- 5.1.2. Numerical convergence study -- 5.1.3. Laminar high Reynolds number boundary layer flow. 5.1.4. Compressible mixing layer in 2D -- 5.2. The Baer-Nunziato model of compressible multi-phase flow -- 5.2.1. Governing PDE -- 5.2.2. A spherical explosion problem -- 6. Concluding Remarks -- References -- Chapter 9: High-Order Finite-Volume Discretization of the Euler Equations on Unstructured Meshes Carl Ollivier-Gooch and Chris Michalak -- 1. Introduction -- 2. Reconstruction -- 2.1. Mathematical basis -- 2.2. Conditioning of the least-squares system -- 3. Limiting for Discontinuous Solutions -- 3.1. Applying limiter to a high-order reconstruction -- 3.2. Accuracy and limiter functions -- 3.3. Preventing unnecessary limiter activation -- 3.3.1. Boundary treatment -- 4. Efficient Convergence -- 4.1. Forming the high-order Jacobian matrix -- 4.2. Preconditioning -- 5. Verification and Results -- 5.1. Ringleb's flow -- 5.2. Limiter behavior for transonic airfoil Flows -- 5.2.1. Accuracy -- 5.2.2. Shock monotonicity -- 5.2.3. Convergence -- 5.3. Explicit Jacobian -- 5.3.1. Cost of evaluating the explicit Jacobian -- 5.3.2. Quality of preconditioning -- 5.3.3. Overall memory and computational cost -- 6. Discussion -- 6.1. Directions for future development -- Acknowledgments -- References -- Chapter 10: A Biased Short Review of Residual Distribution Schemes for Hyperbolic Problems Rémi Abgrall -- 1. Introduction -- 2. Reinterpretation of Finite Volume Schemes -- 3. Residual Distribution Schemes -- 3.1. Case of scalar problems -- 3.2. Extension to systems -- 4. Numerical Examples -- 4.1. Role of the filtering parameter -- 4.2. Compressible flow examples -- 4.2.1. Subsonic flows -- 4.2.2. Scramjet -- 5. Extensions -- 5.1. Unsteady problems -- 5.2. Viscous problems -- 6. Conclusions and Perspectives -- Acknowledgments -- References -- Chapter 11: Radial Basis Function-Based Differential Quadrature (RBF-DQ) Method and Its Applications Chang Shu. 1. Introduction -- 2. Radial Basis Functions (RBFs) for Function Approximation -- 3. Differential Quadrature (DQ) Method for Derivative Approximation -- 4. Global Radial Basis Function-based Differential Quadrature (RBF-DQ) Method -- 5. Local Radial Basis Function-based Differential Quadrature (RBF-DQ) Method -- 6. Numerical Accuracy Analysis for Local MQ-DQ Method -- 7. Application of Local RBF-DQ Method to Simulate Incompressible Flows -- 8. Application of Local RBF-DQ Method to Simulate Compressible Inviscid Flows -- 9. Some Numerical Examples -- 9.1 Poisson equation -- 9.2 Comparative study for lid-driven cavity flow -- 9.3 Flow past a sphere -- 9.4 Transonic flow over a NACA 0012 -- 10. Conclusions -- References -- Chapter 12: Stability and Accuracy Analysis of Spatial Discretizations Chris Lacor and Kris Van den Abeele -- 1. Wave Propagation Analysis of 2D Schemes -- 1.1. SV schemes for triangular cells -- 1.1.1. Second-order schemes -- 1.1.2. Third-order schemes -- 1.1.3. Fourth-order schemes -- 1.1.4. Illustration -- 1.2. SD schemes for triangular cells -- 1.2.1. Second-order schemes -- 1.2.2. Third-order schemes -- 1.3. SD schemes for quadrilateral cells -- 1.3.1. Second-order schemes -- 1.3.2. Third-order schemes -- 1.3.3. Higher-order schemes -- 1.3.4. Illustration -- 2. Conclusions -- References -- Chapter 13: Efficient Relaxation Methods for High-Order Discretization of Steady Problems Georg May and Antony Jameson -- 1. Introduction -- 2. Discretization Methods -- 3. Explicit Multistage Methods -- 4. Implicit Relaxation Methods -- 4.1. Newton-Krylov methods -- 4.2. Implicit Schemes with Finite Time Steps -- 4.3. Matrix-free methods -- 4.4. Preconditioning -- 5. Multilevel Methods -- 5.1. Geometric multigrid -- 5.2. Multi-p methods -- 5.3. Hybrid multilevel schemes -- 6. Conclusion -- References. Chapter 14: High-Order Methods by Correction Procedures Using Reconstructions H. T. Huynh.
Key Features:The first book that covers a wide variety of adaptive high-order CFD methodsDicusses a comprehensive list of topics in adaptive high-order methods, including the methodology, analysis, error estimate, hp-adaptation, solution algorithms, parallel implementation, discontinuity-capturing and aerospace applicationsHighlights the challenges and pacing items in the proliferation of adaptive high order methods in the CFD community.
9789814313193
Differential equations -- Numerical solutions -- Data processing.
Fluid dynamics -- Data processing.
Electronic books.
QA911 -- .A33 2011eb
532.050285
Adaptive High-Order Methods in Computational Fluid Dynamics. - 1 online resource (471 pages) - Advances in Computational Fluid Dynamics Ser. ; v.2 . - Advances in Computational Fluid Dynamics Ser. .
Intro -- CONTENTS -- Preface -- Chapter 1: Discontinuous Galerkin for Turbulent Flows Francesco Bassi, Lorenzo Botti, Alessandro Colombo, Antonio Ghidoni And Stefano Rebay -- 1. Introduction -- 2. DG Solution of the RANS and k-! Equations -- 2.1. Governing equations -- 2.1.1. Surface boundary condition for -- 2.2. DG space discretization -- 2.2.1. Orthonormal and hierarchical basis functions -- 2.3. Time integration -- 2.3.1. Linearly implicit Runge-Kutta schemes -- 2.4. Shock-capturing approach -- 3. Numerical Results -- 3.1. L1T2 3-element airfoil -- 3.2. ONERA M6 wing -- 3.3. DPWIII W1 wing -- 3.4. DLR-F6 wing-body configuration -- 3.5. NASA 65 sweep delta wing -- 4. Final Remarks -- Acknowledgments -- References -- Chapter 2: Massively Parallel Solution Techniques for Higher-Order Finite-Element Discretizations in CFD Laslo T. Diosady and David L. Darmofal -- 1. Introduction -- 2. Schwarz Methods -- 2.1. The case of two subdomains -- 2.2. The case of many subdomains -- 2.3. Large scale CFD applications -- 3. Schur Complement Methods -- 3.1. An interface problem -- 3.2. Classical substructuring methods -- 3.3. Approximate factorizations -- 4. Neumann-Neumann Methods -- 4.1. BDDC and FETI-DP -- 5. Numerical Results -- References -- Chapter 3: Error Estimation and hp-Adaptive Mesh Refinement for Discontinuous Galerkin Methods Tobias Leicht and Ralf Hartmann -- 1. Introduction -- 2. Flow Problem and Its Discretization -- 3. Error Estimation and Local Error Indicators -- 3.1. Single target quantities -- 3.2. Multiple target quantities -- 4. Adaptation Strategies -- 4.1. Comparison of h- and p-type mesh refinement -- 4.2. Combined hp-refinement -- 4.3. hp-indicator in 1D -- 4.4. hp-indicator in multiple dimensions and for systems of equations -- 4.5. Anisotropic h-subdivision -- 5. Adaptive Refinement Algorithm -- 6. Numerical Results. 6.1. Laminar subsonic flow around an airfoil -- 6.2. Transonic flow around an airfoil -- 6.3. Laminar flow around a delta wing -- 6.4. L1T2 three element high lift configuration -- 6.5. Subsonic turbulent flow around the DLR-F6 wing-body configuration -- 7. Conclusion and Outlook -- Acknowledgments -- References -- Chapter 4: A Runge-Kutta based Discontinuous Galerkin Method with Time Accurate Local Time Stepping Gregor J. Gassner, Florian Hindenlang and Claus-Dieter Munz -- 1. Introduction -- 2. General Formulation -- 2.1. The semi discrete form -- 2.2. The fully discrete form -- 2.3. The predictor-corrector formulation -- 3. Beyond the Global Time Integration Paradigm -- 3.1. Time-accurate local time stepping -- 4. Results -- 4.1. Time accuracy -- 4.2. Accuracy for non-linear problems -- 4.3. Application -- 5. Conclusion -- Acknowledgments -- References -- Chapter 5: High-Order Discontinuous Galerkin Methods for CFD Jaime Peraire and Per-Olof Persson -- 1. Introduction -- 2. Governing Equations -- 2.1. The compressible Navier-Stokes equations -- 2.2. Turbulence modeling -- 2.3. Mapping-based ALE formulation for deformable domains -- 2.3.1. The mapping -- 2.3.2. Transformed equations -- 2.3.3. Geometric conservation law -- 3. Numerical Methods -- 3.1. The compact Discontinuous Galerkin method -- 3.2. Stabilization by artificial diffusion -- 3.2.1. Artificial viscosity models -- 3.2.2. Discontinuity sensor -- 3.3. Parallel preconditioned Newton-Krylov solvers -- 3.3.1. Jacobian sparsity pattern -- 3.3.2. Incomplete LU preconditioning -- 3.3.3. Minimum discarded fill element ordering -- 3.3.4. Coarse scale corrections and the ILU/Coarse scale preconditioner -- 3.3.5. Parallelization -- 4. Applications -- 4.1. Aeroacoustics and Kelvin-Helmholtz instability -- 4.2. Implicit large Eddy simulations of flow past airfoil -- 4.3. Transonic turbulent flows. 4.4. Flapping elliptic wings -- 5. Acknowledgements -- References -- Chapter 6: Weighted Non-Oscillatory Limiters for Runge-Kutta Discontinuous Galerkin Methods Jianxian Qiu -- 1. Introduction -- 2. Description of Troubled-Cell Indicators -- 3. WENO Reconstruction as a Limiter for the RKDG Method -- 3.1. WENO reconstruction in one dimensional case -- 3.2. WENO reconstruction in two dimensional case -- 4. HWENO Reconstruction as a Limiter for the RKDG Method -- 4.1. HWENO reconstruction in one dimensional case -- 4.2. HWENO reconstruction in two dimensional case -- 5. Numerical Results -- 6. Concluding Remarks -- References -- Chapter 7: A Venerable Family of Discontinuous Galerkin Schemes for Diffusion Revisited Bram van Leer, Marcus Lo, Rita Gitik and Shohei Nomura -- 1. Introduction -- 2. The ( ,µ)-family -- 3. Operator Form and Fourier Transform -- 4. The ( , µ) Playing Field -- 4.1. The line + µ = 0 -- 4.2. The line + µ = 5 2 -- 4.3. The line - µ = -2 -- 5. Stability Range -- 6. Two Newer Schemes -- 6.1. Recovery scheme ( 1 4, 9 4) -- 6.2. Second Bassi-Rebay scheme (-1,3) -- 7. Schemes Outside the Family -- 7.1. RDG-2x -- 7.2. Poor Man's Recovery scheme -- 7.3. LDG -- 8. Numerical Test -- 9. Conclusion -- References -- Chapter 8: PNPM Schemes on Unstructured Meshes for Time-Dependent Partial Differential Equations Michael Dumbser -- 1. Introduction -- 1.1. Historic background -- 1.2. Governing PDE -- 2. The Unified PNPM Reconstruction Operator on General Unstructured Meshes -- 3. An Approach for High-Order One-Step Time- Discretization of PDE Systems with Stiff Source Terms -- 4. The Fully Discrete PNPM Method -- 4.1. Algorithm summary -- 5. Applications -- 5.1. Compressible Navier-Stokes equations -- 5.1.1. Governing PDE -- 5.1.2. Numerical convergence study -- 5.1.3. Laminar high Reynolds number boundary layer flow. 5.1.4. Compressible mixing layer in 2D -- 5.2. The Baer-Nunziato model of compressible multi-phase flow -- 5.2.1. Governing PDE -- 5.2.2. A spherical explosion problem -- 6. Concluding Remarks -- References -- Chapter 9: High-Order Finite-Volume Discretization of the Euler Equations on Unstructured Meshes Carl Ollivier-Gooch and Chris Michalak -- 1. Introduction -- 2. Reconstruction -- 2.1. Mathematical basis -- 2.2. Conditioning of the least-squares system -- 3. Limiting for Discontinuous Solutions -- 3.1. Applying limiter to a high-order reconstruction -- 3.2. Accuracy and limiter functions -- 3.3. Preventing unnecessary limiter activation -- 3.3.1. Boundary treatment -- 4. Efficient Convergence -- 4.1. Forming the high-order Jacobian matrix -- 4.2. Preconditioning -- 5. Verification and Results -- 5.1. Ringleb's flow -- 5.2. Limiter behavior for transonic airfoil Flows -- 5.2.1. Accuracy -- 5.2.2. Shock monotonicity -- 5.2.3. Convergence -- 5.3. Explicit Jacobian -- 5.3.1. Cost of evaluating the explicit Jacobian -- 5.3.2. Quality of preconditioning -- 5.3.3. Overall memory and computational cost -- 6. Discussion -- 6.1. Directions for future development -- Acknowledgments -- References -- Chapter 10: A Biased Short Review of Residual Distribution Schemes for Hyperbolic Problems Rémi Abgrall -- 1. Introduction -- 2. Reinterpretation of Finite Volume Schemes -- 3. Residual Distribution Schemes -- 3.1. Case of scalar problems -- 3.2. Extension to systems -- 4. Numerical Examples -- 4.1. Role of the filtering parameter -- 4.2. Compressible flow examples -- 4.2.1. Subsonic flows -- 4.2.2. Scramjet -- 5. Extensions -- 5.1. Unsteady problems -- 5.2. Viscous problems -- 6. Conclusions and Perspectives -- Acknowledgments -- References -- Chapter 11: Radial Basis Function-Based Differential Quadrature (RBF-DQ) Method and Its Applications Chang Shu. 1. Introduction -- 2. Radial Basis Functions (RBFs) for Function Approximation -- 3. Differential Quadrature (DQ) Method for Derivative Approximation -- 4. Global Radial Basis Function-based Differential Quadrature (RBF-DQ) Method -- 5. Local Radial Basis Function-based Differential Quadrature (RBF-DQ) Method -- 6. Numerical Accuracy Analysis for Local MQ-DQ Method -- 7. Application of Local RBF-DQ Method to Simulate Incompressible Flows -- 8. Application of Local RBF-DQ Method to Simulate Compressible Inviscid Flows -- 9. Some Numerical Examples -- 9.1 Poisson equation -- 9.2 Comparative study for lid-driven cavity flow -- 9.3 Flow past a sphere -- 9.4 Transonic flow over a NACA 0012 -- 10. Conclusions -- References -- Chapter 12: Stability and Accuracy Analysis of Spatial Discretizations Chris Lacor and Kris Van den Abeele -- 1. Wave Propagation Analysis of 2D Schemes -- 1.1. SV schemes for triangular cells -- 1.1.1. Second-order schemes -- 1.1.2. Third-order schemes -- 1.1.3. Fourth-order schemes -- 1.1.4. Illustration -- 1.2. SD schemes for triangular cells -- 1.2.1. Second-order schemes -- 1.2.2. Third-order schemes -- 1.3. SD schemes for quadrilateral cells -- 1.3.1. Second-order schemes -- 1.3.2. Third-order schemes -- 1.3.3. Higher-order schemes -- 1.3.4. Illustration -- 2. Conclusions -- References -- Chapter 13: Efficient Relaxation Methods for High-Order Discretization of Steady Problems Georg May and Antony Jameson -- 1. Introduction -- 2. Discretization Methods -- 3. Explicit Multistage Methods -- 4. Implicit Relaxation Methods -- 4.1. Newton-Krylov methods -- 4.2. Implicit Schemes with Finite Time Steps -- 4.3. Matrix-free methods -- 4.4. Preconditioning -- 5. Multilevel Methods -- 5.1. Geometric multigrid -- 5.2. Multi-p methods -- 5.3. Hybrid multilevel schemes -- 6. Conclusion -- References. Chapter 14: High-Order Methods by Correction Procedures Using Reconstructions H. T. Huynh.
Key Features:The first book that covers a wide variety of adaptive high-order CFD methodsDicusses a comprehensive list of topics in adaptive high-order methods, including the methodology, analysis, error estimate, hp-adaptation, solution algorithms, parallel implementation, discontinuity-capturing and aerospace applicationsHighlights the challenges and pacing items in the proliferation of adaptive high order methods in the CFD community.
9789814313193
Differential equations -- Numerical solutions -- Data processing.
Fluid dynamics -- Data processing.
Electronic books.
QA911 -- .A33 2011eb
532.050285