Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations.
This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and readily understand their relative advantages and limitations.
1. Introduction - p. xvii 2. Chapter 1: Introduction to the Theory of Hyperbolic Conservation Laws - p. xxiii 3. Chapter 2: The Riemann Problem: Solvers and Numerical Fluxes - p. 18 4. Chapter 3: Classical Finite Volume Methods - p. 54 5. Chapter 4: Sharpening Methods for Finite Volume Schemes - p. 76 6. Chapter 5: ENO and WENO Schemes - p. 102 7. Chapter 6: Stability Properties of the ENO Method - p. 122 8. Chapter 7: Stability, Error Estimate and Limiters of Discontinuous Galerkin Methods - p. 145 9. Chapter 8: HDG Methods for Hyperbolic Problems - p. 171 10. Abstract - p. 171 11. 1 Introduction - p. 174 12. 2 The Acoustics Wave Equation - p. 174 13. 3 The Elastic Wave Equations - p. 181 14. 4 The Electromagnetic Wave Equations - p. 189 15. 5 Bibliographic Notes - p. 191 16. Acknowledgements - p. 195 17. Chapter 9: Spectral Volume and Spectral Difference Methods - p. 197 18. Chapter 10: High-Order Flux Reconstruction Schemes - p. 226 19. Chapter 11: Linear Stabilization for First-Order PDEs - p. 263 20. Abstract - p. 263 21. 1 Friedrichs’ Systems - p. 266 22. 2 Weak Formulation and Well-Posedness for Friedrichs’ Systems - p. 269 23. 3 Residual-Based Stabilization - p. 273 24. 4 Boundary Penalty for Friedrichs’ Systems - p. 277 25. 5 Fluctuation-Based Stabilization - p. 280 26. Chapter 12: Least-Squares Methods for Hyperbolic Problems - p. 288 27. Chapter 13: Staggered and Colocated Finite Volume Schemes for Lagrangian Hydrodynamics - p. 317 28. Chapter 14: High-Order Mass-Conservative Semi-Lagrangian Methods for Transport Problems - p. 352 29. Chapter 15: Front-Tracking Methods - p. 382 30. Chapter 16: Moretti's Shock-Fitting Methods on Structured and Unstructured Meshes - p. 402 31. Chapter 17: Spectral Methods for Hyperbolic Problems - p. 439 32. Chapter 18: Entropy Stable Schemes - p. 466 33. Abstract - p. 466 34. 1 Entropic Systems of Conservation Laws - p. 468 35. 2 Discrete Approximations and Entropy Stability - p. 471 36. 3 Entropy Stable Schemes for Scalar Conservation Laws - p. 473 37. 4 Semidiscrete Schemes for Systems of Conservation Laws - p. 477 38. 5 Fully Discrete Schemes for Systems of Conservation Laws - p. 484 39. 6 Higher-Order Methods - p. 487 40. 7 Multidimensional Systems of Conservation Laws - p. 488 41. Acknowledgements - p. 490 42. Chapter 19: Entropy Stable Summation-by-Parts Formulations for Compressible Computational Fluid Dynamics - p. 493 43. Abstract - p. 496 44. 1 Introduction - p. 496 45. 2 The Compressible NSE - p. 498 46. 3 SBP Operators - p. 500 47. 4 Semidiscrete and Fully Discrete Entropy Analysis - p. 503 48. 5 Entropy Stable Interior Interface Coupling - p. 505 49. 6 Entropy Stable Solid Wall Boundary Conditions - p. 507 50. 7 Entropy Stable WENO Formulations - p. 510 51. 8 Conservation of Entropy in Curvilinear Coordinates - p. 512 52. 9 Results: Accuracy and Robustness - p. 515 53. 10 Conclusions - p. 521 54. Chapter 20: Central Schemes: A Powerful Black-Box Solver for Nonlinear Hyperbolic PDEs - p. 524 55. Chapter 21: Time Discretization Techniques - p. 548 56. Chapter 22: The Fast Sweeping Method for Stationary Hamilton–Jacobi Equations - p. 583 57. Chapter 23: Numerical Methods for Hamilton–Jacobi Type Equations - p. 601 58. Index - p. 627
Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations.
This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and readily understand their relative advantages and limitations.
1. Introduction - p. xvii 2. Chapter 1: Introduction to the Theory of Hyperbolic Conservation Laws - p. xxiii 3. Chapter 2: The Riemann Problem: Solvers and Numerical Fluxes - p. 18 4. Chapter 3: Classical Finite Volume Methods - p. 54 5. Chapter 4: Sharpening Methods for Finite Volume Schemes - p. 76 6. Chapter 5: ENO and WENO Schemes - p. 102 7. Chapter 6: Stability Properties of the ENO Method - p. 122 8. Chapter 7: Stability, Error Estimate and Limiters of Discontinuous Galerkin Methods - p. 145 9. Chapter 8: HDG Methods for Hyperbolic Problems - p. 171 10. Abstract - p. 171 11. 1 Introduction - p. 174 12. 2 The Acoustics Wave Equation - p. 174 13. 3 The Elastic Wave Equations - p. 181 14. 4 The Electromagnetic Wave Equations - p. 189 15. 5 Bibliographic Notes - p. 191 16. Acknowledgements - p. 195 17. Chapter 9: Spectral Volume and Spectral Difference Methods - p. 197 18. Chapter 10: High-Order Flux Reconstruction Schemes - p. 226 19. Chapter 11: Linear Stabilization for First-Order PDEs - p. 263 20. Abstract - p. 263 21. 1 Friedrichs’ Systems - p. 266 22. 2 Weak Formulation and Well-Posedness for Friedrichs’ Systems - p. 269 23. 3 Residual-Based Stabilization - p. 273 24. 4 Boundary Penalty for Friedrichs’ Systems - p. 277 25. 5 Fluctuation-Based Stabilization - p. 280 26. Chapter 12: Least-Squares Methods for Hyperbolic Problems - p. 288 27. Chapter 13: Staggered and Colocated Finite Volume Schemes for Lagrangian Hydrodynamics - p. 317 28. Chapter 14: High-Order Mass-Conservative Semi-Lagrangian Methods for Transport Problems - p. 352 29. Chapter 15: Front-Tracking Methods - p. 382 30. Chapter 16: Moretti's Shock-Fitting Methods on Structured and Unstructured Meshes - p. 402 31. Chapter 17: Spectral Methods for Hyperbolic Problems - p. 439 32. Chapter 18: Entropy Stable Schemes - p. 466 33. Abstract - p. 466 34. 1 Entropic Systems of Conservation Laws - p. 468 35. 2 Discrete Approximations and Entropy Stability - p. 471 36. 3 Entropy Stable Schemes for Scalar Conservation Laws - p. 473 37. 4 Semidiscrete Schemes for Systems of Conservation Laws - p. 477 38. 5 Fully Discrete Schemes for Systems of Conservation Laws - p. 484 39. 6 Higher-Order Methods - p. 487 40. 7 Multidimensional Systems of Conservation Laws - p. 488 41. Acknowledgements - p. 490 42. Chapter 19: Entropy Stable Summation-by-Parts Formulations for Compressible Computational Fluid Dynamics - p. 493 43. Abstract - p. 496 44. 1 Introduction - p. 496 45. 2 The Compressible NSE - p. 498 46. 3 SBP Operators - p. 500 47. 4 Semidiscrete and Fully Discrete Entropy Analysis - p. 503 48. 5 Entropy Stable Interior Interface Coupling - p. 505 49. 6 Entropy Stable Solid Wall Boundary Conditions - p. 507 50. 7 Entropy Stable WENO Formulations - p. 510 51. 8 Conservation of Entropy in Curvilinear Coordinates - p. 512 52. 9 Results: Accuracy and Robustness - p. 515 53. 10 Conclusions - p. 521 54. Chapter 20: Central Schemes: A Powerful Black-Box Solver for Nonlinear Hyperbolic PDEs - p. 524 55. Chapter 21: Time Discretization Techniques - p. 548 56. Chapter 22: The Fast Sweeping Method for Stationary Hamilton–Jacobi Equations - p. 583 57. Chapter 23: Numerical Methods for Hamilton–Jacobi Type Equations - p. 601 58. Index - p. 627
