All Stories

  1. The Treatment of Conservation in the Active Flux method

    Article • June 2020, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  2. A novel numerical scheme based on Active flux method for Hyperbolic heat equations in multidimensional space

    Article • June 2019, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  3. Comparing Active Flux and Discontinuous Galerkin Methods for Compressble Flow

    Article • January 2018, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  4. A Simple Explanation of Superconvergence for Discontinuous Galerkin Solutions to ut+ux=0

    Article • Communications in Computational Physics, March 2017, Global Science Press

    Prof Philip L Roe

  5. Third-order active-flux scheme for advection diffusion: Hyperbolic diffusion, boundary condition, and Newton solver

    Article • Computers & Fluids, February 2016, Elsevier

    Prof Philip L Roe

  6. Continuous adjoint based error estimation and r-refinement for the active-flux method

    Article • January 2016, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe, Krzysztof Fidkowski

  7. Investigations of a New Scheme for Wave Propagation

    Article • June 2015, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  8. New Approaches to Limiting

    Article • June 2015, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  9. Riemann Problem

    Article • January 2015, Springer Science + Business Media

    Prof Philip L Roe

  10. Active Flux for Diffusion

    Article • June 2014, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  11. A new level set model for multimaterial flows

    Article • Journal of Computational Physics, April 2014, Elsevier

    Prof Philip L Roe

  12. A New Level-Set Model for the Representation of Non-Smooth Geometries

    Article • Journal of Scientific Computing, March 2014, Springer Science + Business Media

    Prof Philip L Roe

  13. Understanding Aerodynamics: Arguing from the Real PhysicsD. McLean, Wiley, West Sussex, England, U.K., 2013, 576 pp., $105.

    Article • AIAA Journal, January 2014, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  14. Multidimensional Active Flux Schemes

    Article • June 2013, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  15. Adjoint-Based Error Estimation and Mesh Adaptation for the Active Flux Method

    Article • June 2013, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  16. A Second-Order Finite Volume Method that Reduces Numerical Shockwave Anomalies in One Dimension

    Article • June 2013, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  17. Carbuncle Phenomena and Other Shock Anomalies in Three Dimensions

    Article • AIAA Journal, December 2012, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  18. Entropy-Based Drag-Error Estimation and Mesh Adaptation in Two Dimensions

    Article • Journal of Aircraft, September 2012, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  19. Geometrical shock dynamics and engine unstart

    Article • June 2011, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  20. Shock Capturing Anomalies and the Jump Conditions in One Dimension

    Article • June 2011, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  21. Drag Output Error Estimation Using the Entropy Adjoint Approach

    Article • June 2011, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  22. Active Flux Schemes for Systems

    Article • June 2011, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  23. An Unsteady Entropy Adjoint Approach for Adaptive Solution of the Shallow-Water Equations

    Article • June 2011, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  24. Active Flux Schemes

    Article • January 2011, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  25. Entropy Traces in Lagrangian and Eulerian Calculations

    Article • January 2011, Springer Science + Business Media

    Prof Philip L Roe

  26. Closure to “Numerical Oscillations in Pipe-Filling Bore Predictions by Shock-Capturing Models” by J. G. Vasconcelos, S. J. Wright, and P. L. Roe

    Article • Journal of Hydraulic Engineering, June 2010, American Society of Civil Engineers (ASCE)

    Prof Philip L Roe

  27. Evaluation of Euler Fluxes for Hypersonic Heating Computations

    Article • AIAA Journal, April 2010, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  28. Three-Dimensional Carbuncles and Euler Fluxes

    Article • January 2010, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  29. An Entropy Adjoint Approach to Mesh Refinement

    Article • SIAM Journal on Scientific Computing, January 2010, Society for Industrial & Applied Mathematics (SIAM)

    Prof Philip L Roe

  30. Affordable, entropy-consistent Euler flux functions II: Entropy production at shocks

    Article • Journal of Computational Physics, August 2009, Elsevier

    Prof Philip L Roe

  31. Entropy-Based Mesh Refinement, I: The Entropy Adjoint Approach

    Article • June 2009, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  32. Entropy-Based Mesh Refinement, II: A New Approach to Mesh Movement

    Article • June 2009, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  33. Numerical Oscillations in Pipe-Filling Bore Predictions by Shock-Capturing Models

    Article • Journal of Hydraulic Engineering, April 2009, American Society of Civil Engineers (ASCE)

    Prof Philip L Roe

  34. High-Order Fluctuation-Splitting Schemes for Advection-Diffusion Equations

    Article • January 2009, Springer Science + Business Media

    Prof Philip L Roe

  35. A Proposed Cure to the Carbuncle Phenomenon

    Article • January 2009, Springer Science + Business Media

    Prof Philip L Roe

  36. Evaluation of Euler Fluxes for Hypersonic Flow Computations

    Article • AIAA Journal, January 2009, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  37. Artificial Surface Tension to Stabilize Captured Shockwaves

    Article • June 2008, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  38. An Evaluation of Euler Fluxes for Hypersonic Flow Computations

    Article • June 2007, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  39. Improved Simulation of Flow Regime Transition in Sewers: Two-Component Pressure Approach

    Article • Journal of Hydraulic Engineering, June 2006, American Society of Civil Engineers (ASCE)

    Prof Philip L Roe

  40. Current Issues on Modeling Extreme Inflows in Stormwater Systems

    Article • Journal of Water Management Modeling, January 2006, Computational Hydraulics International

    Prof Philip L Roe

  41. Thin Shock Layer Theory Revisited

    Article • June 2005, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  42. Towards High-Order Fluctuation-Splitting Schemes for Navier-Stokes Equations

    Article • June 2005, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  43. Adaptive-Quadrature Fluctuation-Splitting Schemes for the Euler Equations

    Article • June 2005, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  44. On Carbuncles and Other Excrescences

    Article • June 2005, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  45. Towards a Vorticity Preserving Second Order Finite Volume Scheme Solving the Euler Equations

    Article • June 2005, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  46. A General Theory of Local Preconditioning and Its Application to 2D Ideal MHD Equations

    Article • June 2003, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  47. Bulk viscosity damping for accelerating convergence of low Mach number Euler solvers

    Article • International Journal for Numerical Methods in Fluids, January 2003, Wiley

    Prof Philip L Roe

  48. Toward a General Theory of Local Preconditioning

    Article • June 2002, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  49. Adaptive grid generation by minimizing residuals

    Article • International Journal for Numerical Methods in Fluids, January 2002, Wiley

    Prof Philip L Roe

  50. Vorticity capturing

    Article • June 2001, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  51. A third-order fluctuation splitting scheme that preserves potential flow

    Article • June 2001, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  52. Grids and Solutions from Residual Minimisation

    Article • January 2001, Springer Science + Business Media

    Prof Philip L Roe

  53. Some Properties of Residual Distribution Schemes for the Euler Equations

    Article • January 2001, Springer Science + Business Media

    Prof Philip L Roe

  54. Toward Godunov-Type Methods for Hyperbolic Conservation Laws with Stiff Relaxation

    Article • January 2001, Springer Science + Business Media

    Prof Philip L Roe

  55. A Solution-Adaptive Upwind Scheme for Ideal Magnetohydrodynamics

    Article • Journal of Computational Physics, September 1999, Elsevier

    Prof Philip L Roe

  56. Explorations in Quantum Computing

    Article • AIAA Journal, November 1998, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  57. Linear Bicharacteristic Schemes Without Dissipation

    Article • SIAM Journal on Scientific Computing, September 1998, Society for Industrial & Applied Mathematics (SIAM)

    Prof Philip L Roe

  58. On a Mistaken Notion of “Proper Upwinding”

    Article • Journal of Computational Physics, May 1998, Elsevier

    Prof Philip L Roe

  59. The Harten Memorial Lecture-New Applications of Upwinding

    Article • January 1998, Springer Science + Business Media

    Prof Philip L Roe

  60. Compounded of Many Simples

    Article • January 1998, Springer Science + Business Media

    Prof Philip L Roe

  61. Space-Time Methods for Hyperbolic Conservation Laws

    Article • January 1998, Springer Science + Business Media

    Prof Philip L Roe

  62. On Multidimensional Positively Conservative High-Resolution Schemes

    Article • January 1998, Springer Science + Business Media

    Prof Philip L Roe

  63. Robust Euler codes

    Article • June 1997, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  64. Fluctuation splitting schemes on optimal grids

    Article • June 1997, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  65. Accurate schemes for advection and aeroacoustics

    Article • June 1997, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  66. A Well-Behaved TVD Limiter for High-Resolution Calculations of Unsteady Flow

    Article • Journal of Computational Physics, March 1997, Elsevier

    Prof Philip L Roe

  67. A Brief Introduction to High-Resolution Schemes

    Article • January 1997, Springer Science + Business Media

    Prof Philip L Roe

  68. On Postshock Oscillations Due to Shock Capturing Schemes in Unsteady Flows

    Article • Journal of Computational Physics, January 1997, Elsevier

    Prof Philip L Roe

  69. Progress towards a new computational scheme for aeroacoustics

    Article • June 1995, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  70. An upwind scheme for magnetohydrodynamics

    Article • June 1995, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  71. Book Review Computational Modelling for Fluid Flow and Interfacial Transport

    Article • AIAA Journal, August 1994, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  72. Characteristic-based schemes for dispersive waves I. The method of characteristics for smooth solutions

    Article • Numerical Methods for Partial Differential Equations, September 1993, Wiley

    Prof Philip L Roe

  73. Development of non-dissipative numerical schemes for computational aeroacoustics

    Article • July 1993, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  74. A Multidimensional Flux Function with Applications to the Euler and Navier-Stokes Equations

    Article • Journal of Computational Physics, April 1993, Elsevier

    Prof Philip L Roe

  75. Beyond the Riemann Problem, Part I

    Article • January 1993, Springer Science + Business Media

    Prof Philip L Roe

  76. Adaptive-Mesh Algorithms for Computational Fluid Dynamics

    Article • January 1993, Springer Science + Business Media

    Prof Philip L Roe

  77. Design of optimally smoothing multistage schemes for the euler equations

    Article • Communications in Applied Numerical Methods, October 1992, Wiley

    Prof Philip L Roe

  78. Multi-dimensional schemes for scalar advection

    Article • June 1991, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  79. Design of algorithms for a dispersive hyperbolic problem

    Article • June 1991, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  80. Characteristic time-stepping or local preconditioning of the Euler equations

    Article • June 1991, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  81. Effect of a multi-dimensional flux function on the monotonicity of Euler and Navier-Stokes computations

    Article • June 1991, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  82. A grid-independent approximate Riemann solver with applications to the Euler and Navier-Stokes equations

    Article • January 1991, American Institute of Aeronautics and Astronautics (AIAA)

    Prof Philip L Roe

  83. Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics

    Article • Journal of Computational Physics, April 1986, Elsevier

    Prof Philip L Roe

  84. Discrete Models for the Numerical Analysis of Time-Dependent Multidimensional Gas Dynamics

    Article • January 1986, Springer Science + Business Media

    Prof Philip L Roe

  85. On High-Order Fluctuation-Splitting Schemes for Navier-Stokes Equations

    Article • Springer Science + Business Media

    Prof Philip L Roe

  86. Solving steady mixed conservation laws by elliptic/hyperbolic decomposition

    Article • Springer Science + Business Media

    Prof Philip L Roe

  87. On oscillations due to shock capturing in unsteady flows

    Article • Springer Science + Business Media

    Prof Philip L Roe

  88. Characteristic-based numerical algorithms for stiff hyperbolic relaxation systems

    Article • Springer Science + Business Media

    Prof Philip L Roe