Skip to main content
Article thumbnail
Location of Repository

Topics in Numerical Computation of Compressible Flow

By Hong-Chia Lin

Abstract

This thesis aims to assist the development of a multiblock implicit Navier-Stokes code for hypersonic flow applications. There are mainly three topics, which concern the understanding of basic Riemann solvers, the implementing of implicit zonal method, and grid adaption for viscous flow. Three problems of Riemann solvers are investigated. The post-shock oscillation problem of slowly moving shocks is examined, especially for Roe's Riemann solver, and possible cures are suggested for both first and second order schemes. The carbuncle phenomenon associated with blunt body calculation is cured by a formula based on pressure gradient, which will not degrade the solutions for viscous calculations too much. The grid-dependent characteristic of current upwind schemes is also demonstrated. Several issues associated with implicit zonal methods are discussed. The effects of having different mesh sizes in different zones when shock present are examined with first order explicit scheme and such effects are shown to be unwanted therefore big mesh size change should be avoided. Several implicit schemes are tested for hypersonic flow. The conservative DDADI scheme is found to be the most robust one. A simple and robust implicit zonal method is demonstrated. A proper treatment of the diagonal Jacobian and choosing the updating method are found to be crucial. The final topic concerns the calculation and grid adaption of viscous flow. We study the linear advection-diffusion equation thoroughly. The results are unfortunately not applicable to Navier-Stokes equations directly. Nevertheless a suggestion on the mesh size control for viscous flow is made and demonstrated. An attempt to construct a cell-vertex TVD scheme is described in the appendix

Publisher: Cranfield University
Year: 1990
OAI identifier: oai:dspace.lib.cranfield.ac.uk:1826/4555
Provided by: Cranfield CERES

Suggested articles

Citations

  1. (1986). A Comparison of Cell Centre and Cell Vertex Scheme for the Steady Euler Equations", doi
  2. (1987). A Composite Grid Generation Code for General 3-D Regions", doi
  3. (1988). A Conservative Approach for Flow Field Calculations on Multiple Grids", doi
  4. (1987). A General Three-Dimensional Elliptic Grid Generation Systems on a Composite Block Structure", doi
  5. (1989). A Genuinely Multidimensional Upwind Cell-Vertex Schemes for Euler Equations", doi
  6. (1962). A Multiple Grid Scheme for Solving the Euler Equations", doi
  7. (1985). A New Class of High Accuracy TVD Schemes for Hyperbolic Conservation Laws", doi
  8. (1985). A Relaxation Approach to Patched-Grid Calculations with the Euler Equations", doi
  9. (1987). A Self-Adaptive Gridding for Inviscid Transonic Projectile Aerodynamics Computation", doi
  10. (1989). A Simple Algebraic Grid Adaption Scheme With Applications to Two- and Three-Dimensional Flow Problems", doi
  11. (1988). A Stability Analysis of Various Patched Grid Interface Conditions for Hyperbolic equations",
  12. (1985). A Survey of Dynamically Adaptive Grids in the Numerical Solutions of Partial Differential Equations", doi
  13. (1985). Accuracy of Schemes with Nonuniform Meshes for Compressible Fluid Flows", doi
  14. (1987). Accuracy of Various Schemes for the Numerical Solution of the Euler Equations Governing Inviscid Compressible Flow",
  15. (1987). Adaptive Finite Difference Methods in in Computational Fluid Dynamics, doi
  16. (1987). Adaptive Grid Generation", doi
  17. (1987). Adaptive Grid Scheme Controlling Cell Area/Volume", doi
  18. (1986). An implicit, Conservative, Zonal Boundary Scheme for Euler Equation Calculations", doi
  19. (1981). Approximate Riemann-Solvers, Parameter Vectors and Difference Schemes", doi
  20. (1987). Artificial Dissipation and Central Difference Schemes for the Euler and Navier-Stokes Equations", doi
  21. (1988). Blunt-Body Flow Simulations", doi
  22. (1986). Characteristic-based schemes: for the Euler -Equations", doi
  23. (1984). Computational Fluid Mechanics and Heat Transfer",
  24. (1983). Computational Methods for Fluid Flow", doi
  25. (1985). Conservative Rezoning Algorithm for Gener alized Two-Dimensional Meshes", doi
  26. (1989). Conservative Treatment of Boundary Interface for Overlaid Grids and Multi-level Grid Adaptions ", doi
  27. (1987). Convection Algorithms Based on a Diagonalization Procedure' for the Multidimensional Euler Equations" , AIAA paper 87-1173. doi
  28. (1986). Discrete Models for the Numerical Analysis of Time Dependent Multidimensional Gas Dynamics", doi
  29. (1974). Discrete Shocks", doi
  30. (1984). Efficient Construction and Utilization of Approximate Riemann Solutions", - in-
  31. (1988). Efficient Implementation of Essentially Non-Oscillatory Shock-capturing Scheme", doi
  32. (1987). Error Estimates for Cell-vertex Solutions of the Compressible Euler Equations",
  33. (1987). Euler Solvers for Three Dimensional Supersonic Flow With Subsonic Pockets", doi
  34. (1959). Finite-Difference Method for Numerical Computation of Discontinuous Solution of the Equations of Fluid Dynamics",
  35. (1987). Finite-Volume Methods for the Compressible Navier-Stokes equations", doi
  36. (1973). Flux Corrected Transport: I. SHASTA, a Fluid Transport Algorithm That Works", doi
  37. (1986). Generating Adaptive Grids with Conventional Grid Scheme", doi
  38. (1986). GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems", doi
  39. (1985). Grading Functions and Mesh Redistribution", doi
  40. (1987). Grid Adaption for Hypersonic Flow", doi
  41. (1984). Grid Adaption for Problems in Fluid Dynamics ", doi
  42. (1987). Grid Adaptive Algorithms for the Solution of the Euler Equations on Irregular Grids", doi
  43. (1984). High Resolution Schemes and the Entropy Conditions", doi
  44. (1983). High Resolution Schemes for Hyperbolic Conservation Laws", doi
  45. (1983). High Resolution. Schemes Using Flux Limiters For Hyperbolic Conservation -Laws", doi
  46. (1989). Higher-Order Godunov Methods for General Systems of Hyperbolic Conservation Laws", doi
  47. (1987). Hybrid Krylov Method for Nonlinear Systems of Equations",
  48. (1973). Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves", doi
  49. (1978). Implicit Finite-Difference Simulation of Flow about Arbitrary Two-Dimensional Geometries", doi
  50. (1989). Local Adaptive Mesh Refinement for Shock Hydrodynamics", doi
  51. (1983). Multi-Dimensional Formulation of CSCM - an Upwind Eigenvector Split Method for the Compressible Navier-Stokes Equations", doi
  52. (1986). Multigrid Algorithms for Compressible Flow Calculations", doi
  53. (1986). Multiple Grid and Osher's Scheme for the Efficient Solution of the Steady State Euler Equations", doi
  54. (1990). Numerical Computation of Internal and External Flows", doi
  55. (1985). Numerical Grid Generation, Foundations and Applications",
  56. (1981). Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time Stepping Scheme", doi
  57. (1985). Numerical Study of a Non-centered scheme with Application to Aerodynamics, doi
  58. (1988). Patched-grid Computations of High---Speed Inlet Flows",
  59. (1983). Self Adjusting Grid Methods For One-Dimensional Hyperbolic Conservation Laws", doi
  60. (1987). Self-Adaptive-Grid Method with Application to Airfoil Flow", doi
  61. (1989). Simple Improvements of an upwind TVD scheme for Hypersonic Flow", doi
  62. (1980). Stable and Entropy Satisfying Approximations for Transonic Flow Calculations", doi
  63. (1983). Technique with AIAA-83-1944. et al
  64. (1988). The Behaviour of Flux Difference Splitting Schemes Near Slowly Moving Shock Waves", in "Numerical Methods for Fluid Dynamics III", eds by
  65. (1984). The Piecewise Parabolic Method (PPM), for Gas Dynamical Simulation", doi
  66. (1981). The Use of the Riemann Problem in Finite difference Schemes", doi
  67. (1988). Three Dimensional Adaptive Grid Generation on a Composite Block Grid", doi
  68. (1985). Three Dimensional CSCM Method for the Compressible wavier-Stokes Equations with Application to Multi-Nozzle Exhaust Flow Field", doi
  69. (1986). Three-Dimensional Adaptive Grid Method", doi
  70. (1987). Three-dimensional Euler Solutions on Blocked Grids Using an Implicit Two-pass Algorithm", doi
  71. (1989). Three-Dimensional Simulation of Hypersonic Flows",
  72. (1973). Toward the Ultimate Conservative Difference Scheme I. the Quest of Monotinicity", doi
  73. (1988). Transonic Computations by Multidomain Techniques with Potential and Euler Solvers", doi
  74. (1982). Upwind Difference Schemes for Hyperbolic Systems of Conservation Laws", doi
  75. (1987). Upwind Formulations for, the Euler Equations ", doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.