Finite-Difference Techniques for Vectorized Fluid Dynamics Calculations

1 Introduction.- 2 Computational Techniques for Solution of Convective Equations.- 2.1 Importance of Convective Equations.- 2.2 Requirements for Convective Equation Algorithms.- 2.3 Quasiparticle Methods.- 2.4 Characteristic Methods.- 2.5 Finite-Difference Methods.- 2.6 Finite-Element Methods.- 2.7 Spectral Methods.- 3 Flux-Corrected Transport.- 3.1 Improvements in Eulerian Finite-Difference Algorithms.- 3.2 ETBFCT: A Fully Vectorized FCT Module.- 3.3 Multidimensional FCT.- 4 Efficient Time Integration Schemes for Atmosphere and Ocean Models.- 4.1 Introduction.- 4.2 Time Integration Schemes for Barotropic Models.- 4.3 Time Integration Schemes for Baroclinic Models.- 4.4 Extension to Ocean Models.- 5 A One-Dimensional Lagrangian Code for Nearly Incompressible Flow.- 5.1 Difficulties Encountered in Lagrangian Methods.- 5.2 Adaptive Gridding in a Lagrangian Calculation.- 5.3 The Algorithm and Structure of ADINC.- 5.4 Examples.- 6 Two-Dimensional Lagrangian Fluid Dynamics Using Triangular Grids.- 6.1 Grid Distortion in Two Dimensions.- 6.2 Use of Reconnection to Eliminate Grid Distortion.- 6.3 Numerical Algorithms.- 6.4 Examples.- 7 Solution of Elliptic Equations.- 7.1 Survey of Standard Techniques.- 7.2 A New Direct Solver: The Stabilized Error Vector Propagation Technique (SEVP).- 7.3 Application of Chebychev Iteration to Non-Self-Adjoint Equations.- 8 Vectorization of Fluid Codes.- 8.1 Speed in Hardware.- 8.2 Speed in Fortran.- 8.3 Problems with Causality.- 8.4 Examples.- 8.5 Summary of Parallelism Principles.- Appendix A.- Appendix B.- Appendix C.- Appendix D.- Appendix E.- References.