This work covers the proceedings of an AMS-SIAM Summer Seminar on Applied Mathematics held at Scripps Institution of Oceanography in 1983, whose purpose was to bring scientists interested in computational fluid mechanics together with numerical analysts and mathematicians working in large-scale computations. The complexity of many contemporary problems of fluid mechanics is so great as to tax the capabilities of present-day computers. There is a real need and opportunity for numerical analysis to aid research on the physical problems of achieving optimal utilization of current computers. Fifty lectures were given on subjects equally divided between mathematics and applications. The numerical modeling included geophysical problems of the atmosphere, ocean, and interior of the earth, and planetary, solar, and stellar atmospheres. Applications ranged from idealized turbulence in laboratory convection models to operational weather prediction.Engineering applications included aerodynamics, combustion, and flow in porous media. Recent advances in numerical analysis which have applications to these problems were stressed. These include shock capturing algorithms, spectral methods, boundary treatments, vortex methods, and parallel computing. In addition to specialized research lectures, several speakers gave talks surveying important areas of numerical analysis and computational fluid dynamics.
Part 1: Semi-Lagrangian advective schemes and their use in meteorological modeling by J. R. Bates Adaptive mesh refinement for hyperbolic equations by M. J. Berger Averaged multivalued solutions and time discretization for conservation laws by Y. Brenier Computing with high-resolution upwind schemes for hyperbolic equations by S. R. Chakravarthy and S. Osher Mathematical modeling of the steam-water condensation in a condenser by C. Conca Some theoretical and computational considerations of atmospheric fronts by M. J. P. Cullen and R. J. Purser Numerical solution of Euler's equation by perturbed functionals by S. K. Dey A mathematical model and numerical study of platelet aggregation during blood clotting by A. L. Fogelson Computational methods for discontinuities in fluids by O. A. McBryan Problems and numerical methods of the incorporation of mountains in atmospheric models by F. Mesinger and Z. I. Janjic Discrete shocks for systems of conservation laws by D. Michelson Initial-boundary value problems for incomplete singular perturbations of hyperbolic systems by D. Michelson A mixed finite element method for $3d$ Navier-Stokes equations by J. C. Nedelec Stability of the flow around a circular cylinder to forced disturbances by V. A. Patel Some contributions to the modelling of discontinuous flows by P. Roe Techniques for numerical simulation of large-scale eddies in geophysical fluid dynamics by R. Sadourny Finite difference techniques for nonlinear hyperbolic conservation laws by R. Sanders Conforming finite element methods for incompressible and nearly incompressible continua by L. R. Scott and M. Vogelius Vortex methods and turbulent combustion by J. A. Sethian Numerical solutions of rotating internal flows by C. G. Speziale High resolution TVD schemes using flux limiters by P. Sweby Stability of hyperbolic finite-difference models with one or two boundaries by L. N. Trefethen Matching the Navier-Stokes equations with observations by T. Gal-Chen Dynamics of flame propagation in a turbulent field by A. F. Ghoniem New stability criteria for difference approximations of hyperbolic initial-boundary value problems by M. Goldberg and E. Tadmor A modified finite element method for solving the incompressible Navier-Stokes equations by P. M. Gresho Computational fusion magnetohydrodynamics by R. C. Grimm A finite amplitude eigenmode technique to solve and analyze nonlinear equations by R. Grotjahn Numerical boundary conditions by B. Gustafsson Numerical simulation in three space dimensions of time-dependent thermal convection in a rotating fluid by D. H. Hathaway and R. C. J. Somerville Static rezone methods for tensor-product grids by J. M. Hyman and M. J. Naughton A nonoscillatory shock capturing scheme using flux limited dissipation by A. Jameson; Part 2: The use of spectral techniques in numerical weather prediction by M. Jarraud and A. P. M. Baede Improved flux calculations for viscous incompressible flow by the variable penalty method by H. Kheshgi and M. Luskin TVD schemes in one and two space dimensions by R. J. LeVeque and J. B. Goodman Upwind-difference methods for aerodynamic problems governed by the Euler equations by B. van Leer An MHD model of the earth's magnetosphere by C. C. Wu Application of TVD schemes for the Euler equations of gas dynamics by H. C. Yee, R. F. Warming, and A. Harten Recent applications of spectral methods in fluid dynamics by T. A. Zang and M. Y. Hussaini.