Showing papers by "Stanley Osher published in 1985"

Convergence of Generalized MUSCL Schemes

Abstract: Semidiscrete generalizations of the second order extension of Godunov’s scheme, known as the MUSCL scheme, are constructed, starting with any three point “E” scheme. They are used to approximate scalar conservation laws in one space dimension. For convex conservation laws, each member of a wide class is proven to be a convergent approximation to the correct physical solution. Comparison with another class of high resolution convergent schemes is made.

Large-scale computations in fluid mechanics

Abstract: 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.

Entropy Condition Satisfying Approximations for the Full Potential Equation of Transonic Flow

Abstract: A class of conservative difference approximations for the steady full potential equation was presented. They are, in general, easier to program than the usual density biasing algorithms, and in fact, differ only slightly from them. Rigorous proof indicated that these new schemes satisfied a new discrete entropy inequality, which ruled out expansion shocks, and that they have sharp, steady, discrete shocks. A key tool in the analysis is the construction of a new entropy inequality for the full potential equation itself. Results of some numerical experiments using the new schemes are presented.

A fast, time-accurate, unsteady full potential scheme

Abstract: The unsteady form of the full potential equation is solved in conservation form by an implicit method based on approximate factorization. At each time level, internal Newton iterations are performed to achieve time accuracy and computational efficiency. A local time linearization procedure is introduced to provide a good initial guess for the Newton iteration. A novel flux-biasing technique is applied to generate proper forms of the artificial viscosity to treat hyperbolic regions with shocks and sonic lines present. The wake is properly modeled by accounting not only for jumps in phi, but also for jumps in higher derivatives of phi, obtained by imposing the density to be continuous across the wake. The far field is modeled using the Riemann invariants to simulate nonreflecting boundary conditions. The resulting unsteady method performs well which, even at low reduced frequency levels of 0.1 or less, requires fewer than 100 time steps per cycle at transonic Mach numbers. The code is fully vectorized for the CRAY-XMP and the VPS-32 computers.

Treatment of supersonic flows with embedded subsonic regions

Abstract: A nonlinear method based on the full potential equation in conservation form, cast in an arbitrary coordinate system, has been developed to treat predominantly supersonic flows with embedded subsonic regions. This type of flow field occurs frequently near the fuselage/canopy junction area and wing leading-edge regions for a moderately swept fighter configuration. The method uses the theory of characteristics to accurately monitor the type-dependent flowfield. A conservative switching scheme is developed to handle the transition from the supersonic marching algorithm to a subsonic relaxation procedure, and vice versa. An implicit approximate factorization scheme is employed to solve the finite differenced equation. Results are shown for a few configurations, including a wing/body/wake realistic fighter model having embedded subsonic regions.

Large-Scale Computations in Fluid Mechanics. Lectures in Applied Mathematics Held at San Diego, California on 27 June - 8 July 1983. Volume 22. Part 1,

Abstract: : The purpose of this seminar was to bring scientists interested in computational fluid mechanics together with numerical analysts and mathematicians working in large-scale computations. 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. Fifty lectures were given during the two-week seminar; this book containing the proceedings is the result. The subject matter of the lectures was equally divided between mathematics and applications. In addition to specialized research lectures, several speakers gave talks surveying important areas of numerical analysis and computational fluid dynamics.

Large-scale computations in fluid mechanics; Proceedings of the Fifteenth Summer Seminar on Applied Mathematics, University of California, La Jolla, CA, June 27-July 8, 1983. Parts 1 & 2

Abstract: Papers are presented on such topics as the use of semi-Lagrangian advective schemes in meteorological modeling; computation with high-resolution upwind schemes for hyperbolic equations; dynamics of flame propagation in a turbulent field; a modified finite element method for solving the incompressible Navier-Stokes equations; computational fusion magnetohydrodynamics; and a nonoscillatory shock capturing scheme using flux-limited dissipation. Consideration is also given to the use of spectral techniques in numerical weather prediction; numerical methods for the incorporation of mountains in atmospheric models; techniques for the numerical simulation of large-scale eddies in geophysical fluid dynamics; high-resolution TVD schemes using flux limiters; upwind-difference methods for aerodynamic problems governed by the Euler equations; and an MHD model of the earth's magnetosphere.

Large-scale computations in fluid mechanics : Proceedings of the fifteenth AMS-SIAM summer seminar on applied mathematics held at Scripps Institution of Oceanography

Abstract: 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.