Relaxation solution of the full Euler equations

A numerical procedure for the relaxation solution of the full steady Euler equations is described. By embedding the Euler system in a second order surrogate system, central differencing may be used in subsonic regions while retaining matrix forms well suited to iterative solution procedures and convergence acceleration techniques. Hence, this method allows the development of stable, fully conservative differencing schemes for the solution of quite general inviscid flow problems. Results are presented for both subcritical and shocked supercritical internal flows. Comparisons are made with a standard time dependent solution algorithm

An alternative approach to the numerical simulation of steady inviscid flow

A numerical procedure for the efficient simulation of steady inviscid flow is described and its utility demonstrated. Application of the surrogate equation technique allows the formulation of stable, fully conservative, type dependent finite difference equations for use in obtaining numerical solutions to systems of first order partial differential equations, such as the steady state Euler equations or their various approximations. Computational results are presented for the full Euler equations and for the transonic disturbance equations. For the latter case, a computational efficiency greater than that obtained by means of the standard perturbation potential approach is indicated

Surrogate-equation technique for simulation of steady inviscid flow

A numerical procedure for the iterative solution of inviscid flow problems is described, and its utility for the calculation of steady subsonic and transonic flow fields is demonstrated. Application of the surrogate equation technique defined herein allows the formulation of stable, fully conservative, type dependent finite difference equations for use in obtaining numerical solutions to systems of first order partial differential equations, such as the steady state Euler equations. Steady, two dimensional solutions to the Euler equations for both subsonic, rotational flow and supersonic flow and to the small disturbance equations for transonic flow are presented

Convergence acceleration of viscous flow computations

A multiple-grid convergence acceleration technique introduced for application to the solution of the Euler equations by means of Lax-Wendroff algorithms is extended to treat compressible viscous flow. Computational results are presented for the solution of the thin-layer version of the Navier-Stokes equations using the explicit MacCormack algorithm, accelerated by a convective coarse-grid scheme. Extensions and generalizations are mentioned

Multiple-grid convergence acceleration of viscous and inviscid flow computations

A multiple-grid algorithm for use in efficiently obtaining steady solution to the Euler and Navier-Stokes equations is presented. The convergence of a simple, explicit fine-grid solution procedure is accelerated on a sequence of successively coarser grids by a coarse-grid information propagation method which rapidly eliminates transients from the computational domain. This use of multiple-gridding to increase the convergence rate results in substantially reduced work requirements for the numerical solution of a wide range of flow problems. Computational results are presented for subsonic and transonic inviscid flows and for laminar and turbulent, attached and separated, subsonic viscous flows. Work reduction factors as large as eight, in comparison to the basic fine-grid algorithm, were obtained. Possibilities for further performance improvement are discussed

Multiple-grid acceleration of Lax-Wendroff algorithms

A technique for accelerating the convergence of a one-step Lax-Wendroff method to a steady-state solution is discussed and its applicability extended to the more general class of two-step Lax-Wendroff methods. Several two-step methods which lead to quite efficient multiple grid algorithms are discussed. Computational results are presented using the full two dimensional Euler equations for both subcritical and shocked supercritical flows. Extensions and generalizations are mentioned

Current economic and sensitivity analysis for ID slicing of 4 inch and 6 inch diameter silicon ingots for photovoltaic applications

The economics and sensitivities of slicing large diameter silicon ingots for photovoltaic applications were examined. Current economics and slicing add on cost sensitivities are calculated using variable parameters for blade life, slicing yield, and slice cutting speed. It is indicated that cutting speed has the biggest impact on slicing add on cost, followed by slicing yield, and by blade life as the blade life increases

Haldane fractional statistics in the fractional quantum Hall effect

We have tested Haldane's ``fractional-Pauli-principle'' description of excitations around the $\nu = 1/3$ state in the FQHE, using exact results for small systems of electrons. We find that Haldane's prediction $\beta = \pm 1/m$ for quasiholes and quasiparticles, respectively, describes our results well with the modification $\beta_{qp} = 2-1/3$ rather than $-1/3$. We also find that this approach enables us to better understand the {\it energetics\/} of the ``daughter'' states; in particular, we find good evidence, in terms of the effective interaction between quasiparticles, that the states $\nu = 4/11$ and 4/13 should not be stable.Comment: 9 pages, 3 Postscript figures, RevTex 3.0. (UCF-CM-93-005