James H. Strickland

A two-dimensional fast solver for arbitrary vortex distributions

A method which is capable of an efficient calculation of the two-dimensional stream function and velocity field produced by a large system of vortices is presented in this report. This work is based on the adaptive scheme of Carrier, Greengard, and Rokhlin with the added feature that the evaluation or target points do not have to coincide with the location of the source or vortex positions. A simple algorithm based on numerical experiments has been developed to optimize the method for cases where the number of vortices N{sub V} differs significantly from the number of target points N{sub T}. The ability to specify separate source and target fields provides an efficient means for calculating boundary conditions, trajectories of passive scalar quantities, and stream-function plots, etc. Test cases have been run to benchmark the truncation errors and CPU time savings associated with the method. For six terms in the series expansions, non-dimensional truncation errors for the magnitudes of the complex potential and velocity fields are on the order of 10{sup {minus}5} and 10{sup {minus}3} respectively. The authors found that the CPU time scales as {radical}(N{sub V}N{sub T}) for N{sub V}/N{sub T} in the range of 0.1 to 10. For {radical}(N{sub V}N{sub T}) less than 200, there is virtually no CPU time savings while for {radical}N{sub V}N{sub T} roughly equal to 20,000, the fast solver obtains solutions in about 1% of the time required for the direct solution technique depending somewhat upon the configuration of the vortex field and the target field.

A gridless solution of the radiative transfer equation for fire and combustion calculations

A gridless technique for the solution of the integral form of the radiative heat flux equation for emitting and absorbing media is presented. The technique was developed to yield solutions of participating media radiative heat transfer in a manner compatible with numerical simulation of the flow and temperature field by gridless vortex and transport element methods, respectively. Additional utility for subgrid analyses, in conjunction with direct numerical simulation or reduced dimensional mixing and turbulence models is noted. Results are compared to established and newly developed closed-form solutions for transport with uniform properties in a planar media. Significant errors in alternative techniques that include simplifications of the governing equations are illustrated by direct comparison. Radiative transfer analyses of highly resolved temperature fields representative of single and multiple (150) flame sheets are performed. Multipole fast solvers for the exponential integrals in the radiative tran...

A 3-D Vortex Code for Parachute Flow Predictions: VIPAR Version 1.0

This report describes a 3-D fluid mechanics code for predicting flow past bluff bodies whose surfaces can be assumed to be made up of shell elements that are simply connected. Version 1.0 of the VIPAR code (Vortex Inflation PARachute code) is described herein. This version contains several first order algorithms that we are in the process of replacing with higher order ones. These enhancements will appear in the next version of VIPAR. The present code contains a motion generator that can be used to produce a large class of rigid body motions. The present code has also been fully coupled to a structural dynamics code in which the geometry undergoes large time dependent deformations. Initial surface geometry is generated from triangular shell elements using a code such as Patran and is written into an ExodusII database file for subsequent input into VIPAR. Surface and wake variable information is output into two ExodusII files that can be post processed and viewed using software such as EnSight{trademark}.

Extension of the gridless vortex method into the compressible flow regime

This paper proposes an extension of the gridless vortex method into the compressible flow regime. The proposed method consists of tracking particles in the flow that carry vorticity, divergence, temperature and density. The particle velocity is given by the Helmholtz decomposition law, which is approximated using the trapezoid rule. The evolution equations for the particle vorticity, divergence, temperature and density are evaluated using finite differences or least squares approximations for all derivatives. The method is applied to an isentropic model problem and compared to solutions obtained using an Eulerian scheme. Difficulties with the least squares approximation and with boundary conditions are discussed. This article was chosen from selected Proceedings of the 4th International Workshop on Vortex Flows and Related Numerical Methods (UC Santa-Barbara, 17-20 March 2002) ed E Meiburg, G H Cottet, A Ghoniem and P Koumoutsakos.

Development of a massively parallel parachute performance prediction code

The Department of Energy has given Sandia full responsibility for the complete life cycle (cradle to grave) of all nuclear weapon parachutes. Sandia National Laboratories is initiating development of a complete numerical simulation of parachute performance, beginning with parachute deployment and continuing through inflation and steady state descent. The purpose of the parachute performance code is to predict the performance of stockpile weapon parachutes as these parachutes continue to age well beyond their intended service life. A new massively parallel computer will provide unprecedented speed and memory for solving this complex problem, and new software will be written to treat the coupled fluid, structure and trajectory calculations as part of a single code. Verification and validation experiments have been proposed to provide the necessary confidence in the computations.

VFLOW2D - A Vorte-Based Code for Computing Flow Over Elastically Supported Tubes and Tube Arrays

A numerical flow model is developed to simulate two-dimensional fluid flow past immersed, elastically supported tube arrays. This work is motivated by the objective of predicting forces and motion associated with both deep-water drilling and production risers in the oil industry. This work has other engineering applications including simulation of flow past tubular heat exchangers or submarine-towed sensor arrays and the flow about parachute ribbons. In the present work, a vortex method is used for solving the unsteady flow field. This method demonstrates inherent advantages over more conventional grid-based computational fluid dynamics. The vortex method is non-iterative, does not require artificial viscosity for stability, displays minimal numerical diffusion, can easily treat moving boundaries, and allows a greatly reduced computational domain since vorticity occupies only a small fraction of the fluid volume. A gridless approach is used in the flow sufficiently distant from surfaces. A Lagrangian remap scheme is used near surfaces to calculate diffusion and convection of vorticity. A fast multipole technique is utilized for efficient calculation of velocity from the vorticity field. The ability of the method to correctly predict lift and drag forces on simple stationary geometries over a broad range of Reynolds numbers is presented.