Parallel Computational Fluid Dynamics '99

Towards Teraflops, Optimization and Novel Formulations

D. Keyes, A. Ecer, N. Satofuka, P. Fox, Jacques Periaux

• Publisher: North Holland
• Year: 2000
• Print ISBN: 9780444828514
• eBook ISBN: 9780080538389
• Topic: Mathematics
• Subtopic: Mathematical Analysis
• Index: Mathematics

Contributed presentations were given by over 50 researchers representing the state of parallel CFD art and architecture from Asia, Europe, and North America. Major developments at the 1999 meeting were: (1) the effective use of as many as 2048 processors in implicit computations in CFD, (2) the acceptance that parallelism is now the 'easy part' of large-scale CFD compared to the difficulty of getting good per-node performance on the latest fast-clocked commodity processors with cache-based memory systems, (3) favorable prospects for Lattice-Boltzmann computations in CFD (especially for problems that Eulerian and even Lagrangian techniques do not handle well, such as two-phase flows and flows with exceedingly multiple-connected demains with a lot of holes in them, but even for conventional flows already handled well with the continuum-based approaches of PDEs), and (4) the nascent integration of optimization and very large-scale CFD. Further details of Parallel CFD'99, as well as other conferences in this series, are available at http://www.parcfd.org

CONTRIBUTED PAPERS

Efficient Parallel Implementation of a Compact Higher-Order Maxwell Solver Using Spatial Filtering

Ramesh K. Agarwal, National Institute for Aviation Research, Wichita State University, Wichita, KS 67260-0093, USA

This paper describes the parallel implementation of a Maxwell equations solver on a cluster of heterogeneous workstations. The Maxwell solver, designated ANTHEM, computes the electromagnetic scattering by two-dimensional perfectly-conducting and dielectric bodies by solving Maxwell equations in frequency domain. The governing equations are derived by writing Maxwell equations in conservation-law form for scattered field quantities and then assuming a single-frequency incident wave. A pseudo-time variable is introduced, and the entire set of equations is driven to convergence by an explicit/point-implicit four-stage Runge-Kutta time-marching finite-volume scheme. Higher-order implicit spatial filtering is used in conjunction with a higher-order compact scheme for spatial discretization, to filter undesirable oscillations. Far-field boundary conditions are computed using the method of Giles and Shu. Results are compared with known analytic solutions and the method-of-moments. The results indicate that, although compact schemes satisfy the stringent requirements of an accurate electromagnetic computation, spatial filtering is important as it provides an excellent alternative to grid refinement at a fraction of the computational cost. Parallelization on heterogeneous workstations is accomplished by using PVM software for process control and communication. Excellent parallel efficiency is obtained, although it is somewhat dependent on the domain decomposition strategy.

1 INTRODUCTION

Recently, there has been much interest in developing numerical methods for accurate determination of electromagnetic signatures to assist in the design and analysis of low observables. The method-of-moments (MoM) has long been used for calculation of surface currents for predicting radar-cross-sections (RCS) of scattering bodies. Although MoM has been established as the most direct and accurate means of predicting RCS of two-dimensional bodies and bodies of revolution, in general, MoM is difficult to apply to arbitrary three-dimensional bodies and geometrically complex dielectrics, and loses accuracy for high-frequency incident waves. In recent years, alternatives to MoM have been developed. Many of these new techniques are based on the landmark contribution of Yee [1]. Finite-difference (FD) techniques have been developed by Goorjian [2], Taflove [3], Shankar et al. [4], and Britt [5], among others. Finite-element methods (FEM) have been applied by McCartin et al. [6] and Bahrmasel and Whitaker [7], among others. Hybrid FD/MoM and FEM/MoM techniques have also been investigated by Taflove and Umashankar [8], and Wang et al. [9] respectively. All of these alternatives have the potential to overcome one or more of the limitations of MoM techniques.

Recently, a new computational electromagnetics (CEM) method has been presented for computing solutions to Maxwell Equations [10]. In this method, Maxwell equations are cast in the hyperbolic conservation law form in curvilinear coordinates. The equations are solved in the time domain using the method of lines, which decouples the temporal terms from the spatial terms. For frequency domain calculations, time dependence is taken out of the conservation form of the equations by assuming a single frequency incident wave, and a pseudo-time variable is introduced; this formulation then allows the same algorithm to be applicable for frequency domain calculations as employed for time domain calculations. An explicit node based finite volume algorithm is developed wherein the spatial terms are discretized using a four-stage explicit/point-implicit Runge-Kutta time stepping scheme. A sixth-order explicit compact dissipation operator is added to stabilize the algorithm and damp the unwanted oscillations. A novel analytic treatment is developed for both the dielectric and far-field radiation boundary conditions. The CEM solver based on this algorithm is capable of computing scattering by geometrically complex two-dimensional dielectric bodies in both the frequency domain and time domain. The CEM solver, designated ANTHEM, has been validated by performing computations in frequency domain for perfectly conducting and dielectric scattering bodies such as cylinders, airfoils, and ogives. The CEM solver ANTHEM was recently parallelized on a cluster of heterogeneous workstations [11] by using PVM software for process control and communication [12]. The influence of domain decomposition strategies on parallel efficiency, especially for dielectric bodies which include material interfaces, was discussed.

In this paper, the convergence characteristics of ANTHEM are significantly enhanced by implementing an implicit sixth-order compact filter suggested by Visbal and Gaitonde [13]. This type of filter is very effective in eliminating the unwanted high-frequency waves, the so-called q-waves [14]. The improved ANTHEM is again parallelized on a cluster of heterogeneous workstations using PVM. Spatial filtering results in 30% fewer iterations needed for convergence to a desired accuracy.

2 GOVERNING EQUATIONS

In the a...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• PREFACE
• ACKNOWLEDGMENTS
• SCIENTIFIC COMMITTEE of the Parallel CFD Conferences 1998-1999
• LIST OF PARTICIPANTS in Parallel CFD’99
• Conference Photograph
• PLENARY PAPERS
• CONTRIBUTED PAPERS