Alfred A. Lorber
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Parallel-Vector Computer Simulation of Navier Stokes
Problems Using a Novel Runge-Kutta Recursion
Research is currently being performed in three main interrelated
areas for computer simulation of viscous flow problems on
supercomputers:
- The development of a new
family of Runge-Kutta time-iterative
recursions for solving the discretized flow problem.
- The formulation of efficient vector-parallel algorithms for
these RK schemes to permit fast scalable parallel computations.
- The development of a graphical user interface to facilitate
application of the simulation on advanced parallel architectures.
In this work, simulation time is reduced by developing novel
parallel RK integration schemes which are shown to achieve both high
floating point execution rates and accelerated convergence. These
schemes are used to solve the non-linear ODE system resulting from the
discretization of a stream function-vorticity formulation of the
compressible Navier-Stokes equations. Various methods of
parallelizing the RK schemes are investigated, leading to computations
in excess of eight billion floating point operations per second. In
addition, a methodology for choosing parameters which provide
accelerated convergence for the RK schemes based on Chebyshev-type
iterative methods for the solution of linear ODE's are developed and
demonstrated. To investigate the program usability issue, a prototype
graphical user interface for use with fluid flow analysis programs has
been written.
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