Efficient iterative methods applied to the solution of transonic flows

Journal Article · Thu Feb 01 04:00:00 EST 1996 · Journal of Computational Physics

DOI:https://doi.org/10.1006/jcph.1996.0031· OSTI ID:263368

Wissink, A M ^[1]; Lyrintzis, A S ^[2]; Chronopoulos, A T ^[3]

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1. Univ. of Minnesota, Minneapolis, MN (United States)
2. Purdue Univ., West Lafayette, IN (United States)
3. Wayne State Univ., Detroit, MI (United States)

We investigate the use of an inexact Newton`s method to solve the potential equations in the transonic regime. As a test case, we solve the two-dimensional steady transonic small disturbance equation. Approximate factorization/ADI techniques have traditionally been employed for implicit solutions of this nonlinear equation. Instead, we apply Newton`s method using an exact analytical determination of the Jacobian with preconditioned conjugate gradient-like iterative solvers for solution of the linear systems in each Newton iteration. Two iterative solvers are tested; a block s-step version of the classical Orthomin(k) algorithm called orthogonal s-step Orthomin (OSOmin) and the well-known GIVIRES method. The preconditioner is a vectorizable and parallelizable version of incomplete LU (ILU) factorization. Efficiency of the Newton-Iterative method on vector and parallel computer architectures is the main issue addressed. In vectorized tests on a single processor of the Cray C-90, the performance of Newton-OSOmin is superior to Newton-GMRES and a more traditional monotone AF/ADI method (MAF) for a variety of transonic Mach numbers and mesh sizes. Newton- GIVIRES is superior to MAF for some cases. The parallel performance of the Newton method is also found to be very good on multiple processors of the Cray C-90 and on the massively parallel thinking machine CM-5, where very fast execution rates (up to 9 Gflops) are found for large problems. 38 refs., 14 figs., 7 tabs.

• OSTI ID: 263368
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 2 Vol. 123; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
99 GENERAL AND MISCELLANEOUS
CONVERGENCE
EFFICIENCY
NEWTON METHOD
PARALLEL PROCESSING
TRANSONIC FLOW