An analysis of 3D particle path integration algorithms

Journal Article · Mon Jan 01 04:00:00 EST 1996 · Journal of Computational Physics

DOI:https://doi.org/10.1006/jcph.1996.0015· OSTI ID:191982

Darmofal, D L ^[1]; Haimes, R ^[2]

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1. Texas A & M Univ., College Station, TX (United States)
2. MIT, Cambridge, MA (United States)

Several techniques for the numerical integration of particle paths in steady and unsteady vector (velocity) fields are analyzed. Most of the analysis applies to unsteady vector fields, however, some results apply to steady vector field integration. Multistep, multistage, and some hybrid schemes are considered. It is shown that due to initialization errors, many unsteady particle path integration schemes are limited to third-order accuracy in time. Multistage schemes require at least three times more internal data storage than multistep schemes of equal order. However, for timesteps within the stability bounds, multistage schemes are generally more accurate. A linearized analysis shows that the stability of these integration algorithms are determined by the eigenvalues of the local velocity tensor. Thus, the accuracy and stability of the methods are interpreted with concepts typically used in critical point theory. This paper shows how integration schemes can lead to erroneous classification of critical points when the timestep is finite and fixed. For steady velocity fields, we demonstrate that timesteps outside of the relative stability region can lead to similar integration errors. From this analysis, guidelines for accurate timestep sizing are suggested for both steady and unsteady flows. In particular, using simulation data for the unsteady flow around a tapered cylinder, we show that accurate particle path integration requires timesteps which are at most on the order of the physical timescale of the flow.

• OSTI ID: 191982
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 1 Vol. 123; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
66 PHYSICS
99 GENERAL AND MISCELLANEOUS
ALGORITHMS
INTEGRAL EQUATIONS
NUMERICAL SOLUTION
STEADY FLOW
THREE-DIMENSIONAL CALCULATIONS
UNSTEADY FLOW