Mesh refinement and modelling errors in flow simulation

Transcription

1 Copyright 1996, American Institute of Aeronautics and Astronautics, Inc. AIAA Meeting Papers on Disc, June 1996 A , N J-1796, N I-0079, F , AIAA Paper Mesh refinement and modelling errors in flow simulation Antony Jameson Princeton Univ., NJ Luigi Martinelli Princeton Univ., NJ AIAA, Fluid Dynamics Conference, 27th, New Orleans, LA, June 17-20, 1996 We present a perspective on verification and validation of CFD tools for analysis and design, identifying principal sources of error due to approximations in the physical model, numerical discretization, and implementation. Issues in algorithm design and trade-offs between modelling accuracy and computational costs are discussed in detail. Computational examples are drawn from the authors work in several applications areas. (Author) Page 1

2 Mesh Refinement and Modelling Errors in Flow Simulation Antony Jameson* and Luigi Martinelli' Department

3 Validation of the numerical method means confirmation that the actual implementation in software converges

4 7 InritcU, Irrataional Linear Figure 1: Hierarchy of Fluid Flow Models tential flow equation

5 Section

6

7 4a: C p after 35 Cycles. i = , C d = Wmt 4b: Convergence. Figure 4: NACA-0012 Airfoil at Mach and a = 1.25 H-CUSP Scheme. OH* WOO MOO IMWI C t 5a: C p after 35 Cycles. _. r

8 L++* *' & 5 _ +JW** <^ 6a: 12.50% Span.

9 In the pressure distributions the pressure coefficient Cr, i p ~ p ~ is plotted with the negative (suction) ^ ^Poo9So pressures upward, so that the upper curve represents the flow over the upper side of a lifting airfoil. The convergence histories show the mean rate of change of the density, and also the total number of supersonic points

10 Sonic Boom Prediction, Micb Fufce Cudtkwnts. Maca

11 This motivates the introduction of dual meshes for

12 0.0 *-' ' Blasius Solution x/l=.23 x/l=.43

13 10 Momentum thickness

14 Also, this flow condition tests the numerical scheme toward its limit of applicability as A/oo -> 0, and the flow becomes incompressible.

15 -2.5 F n. U o Experimcnt(uppcr) H 1.5

16 Figure Jt/Cr 0.1 MVlER-STOCt - [UU* Figure 16: Comparison with Experimental data Laminar Flow over A Delta Wing

17 Pressure Distribution span Pressure Distribution Pressure Distribution oo a: ot U span Figure

18 x/c = x/c = Figure 20: Iso-countours of Computed Total Pressure Coefficient

19 and a period of forced oscillations are chosen to be

20 u. WVISCIO FLOW OVER AN OSCILLATING CVLWOtfl

21 Figure 28: Mach Number Contours. Pitching Airfoil Case. Second Order rme-accurate Scheme*

22 validation problem. This

23 Source [43] [33] [17] [44] [17] Quantity St St St Cpb Cpb B C Table

24 is logically consistent, and that it is approximated by a correct numerical method, which is in turn implemented in a correct computer program. Only then can

25 number wall-bounded flows. AIAA Paper

26 [28]

27 Copyright 1996, American Institute of Aeronautics and Astronautics, Inc.