Potential flow codes represent an extremely
efficient and accurate means to compute unseparated flow around complex
geometries. The aim of this code project was to develop a code capable of
rapidly solving potential problems around complex geometries in a rapid,
handsoff manner.
FastAero2D
FastAero2D is a twodimensional potential flow solver
coupled with a simple springmass representation of the structural dynamics.
The 2Dimensional potential flow code exploits and iterative GMRES [6] solver
for rapidly solving the linear system. The potential flow problem is discretized using linear basis functions on flat panels.
Both a thin surface (velocity) formulation and a thick body (Greens Theorem
Thick Body Formulation) have been developed. The unsteady 2D wake vorticity is represented using a linear element freely convecting, selfinfluencing wake. As a result the wake
will convect and rollup under the local velocity
influence (as seen in figure 1).
Figure 1: An example of the
2Dimensional FastAero code applied to a simple heaving wing
motion. In this example the fluid structure interaction is simplified using a leading
edge spring to allow compliance. Although this model is a realistic model of
natural flight, the example lends insight into the effect of leading edge
torsion rod or bone compliance.
FastAero3D
FastAero3D[1] is
an advanced, 3Dimensional unsteady panel method solver developed at MIT. The code incorporates an
accelerated iterative solution approach through the use of the precorrectedFFT[3] and Fast Multipole Algorithms[4] (Matrix Vector Product (MVP) acceleration). Through the use of matrixmultiply
accelerations, intermediate timestep solutions can be performed very rapidly.
As such, the solution of highly resolved unsteady potential flows is possible.
Figure: A plot of the FastAero3D solution around a business jet configuration. In this
image the features of the FastAero3D solution are illustrated. The body of the business jet is represented using a
boundary element surface triangular discretization.
The localized vorticity in the wake is represented using
the vortex particle method (VPM).
References
[1]
Willis, D.J., Peraire, J. White, J.K., A combined pFFTmultipole tree code, unsteady panel method with vortex
particle wakes, 43rd AIAA Aerospace Sciences Meeting and Exhibit, AIAA
20050854, Reno, NV, Jan. 2005.
[2] Willis, D.J., Peraire, J. White, J.K., 'A quadratic basis
function, quadratic geometry, high order panel method' presented at 44th AIAA Aerospace Sciences Meeting, AIAA20061253,
Reno
,
Nevada
, 2006.
[3]
Philips, J.R., White, J.K., A PrecorrectedFFT
Method for Capacitance Extraction of Complicated 3D Structures, Proc. of the
IEEE/ACM International Conference on ComputerAided Design, pp. 268271,
November 1994.
[4] Greengard, L., Rokhlin, V. A
Fast Algorithm for Particle Simulations, J. Comput. Phys. 73, 325 (1987).
[5] Rehbach,
C. Calcul numerique d’ecoulement tridimensionels instationaires avec nappes tourbillonnaires, La Recherche Aerospatiale, pp. 289298, 1977.
[6] Saad, Y. and Schultz, M. H. 1986. GMRES: a
generalized minimal residual algorithm for solving nonsymmetric linea systems.
SIAM
J. Sci. Stat. Comput.
7, 3 (Jul. 1986), 856869.
The current project has been funded by several different sources at different times. We are very thankful to the following funding sources:
SingaporeMIT Alliance (SMA), National Science Foundation (NSF), Natural Science and Engineering Councile of Canada (NSERC), and the Air Force Office of Scientific Research.
