Aerodynamics and Design for Ultra-Low Reynolds Number Flight

Chapter 2
What is being sought here, and in the next chapter, is the foundation of a new knowledge
base for airfoils used in ultra-low Reynolds number applications, or, in the very least,
confirmation that the reach of current knowledge extends to this regime. The
exploration of this new regime requires the use of computational tools that are largely
untested for this application. The goal of this chapter is to describe these tools, their
implementation, and the necessary validation completed before the course of research
could begin.
2.2 Incompressible Navier-Stokes Solver
The two-dimensional computational analyses make extensive use of the INS2d
incompressible Navier-Stokes solver developed by Rogers [12, 13]. This code utilizes
the artificial compressibility method, first introduced by Chorin [14], to deal with
incompressible flows. It is capable of both steady and time-accurate computations using
single grids, Chimera over-set grids, and moving grids for relative motion of multiple
solid bodies. Only the single grid, steady and time-accurate capabilities are used in the
current work.
2.2.1 Artificial Compressibility
Navier-Stokes solvers for the compressible flow equations generally require some form
of preconditioning at very low Mach numbers. As the Mach number is decreased, the
flow field approaches the incompressible limit. The character of the governing
equations goes from hyperbolic to elliptic and the speed of sound becomes infinite.
Typical artificial dissipation schemes introduce an amount of spurious dissipation that is
proportional to the speed of sound. Because of this, hyperbolic flow solvers are not well
suited to accurately solve elliptic problems.
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