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Efficient Two-Dimensional Solution Methods for the Navier-Stokes Equations

ARC2D is a computational fluid dynamics (CFD) program for two-dimensional airfoil and simply connected geometries. The program uses implicit finite-difference techniques to solve two-dimensional Euler equations and Navier-Stokes equations. It is based on the Beam and Warning implicit approximate factorization algorithm in generalized coordinates, in a variety of block or diagonal forms. The methods are either time-accurate (e.g., dual-time-stepping or Runge-Kutta methods) or accelerated non-time-accurate steady-state schemes. The evolution of the solution through time is physically realistic; good solution accuracy is dependent on mesh spacing and boundary conditions.

The mathematical development of ARC2D begins with the strong conservation law form of the two-dimensional Reynolds-Averaged Navier-Stokes (RANS) equations, which admit shock capturing. The Navier-Stokes equations are transformed from Cartesian coordinates to generalized curvilinear coordinates in a manner that permits one computational code to serve a wide variety of physical geometries and grid systems. ARC2D includes an algebraic mixing length model and one-equation models (e.g., Spalart-Allmaras) to approximate the effect of turbulence. In cases of high Reynolds number viscous flows, thin layer approximation can be applied.

The software allows for a variety of solution methods to two-dimensional aerodynamics problems, and includes a number of examples, such as those encountered in flows with shocks. The user has considerable flexibility in assigning geometry and developing grid patterns (includes internal grid generation), as well as in assigning various forms of boundary conditions.

This work was done by Thomas Pulliam of Ames Research Center. This software is available for use. To request a copy, please visit here.