The collaborative team built the UFS on a tree-based Gerris Flow Solver framework with a dynamically adaptive grid and the support of complex solid boundaries.⁵ This architecture allows the shape of a boundary—a spacecraft, for example—to be specified using common geometry tools and inserted into a computational domain as a standard file. The solver automatically generates the computational grid, refining it near the boundary where necessary. In the process of simulation, the grid can automatically adapt (refine or coarsen) according to flow patterns. The steep parameter gradients of shock waves, for example, would dictate a refined grid structure. Depending on local continuum breakdown criteria, the UFS can automatically switch between the deterministic Boltzmann solver and the continuum solvers. The parallelized code can run on multiprocessor systems, solving complex three-dimensional geometries in single-component atomic gases.

The UFS enables accurate and efficient simulation of gas flows for the entire Kn range. Figure 2 (see page 22) illustrates a twodimensional (2-D) simulation of supersonic gas flow (at Mach=3) around a cylinder for three different Kn values. The left side of each image depicts the density profiles, and the right side shows the computational grid and separation of the kinetic (red) and continuum (white) domains. Figure 3 (see page 22) shows UFS simulation results for a nozzle with subsonic flow (Mach=0.2) at the nozzle entry for Kn values=0.01 and 0.001. The UFS employed both the Boltzmann and Euler solvers to perform these calculations. The grid adaptation is based on the parameter δ = log (ρ) + log (μ), where ρ is the gas density and μ is the gas velocity.

In conclusion, the UFS is capable of automatically switching between a deterministic Boltzmann solver and a continuum kinetic solver depending on local gradients of gas density, flow velocity, and temperature. Currently, scientists are developing extensions to the UFS code to treat multicomponent mixtures and molecular gases with internal degrees of freedom. With these extensions, the UFS will be valuable for such practical applications as the simulation of transatmospheric flights at hypersonic velocities and space exploration analysis. The UFS will also be extremely valuable for advanced material processing and semiconductor manufacturing, primarily for flows at low speed, where species transport is induced by temperature gradients in low-pressure plasma processing reactors.

The UFS team has developed a Web site containing additional technical information, including results from case studies and contact information. This content is accessible at http://info-ufs.wpafb.af.mil/UFS_index.html.

Dr. V. I. Kolobov (CFD Research Corporation) and Ms. Melissa Withrow (Azimuth Corporation), of the Air Force Research Laboratory’s Air Vehicles Directorate, wrote this article. For more information, contact TECH CONNECT at (800) 203-6451 or place a request at http://www.afrl.af.mil/techconn_index.asp. Reference document VA-H-05-12.

References

¹ Aristov, V. V., et al. “Construction of a Unified Continuum/Kinetic Solver for Aerodynamic Problems.” AIAA Journal of Spacecraft and Rockets, vol 42, no 4 (2005): 598.
² Aristov, V. V. “Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows.” Dordrecht, Kluwer Academic Publishers, 2001.
³ Tcheremissine, F. G. “Direct Numerical Solution of the Boltzmann Equation.” RAREFIED GAS DYNAMICS: 24th International Symposium on Rarefied Gas Dynamics, AIP Conference Proceedings 762. Monopoli, Bari, Italy (Jul 04): 677.
⁴ Xu, K. “A Gas-Kinetic BGK Scheme for the Navier-Stokes Equations and Its Connection With Artificial Dissipation and Godunov Method.” Journal of Computational Physics, vol 171 (2001): 289- 335.
⁵ Popinet, S. “Gerris: A Tree-Based Adaptive Solver for the Incompressible Euler Equations in Complex Geometries.” Journal of Computational Physics, vol 190 (2003): 572.