Unified Flow Solver

The Unified Flow Solver enables accurate and efficient simulation of gas flows for the entire range of Knudsen numbers.

A variety of gas flow problems are characterized by the presence of rarefied and continuum domains. In a rarefied domain, the mean free path of gas molecules is comparable to (or larger than) a characteristic scale of the system. The rarefied domains are best described by particle models such as Direct Simulation Monte Carlo (DSMC); or, they involve solution of the Boltzmann kinetic equation for the particle distribution function. The continuum flows are best described by Euler or Navier-Stokes equations in terms of average flow velocity, gas density, and temperature and are solved by computational fluid dynamics (CFD) codes. The development of hybrid solvers combining kinetic and continuum models has been an important area of research over the last decade. Potential applications of such solvers range from high-altitude flight to gas flow in microsystems.

The key parameter governing selection of the appropriate physical model is the Knudsen number (Kn), defined as the ratio of the local mean free path to the characteristic size of the system. For flights at high altitude, where the atmospheric density is relatively low, the Kn is essentially a representation of gas density, which is the predominant factor that mandates model selection. For gas flows in microsystems, the small dimension of the system has the most influence on the Kn and therefore dictates selection of a kinetic model.

Until recently, most attempts to create hybrid gas flow solvers have involved coupling DSMC codes with CFD codes.¹ As part of a Small Business Innovation Research project, AFRL partnered with CFD Research Corporation and the Russian Academy of Sciences to develop a Unified Flow Solver (UFS) based on the direct numerical solution (DNS) of the Boltzmann transport equation combined with kinetic schemes for the CFD equations. Choosing a DNS rather than a DSMC-based approach enabled the developers to use similar numerical techniques for the rarefied and continuum domains and thus facilitate coupling of the rarefied and continuum solvers. The UFS can automatically identify kinetic and continuum domains using preestablished criteria, introduce and remove kinetic patches, and select suitable solvers to maximize the accuracy and efficiency of simulations.

Figure 1 shows the key components of the UFS. The Boltzmann kinetic solver implemented in the UFS utilizes the numerical algorithms and computational methods described by Aristov and Tcheremissine.^2,3 The continuum solvers are based on kinetic schemes employing numerical algorithms similar to those of the Boltzmann solver.⁴ The remaining UFS components include criteria for domain decomposition into rarefied and continuum parts and coupling algorithms.