FRIDAY, March 2, 2007
Time: 1:00 PM
EDUC 210

Title: Kinetic Schemes for Non-Equilibrium Hypersonic Flows

Wei Liao
Old Dominion University

The modeling and simulation capabilities for non-equilibrium hypersonic flows are crucial to hypersonic and supersonic transport and space exploration. The conventional computational fluid dynamics (CFD) methods based on the Navier-Stokes equations cannot adequately model non-equilibrium hypersonic flows, because some non-equilibrium effects are beyond the validity of the continuum theory. While very effective for high-speed and highly rarefied gases, the direct simulation Monte Carlo (DSMC) method has two severe limitations: the numerical noise due to its stochastic nature and its time-step limited by the mean-free-time. The former limitation makes it very difficult to couple the DSMC method with any deterministic CFD methods. And the latter makes it computationally prohibitive to use the DSMC method in near-continuum regime. It is therefore a challenge to formulate a physics-based CFD method valid for both equilibrium and non-equilibrium hypersonic flows in a wide range of Mach, Knudsen and Reynolds numbers.

In this presentation, I will discuss the gas-kinetic scheme (GKS), a unified approach for the thermodynamical equilibrium and non-equilibrium flow regimes based on the Botzmann equation. The GKS is a finite volume method based on truncation of the Chapman-Enskog expansion. One can use the GKS method to simulate the fully compressible Navier-Stokes equations by maintaining only up to the 2nd order Chapman-Enskog expansion. One can also expend the GKS method to simulate non-equilibrium flows by incorporating higher order terms. The fluxes in the GKS method can include the non-equilibrium effects beyond the linear constitutive relations and Fournier's laws. Therefore, we can use the GKS to model both equilibrium and non-equilibrium flows with non-zero Knudsen number. We will use the GKS to simulate: (1) hypersonic flow past a hollow cylinder flare at Mach number of 9.91 and (2) shock structures of Argon gas at Mach numbers of 8.0, 9.0, and 25.0. Our results clearly show that the gas-kinetic schemes can indeed simulate both the equilibrium and non-equilibrium flows. Finally, I will briefly discuss our plan to develop a large-scale simulation capability based on kinetic methods for realistic engineering applications.