Kinetic Modeling and Simulation of Hypersonic, Shock-Boundary Layer Interactions using Petascale Computing

Deborah Levin, University of Illinois at Urbana-Champaign

Usage Details

The Boltzmann Equation (BE) of transport represents the most general formulation of gas dynamics, however, direct solutions of the integro-differential equations are only possible for simple cases. In the continuum flow limit, the conservation equations for chemically reacting flows may be modeled using the Navier-Stokes (NS) equations or if the flow is inviscid using Euler's equations. However, in flows with strong shocks, such as occur in hypersonic shock-boundary layers, the steep gradients that are formed and the strong thermochemical nonequilibrium preclude the use of continuum approaches. In such cases, the Direct Simulation Monte Carlo (DSMC) method is a widely used probabilistic particle based method that provides a numerical solution to the BE if its numerical parameters are correctly chosen. In the DSMC method, the flow is modeled by a series of collisions that occur by using simulated or numerical particles that each represents a large number of real molecules. The approach is computationally tractable and inherently parallel because particle collisions and movement are decoupled based on the idea that there are a sufficient number of collisions and the use of a time step that is small compared to the mean time between collisions. Applications of the DSMC approach range from flows in the space environment to vacuum processes where the characteristic length of the flow is of the same order as the mean free path of the molecules.

We have developed an in-house novel DSMC code known as Scalable Unstructured Gas dynamics Adaptive Refinement (SUGAR) which uses Adaptive Mesh Refinement (AMR)/Octree grids to model multi-scale physics, a robust cut cell method to simulate complex geometries, and Message Passing Interface to harness the computational power of modern computing architectures for parallel computing. At present, the SUGAR code can simulate supersonic weakly ionized plasma expansions, hypersonic flows of diatomic gases, and there is an ongoing effort to implement chemical models that would allow for the simulation of gases of practical interest such as air. During the last year under our previous Blue Waters project, "High-performance Computing of Hypersonic, Shock-shock Interactions using Kinetic, Particle Approaches," we were able to model hypersonic flows over embedded geometries, as well as, use the Blue Waters resources to quantify the scaling that we could achieve and identify the present performance bottlenecks. Our ultimate goal is to use Blue Waters to study laminar, boundary layer-shock and shock-shock interactions from hypersonic flows about a double-wedge configuration at a very low Knudsen number. This case is particularly challenging for a number of reasons: (1) The physics of the separating and reattaching flow for the aspect ratio of the model used in the experiments requires 3-D instead of 2-D DSMC simulations which in turn require much higher numbers of particles. (2) Although the Mach number of the flow is relatively low, physical models that take into account thermal and chemical modes of interaction among diatomic gases must be included. (3) A high level of spatial refinement is needed to capture shock-shock and shock-boundary layer interactions that create regions of separation and shear layers. (4) Measurements that we wish to simulate were obtained at conditions of relatively high number density for DSMC. Although the Knudsen number is very low in these flows, comparisons of DSMC with NS simulations continue to show that a kinetic formulation is required to model velocity-slip which is found to affect the separation and reattachment points through the formation of the recirculation bubble in similar measurements. Thus, the problem is computationally very expensive and such simulations can only be performed on a petascale facility such as Blue Waters.