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

Deborah Levin, University of Illinois at Urbana-Champaign

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Deborah Levin, Ozgur Tumuklu, Saurabh Sawant, Jonathan Morgan, Nakul Nuwal

Hypersonic flow over configurations such as a double wedge at continuum-like free stream conditions has been a challenging problem because of the multiple shock-shock and shock-boundary layer interaction, separated flows near the hinge, sheer layer, and three-dimensional effcts. These conditions generate a mesh that is highly non-uniform because of very high levels of refinement near the surface due to extremely high flow macroparameter gradients. The Octree cells lying in this region are highly refined as compared to those in the free stream and inside the geometry. Therefore, these cells have to perform a lot of work while others wait idle at the end of each time step. This is unfavorable as the full capacity of all the processors is not utilized and we essentially see a high degree of imbalance of the load among the processors. Furthermore, at high computational loads the communication time starts to increase.

Yet the direct simulation Monte Carlo (DSMC) method of Bird is computationally tractable and inherently parallel because particle collisions and movement are decoupled based on the idea that the flow is composed of binary collisions and the use of a time step that is small compared to the mean time between collisions. The DSMC approach is a widely used probabilistic particle based method that provides a numerical solution to the Boltzmann Equation (BE) of transport if its numerical parameters are correctly chosen. The BE represents the most general formulation of gas dynamics, however, direct solutions of the integro-differential equations are only possible for simple cases. 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. 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. But, in flows with strong shocks, such as occur in hypersonic shock-boundary layers, the steep gradients that are formed and the strong thermo-chemical nonequilibrium preclude the use of continuum approaches. Our goal this year is to extend our DSMC studies to modeling the time-dependent, unsteady nature of the shock-shock and shock-boundary layer interactions.