A. B. Morris

Monte Carlo solution of the Boltzmann equation via a discrete velocity model

A new discrete velocity scheme for solving the Boltzmann equation is described. Directly solving the Boltzmann equation is computationally expensive because, in addition to working in physical space, the nonlinear collision integral must also be evaluated in a velocity space. Collisions between each point in velocity space with all other points in velocity space must be considered in order to compute the collision integral most accurately, but this is expensive. The computational costs in the present method are reduced by randomly sampling a set of collision partners for each point in velocity space analogous to the Direct Simulation Monte Carlo (DSMC) method. The present method has been applied to a traveling 1D shock wave. The jump conditions across the shock wave match the Rankine-Hugoniot jump conditions. The internal shock wave structure was compared to DSMC solutions, and good agreement was found for Mach numbers ranging from 1.2 to 10. Since a coarse velocity discretization is required for efficient calculation, the effects of different velocity grid resolutions are examined. Additionally, the new schemes performance is compared to DSMC and it was found that upstream of the shock wave the new scheme performed nearly an order of magnitude faster than DSMC for the same upstream noise. The noise levels are comparable for the same computational effort downstream of the shock wave.

Plume Impingement on a Dusty Lunar Surface

A loosely coupled continuum‐DSMC solver is used to simulate the interaction between the exhaust from a rocket engine with the lunar surface. This problem is of particular interest because the high velocity dust spray can damage nearby structures. The flow field is challenging to simulate because continuum assumptions are no longer valid in the far field, while in the near field DSMC becomes impractical because of the high collision rate. In the current work the high density core of the rocket plume is modeled with NASA’s continuum flow solver, DPLR [1]. Since the two solvers are loosely coupled, i.e. one‐way coupling from the DPLR to the DSMC regimes, the interface between the two solvers is placed in the supersonic region above the surface shock. At the lunar surface, a boundary layer develops and the shear stress causes dust grains to slide and eventually enter the flow field. Robert’s theory of dust entrainment [2,3] is used to predict how much dust is lofted into the flow field by the near surface flo...

Approach for Modeling Rocket Plume Impingement and Dust Dispersal on the Moon

When a lander approaches the lunar surface, the plume from the descent engine impinges on the ground and entrains loose regolith into a high-velocity spray. This problem is simulated with a hybrid ...

Variance Reduction for a Discrete Velocity Gas

We extend a variance reduction technique developed by Baker and Hadjiconstantinou [1] to a discrete velocity gas. In our previous work, the collision integral was evaluated by importance sampling of collision partners [2]. Significant computational effort may be wasted by evaluating the collision integral in regions where the flow is in equilibrium. In the current approach, substantial computational savings are obtained by only solving for the deviations from equilibrium. In the near continuum regime, the deviations from equilibrium are small and low noise evaluation of the collision integral can be achieved with very coarse statistical sampling. Spatially homogenous relaxation of the Bobylev‐Krook‐Wu distribution [3,4], was used as a test case to verify that the method predicts the correct evolution of a highly non‐equilibrium distribution to equilibrium. When variance reduction is not used, the noise causes the entropy to undershoot, but the method with variance reduction matches the analytic curve for the same number of collisions. We then extend the work to travelling shock waves and compare the accuracy and computational savings of the variance reduction method to DSMC over Mach numbers ranging from 1.2 to 10.We extend a variance reduction technique developed by Baker and Hadjiconstantinou [1] to a discrete velocity gas. In our previous work, the collision integral was evaluated by importance sampling of collision partners [2]. Significant computational effort may be wasted by evaluating the collision integral in regions where the flow is in equilibrium. In the current approach, substantial computational savings are obtained by only solving for the deviations from equilibrium. In the near continuum regime, the deviations from equilibrium are small and low noise evaluation of the collision integral can be achieved with very coarse statistical sampling. Spatially homogenous relaxation of the Bobylev‐Krook‐Wu distribution [3,4], was used as a test case to verify that the method predicts the correct evolution of a highly non‐equilibrium distribution to equilibrium. When variance reduction is not used, the noise causes the entropy to undershoot, but the method with variance reduction matches the analytic curve for ...

Improvement of a Discrete Velocity Boltzmann Equation Solver With Arbitrary Post‐Collision Velocities

We present a discrete velocity scheme which solves the Boltzmann equation and show numerical results for homogeneous relaxation problems. Although direct simulation of the Boltzmann equation can be efficient for transient problems, computational costs have restricted its use. A velocity interpolation algorithm enables us to select post‐collision velocity pairs not restricted to those that lie precisely on the grid. This allows efficient evaluation of the replenishing part of the collision integral with reasonable accuracy. In previous work [1] the scheme was demonstrated with the depleting terms evaluated exactly, which made the method of O(N2) where N is the number of grid points in the velocity space. In order to reduce the computational cost, we have developed an acceptance‐rejection scheme to enable more efficient evaluation of the depleting term. We show that the total collision integral can be evaluated accurately in combination with the mapping scheme for the replenishing term. To improve our schem...

Lunar Dust Transport Resulting from Single- and Four-Engine Plume Impingement

When the exhaust plume from a descent engine impinges on the lunar surface, loose regolith can erode and become entrained into a high-velocity spray. These processes are simulated in this work by several integrated models: a hybrid continuum–kinetic solver for the gas flowfield, a coupled two-phase flow model for a polydisperse distribution of grain sizes, and a model for inelastic grain–grain collisions. The continuum regime is modeled with the data-parallel line relaxation code, and the kinetic modeling is done via the direct-simulation Monte Carlo method. Simulation results are first presented for a single-engine lander hovering at different altitudes. Surface stresses and the resulting dust erosion are compared to classical theory, and correction terms are introduced to improve agreement. The velocities of different-sized particles and particle mass fluxes are shown for different hovering altitudes. For a four-engine lander, there are multiple plume–plume and plume–surface interactions that result in ...

Far Field Deposition Of Scoured Regolith Resulting From Lunar Landings

As a lunar lander approaches a dusty surface, the plume from the descent engine impinges on the ground, entraining loose regolith into a high velocity dust spray. Without the inhibition of a background atmosphere, the entrained regolith can travel many kilometers from the landing site. In this work, we simulate the flow field from the throat of the descent engine nozzle to where the dust grains impact the surface many kilometers away. The near field is either continuum or marginally rarefied and is simulated via a loosely coupled hybrid DSMC - Navier Stokes (DPLR) solver. Regions of two-phase and polydisperse granular flows are solved via DSMC. The far field deposition is obtained by using a staged calculation, where the first stages are in the near field where the flow is quasi-steady and the outer stages are unsteady. A realistic landing trajectory is approximated by a set of discrete hovering altitudes which range from 20m to 3m. The dust and gas motions are fully coupled using an interaction model that conserves mass, momentum, and energy statistically and inelastic collisions between dust particles are also accounted for. Simulations of a 4 engine configuration are also examined, and the erosion rates as well as near field particle fluxes are discussed.