# Hybrid Particle Scheme for Modeling Atmospheric Entry Flows

This project involves the development and application of a hybrid particle scheme, based on the direct simulation Monte Carlo (DSMC) method [1], for aerothermodynamics analysis of atmospheric entry flows involving a wide range of Knudsen number (Kn) regimes. An atmospheric entry vehicle typically experiences a very large range of Kn regimes in different flowfield regions, and at different points in the flight trajectory. Particularly at high altitudes during Earth entry, various portions of the flowfield may simultaneously experience local conditions ranging from free molecular to continuum flow, with much of the flowfield in transition Kn regimes where both the Navier-Stokes equations and free molecular approximations are invalid. This kind of mixed flow is called a multiscale flow. For example, local gradient-based Kn values may by very large within the bow shock, the near-wall portion of the forebody boundary layer, the high-gradient region near the shoulder, and much of the wake region downstream of the vehicle (Figure 1). While the DSMC method typically provides the best combination of efficiency and accuracy in simulating these high Kn regions, DSMC may be prohibitively expensive when applied to low Kn regions - such as the high density inviscid shock layer region - for which continuum stimulation approaches are equally accurate and far more efficient.

Figure 1: An example of multiscale flow mixed with continuum and non-continuum regions.

To provide an optimal balance of accuracy and efficiency in simulating this type of flow, a hybrid scheme is typically used. Here DSMC is applied in high Kn regions, a continuum technique is applied in low Kn regions, and additional calculations are performed for identification of continuum breakdown boundaries and two-way coupled information exchange across these boundaries. Most work on hybrid code development for simulating atmospheric entry type flows has focused on coupling DSMC to a Navier-Stokes computational fluid dynamics (CFD) algorithm [2-5]. In this project, we use DSMC in high Kn regions and apply a new DSMC-based low diffusion (LD) particle method in low Kn continuum regions [6,7].

The hybrid LD-DSMC approach [8] utilized here has several advantages over a hybrid CFD-DSMC scheme: First, the LD method may be implemented with relative ease in an existing DSMC code, and there is no requirement to couple two separate codes within a single numerical framework. Second, strongly coupled information exchange across continuum breakdown boundaries is accomplished very simply by passing particles in both directions between LD and DSMC domains. In contrast, hybrid CFD-DSMC schemes typically allow only weak coupling between continuum and rarefied regions, and complicated additional procedures are required for information exchange between CFD and DSMC modules [2,3]. Third, by tracking particles over the full computational domain, the LD-DSMC scheme allows consistent representation of nonequilibrium vibrational and/or rotational energy distributions across the entire simulated flowfield. Finally, similar or identical probabilistic models for various physical phenomena can potentially be used in the LD method as in DSMC. Such phenomena include rotational-translational and vibrational-translational energy exchange, chemical reactions, condensed phase particulate transport, and gas radiation. The main difference between the LD method and DSMC is the set of procedures used to update particle properties during each time step [6]. In DSMC these update procedures are carried out by selecting particles to participate in binary collisions, whereas in the LD method an alternate set of calculations are performed: First, cell-based quantities, such as bulk velocity and temperature, are computed for each cell by averaging among all particles currently assigned to the cell. These cell quantities are determined as functions of particle temperature and bulk velocity values, which are included in the particle data structure along with other values (such as a position vector and a separate velocity for particle movement) also used in DSMC.

To employ both LD and DSMC methods as a part of the hybrid scheme, it is necessary to determine continuum breakdown to allocate cells to LD and DSMC domains. LD-DSMC domain decomposition is determined based on the following gradient length local Knudsen number,

$Kn_{GLL,max}=max\left(\frac{\lambda}{\rho}\left|\nabla\rho\right|,\frac{\lambda}{T}\left|\nabla T\right|,\frac{\lambda}{a}\left|\nabla u\right|\right)$

After assigning LD and DSMC domains, information must be transferred across each domain boundary. Two layers of overlapping cells are employed along the boundary between DSMC and LD domains, and are designated as buffer regions A and B. These buffer regions are used for information exchange between the DSMC and LD domains. The relative locations of these buffer regions are illustrated in Figure 2.

Figure 2: Location of buffer regions in a hybrid simulation.

The LD-DSMC hybrid scheme is useful to analyze multiscale flows involving a wide range of Knudsen number regimes. Figure 2 shows continuum breakdown domain boundaries based on the maximum gradient length Knudsen number, KnGLL,max. The upper half is from DSMC and the lower half is from the LD-DSMC hybrid simulation. The LD domain includes near-equilibrium regions in the freestream and aftershock, whereas the DSMC domain comprises the remaining portions of the bow shock and wake where a high degree of nonequilibrium is observed.

Figure 3: Contours of maximum gradient length local Knudsen number, KnGLL,max, and domain decomposition regions (upper: DSMC, lower: LD-DSMC hybrid).

### Acknowledgments

Financial support for this work provided by NASA through grant NNX08AD02A.

### References

1. Bird, G. A., Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon Press, Oxford, 1994.
2. Schwartzentruber, T. E., and Boyd, I. D., "A Modular Particle-Continuum Numerical Method for Hypersonic Non-equilibrium Gas Flows," Journal of Computational Physics, Vol. 225, 2007, pp. 1159-1174.
3. Lian, Y.-Y., Wu, J.-S., Cheng, G., and Koomullil, R., "Development of a Parallel Hybrid Method for the DSMC and NS Solver," AIAA Paper 2005-0435, 2005.
4. Garcia, A. L., Bell, J. B., Crutchfield, W. Y., and Alder, B. J., "Adaptive Mesh and Algorithm Refinement Using Direct Simulation Monte Carlo," Journal of Computational Physics, Vol. 154, 1999, pp. 134-155.
5. Hash, D. B., and Hassan, H. A., "Assessment of Schemes for Coupling Monte Carlo and Navier-Stokes Solution Methods," Journal of Thermophysics and Heat Transfer, Vol. 10, No. 2, 1996, pp. 242-249.
6. Burt, J. M., and Boyd, I. D., "A Low Diffusion Particle Method for Simulating Compressible Inviscid Flows," Journal of Computational Physics, Vol. 227, 2008, pp. 4653-4670.
7. Burt, J. M., and Boyd, I. D., "Extension of a Multiscale Particle Scheme to Near-Equilibrium Viscous Flows," AIAA Journal, Vol. 47, No. 6, 2009, pp. 1507-1517.

### Recent Publications

1. Eunji Jun and Boyd. I.D., "Assessment of an All-Particle Hybrid Method for Hypersonic Rarefied Flow", AIAA Paper 2013-1203, Jan. 2013.