Unsteady 3D-3V ESBGK Solver in MEMOSA

Graduate Students: Sruti Chigullapalli, Andrew Weaver Collaborators: Dr. Sanjay Mathur, Dr. Gazi Yidirm, Prof. Jayathi Murthy (Purdue PRISM Center)

Development of RF MEMS switches and resonators require improved understanding of unsteady rarefied gas dynamics at the microscale. Accurate simulation of these flows demands new approaches combining both continuum and rarefied fluid dynamics formulations.

Main objectives: Develop unsteady rarefied solver integrated with the FVM MEMOSA and apply it to study PRISM device damping.

Fluid solver [1] in MEMOSA utilizes a unified finite-volume method (FVM) approach for continuum and rarefied domains. The rarefied flow formulation is based on model kinetic equations with ES-BGK collision relaxation with a conservative discrete-ordinate velocity method. This is the first ever unsteady 3D-3V deterministic parallel kinetic solver. The numerical solution approach comprises the discrete velocity method in the velocity space, shown in Fig. 1 and the finite volume method in the physical space.

The solver was verified by comparison with analytical solution for the Couette flow problem in Fig2. and solution from the steady 2D ESBGK solver for 2d Squeeze film damping as shown in Fig3.

Fig 4: Knudsen number based on gap size and local pressure Fig 5: a) Initial mesh b) Deformed mesh c) Deflection and velocity of beam predicted by prism coarse-grain model

Fig 7: Parallel efficiency of the 3D ESBGK solver using spatial domain decomposition: The solver was tested on up to 512 processors on HERA and gave good scaling upto 55. On 128 processors the solver took about 9.6 seconds for each iteration.

Fig 6: Flowfields and streamtraces for 3D ESBGK solution.

(a) Pressure contours on the bottom side of beam with 3d stream traces;

2D slices near (b) anchor and (c) beam center.

REFERENCES:

1) G.A. Bird, Molecular Gas Dynamics and Direct Simulation of Gas Flows. Oxford University Press, New York, 2 rev edition, 1994.

2) S. Chigullapalli, A. Venkattraman, M.S. Ivanov, and A.A. Alexeenko, "Entropy Considerations in Numerical Simulation of Non-Equilibrium Rarefied Flows”, 229 pp: 2139–2158, 2010.

3) S.R. Mathur and J.Y. Murthy, "A pressure-based method for unstructured meshes", Numerical Heat Transfer, Part B: Fundamentals, 31(2) pp: 195-215, 1997

4) S. R. Mathur, L. Sun and J. Y. Murthy. An unstructured finite volume method for incompressible flows with complex immersed boundaries. Numerical Heat Trasfer, Part B: Fundamentals, 58(4):217–241, 2010.also IMECE2009-12917, ASME IMECE, Nov. 2009.

5) L. Mieussens and H. Struchtrup. Numerical comparison of Bhatnagar-Gross-Krook models with proper Prandtl number. Physics of Fluids, 16(8):2797–2813, 2004.

6) B. Shizgal. A gaussian quadrature procedure for use in the solution of the Boltzmann equation and related problems. Journal of Computational Physics, 41:309–328.