In this paper we present a numerical scheme to simulate a moving rigid body with arbitrary shape suspended in a rarefied gas. The rarefied gas is simulated by solving the Boltzmann equation using a DSMC particle method. The motion of the rigid body is governed by the Newton-Euler equations, where the force and the torque on the rigid body is computed from the momentum transfer of the gas molecules colliding with the body. On the other hand, the motion of the rigid body influences the gas flow in its surroundings. We validate the numerical results by testing the Einstein relation for Brownian motion of the suspended particle. The translational as well as the rotational degrees of freedom are taken into account. It is shown that the numerically computed translational and rotational diffusion coefficients converge to the theoretical values.

The force and torque on a Janus sphere moving in a rarefied gas with a thermal gradient are calculated. The regime of large Knudsen number is considered, with the momenta of impinging gas molecules either obtained from a Chapman-Enskog distribution or from a binary Maxwellian distribution between two opposing parallel plates at different temperature. The reflection properties at the surface of the Janus particle are characterized by accommodation coefficients having constant but dissimilar values on each hemisphere. It is shown that the Janus particle preferentially orients such that the hemisphere with a larger accommodation coefficient points towards the lower temperature. The thermophoretic velocity of the particle is computed, and the influence of the thermophoretic motion on the magnitude of the torque responsible for the particle orientation is studied. The analytical calculations are supported by Direct Simulation Monte Carlo results, extending the scope of the study towards smaller Knudsen numbers. The results shed light on the efficiency of oriented deposition of nanoparticles from the gas phase onto a cold surface. arXiv:1807.04987v1 [physics.flu-dyn]

A refined Monte Carlo (MC) simulation procedure and an Effective Medium Approximation (EMA) are presented for solving the stochastic subsurface flow problem. The refined MC simulation procedure uses analytical means to estimate the sample size by controlling the error incurred in using the sample average in place of its population mean at a chosen confidence level for the pressure head. Also, an unbiased estimator of the pressure head that takes advantage of its correlation with the saturated conductivity to reduce its variance is proposed. This reduced variance results in a smaller width of uncertainty about the predicted pressure head thereby improving the precision. The EMA permits one to solve the stochastic subsurface flow problem in a single run to generate the expected pressure head field with the aid of a field‐scale effective hydraulic conductivity that has a form similar to the Gardner equation. Both the MC and the EMA approaches perform well when applied to example problems taken from the literature.

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