Application of Gaussian Moment Closure to Microscale Flows with Moving Embedded Boundaries

摘要

The application of the Gaussian moment closure to continuum and microscale flows with embedded, and possibly moving, boundaries is considered. The Gaussian moment closure is briefly reviewed, as is an extension that allows for the treatment of flow of diatomic gases. A parallel upwind, finite volume scheme with adaptive mesh refinement using a Roe-type numerical flux function is described for solving the hyperbolic system of partial differential equations arising from this closure on multiblock meshes with embedded and possibly moving boundaries. The purely hyperbolic nature of moment equations makes them particularly insensitive to discretizations involving grids with irregularities. Typical of adaptive mesh-refinement, embedded-boundary, and Cartesian cut-cell treatments, mesh irregularities are difficult to deal with when second derivatives are required by the physical model. Such is the case for the Navier-Stokes equations. Numerical solutions to mathematical descriptions involving second derivatives show significantly degraded solution quality as compared to solutions of first-order quasi-linear moment equations. Solid-wall boundary conditions are implemented via a Knudsen-layer approximation. Comparisons are made between numerical solutions of the Gaussian model on both body-fitted meshes and meshes with embedded boundaries, as well as to experimental and approximate analytic results for a variety of flow problems. The benefits and potential of the proposed approach for unsteady microscale flow applications having complex geometries are clearly demonstrated.