Application of the 10-Moment Model to MEMS Flows

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76601/1/AIAA-2005-1398-586.pd

Discontinuous Galerkin Methods for Extended Hydrodynamics.

This dissertation presents a step towards high-order methods for continuum-transition flows. In order to achieve maximum accuracy and efficiency for numerical methods on a distorted mesh, it is desirable that both governing equations and corresponding numerical methods are in some sense compact. We argue our preference for a physical model described solely by first-order partial differential equations called hyperbolic-relaxation equations, and, among various numerical methods, for the discontinuous Galerkin method. Hyperbolic-relaxation equations can be generated as moments of the Boltzmann equation and can describe continuum-transition flows. Two challenging properties of hyperbolic-relaxation equations are the presence of a stiff source term, which drives the system towards equilibrium, and the accompanying change of eigenstructure. The first issue can be solved by an implicit treatment of the source term. To cope with the second difficulty, we develop a space-time discontinuous Galerkin method, based on Huynh’s “upwind moment scheme.” It is called the DG(1)–Hancock method. The DG(1)–Hancock method for one- and two-dimensional meshes is described, and Fourier analyses for both linear advection and linear hyperbolic-relaxation equations are conducted. The analyses show that the DG(1)–Hancock method is not only accurate but efficient in terms of turnaround time in comparison to other semiand fully discrete finite-volume and discontinuous Galerkin methods. Numerical tests confirm the analyses, and also show the properties are preserved for nonlinear equations; the efficiency is superior by an order of magnitude. Subsequently, discontinuous Galerkin and finite-volume spatial discretizations are applied to more practical equations, in particular, to the set of 10-moment equations, which are gas dynamics equations that include a full pressure/temperature tensor among the flow variables. Results for flow around a micro-airfoil are compared to experimental data and to solutions obtained with a Navier–Stokes code, and with particle-based methods. While numerical solutions in the continuum regime for both the 10-moment and Navier–Stokes equations are similar, clear differences are found in the continuum-transition regime, especially near the stagnation point, where the Navier–Stokes code, even when implemented with wall-slip, overestimates the density.Ph.D.Aerospace Engineering and Scientific ComputingUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/58411/4/ysuzuki_1.pd

Generating Inviscid and Viscous Fluid Flow Simulations over a Surface Using a Quasi-simultaneous Technique

A fluid-flow simulation over a computer-generated surface is generated using a quasi-simultaneous technique. The simulation includes a fluid-flow mesh of inviscid and boundary-layer fluid cells. An initial fluid property for an inviscid fluid cell is determined using an inviscid fluid simulation that does not simulate fluid viscous effects. An initial boundary-layer fluid property a boundary-layer fluid cell is determined using the initial fluid property and a viscous fluid simulation that simulates fluid viscous effects. An updated boundary-layer fluid property is determined for the boundary-layer fluid cell using the initial fluid property, initial boundary-layer fluid property, and an interaction law. The interaction law approximates the inviscid fluid simulation using a matrix of aerodynamic influence coefficients computed using a two-dimensional surface panel technique and a fluid-property vector. An updated fluid property is determined for the inviscid fluid cell using the updated boundary-layer fluid property

Small Angle X-Ray Scattering Imaging of Soft Tissue by Using Laue Diffraction Optical System

We performed a feasibility study of Small angle X-ray scattering imaging under the condition of X-ray bright field imaging by Laue crystal diffraction optics of X-ray dark-field imaging that works as an angular analysis. Collagen in chicken tibia containing abundant soft fibrous tissue was chosen as a specimen. In traditional Small angle X-ray scattering optical system, we can derive the structure information of sample by calculating q value which is available from a scattering pattern. Thus it is usually necessary to conduct a 2D scan in order to obtain scattering image. In this paper it is described by a method by which not only small angle X-ray scattering imaging is available directly but also bright-field imaging and dark-field imaging can be obtained at the same time. As the first step, the feasibility of the imaging method should be confirmed by taking pictures of the samples with known periodic length. The preliminary test showed that the collgan’s lattice spacing d is 65.1 nm that was also taken photos by scanning electron microscopy. By rotating Laue angular analyzer by 112 arcseconds small angle X-ray scattering image appeared in bright-field

Vacuum type of SU(2) gluodynamics in maximally Abelian and Landau gauges

The vacuum type of SU(2) gluodynamics is studied using Monte-Carlo simulations in maximally Abelian (MA) gauge and in Landau (LA) gauge, where the dual Meissner effect is observed to work. The dual Meissner effect is characterized by the coherence and the penetration lengths. Correlations between Wilson loops and electric fields are evaluated in order to measure the penetration length in both gauges. The coherence length is shown to be fixed in the MA gauge from measurements of the monopole density around the static quark-antiquark pair. It is also shown numerically that a dimension 2 gluon operator A^+A^-(s) and the monopole density has a strong correlation as suggested theoretically. Such a correlation is observed also between the monopole density and A^2(s)= A^+A^-(s) + A^3A^3(s) condensate if the remaining U(1) gauge degree of freedom is fixed to U(1) Landau gauge (U1LA). The coherence length is determined numerically also from correlations between Wilson loops and A^+A^-(s) and A^2(s) in MA + U1LA gauge. Assuming that the same physics works in the LA gauge, we determine the coherence length from correlations between Wilson loops and A^2(s). Penetration lengths and coherence lengths in the two gauges are almost the same. The vacuum type of the confinement phase in both gauges is near to the border between the type 1 and the type 2 dual superconductors.Comment: 13 pages, 22 figures, RevTeX 4 styl

Ground-state properties of neutron-rich Mg isotopes

We analyze recently-measured total reaction cross sections for 24-38Mg isotopes incident on 12C targets at 240 MeV/nucleon by using the folding model and antisymmetrized molecular dynamics(AMD). The folding model well reproduces the measured reaction cross sections, when the projectile densities are evaluated by the deformed Woods-Saxon (def-WS) model with AMD deformation. Matter radii of 24-38Mg are then deduced from the measured reaction cross sections by fine-tuning the parameters of the def-WS model. The deduced matter radii are largely enhanced by nuclear deformation. Fully-microscopic AMD calculations with no free parameter well reproduce the deduced matter radii for 24-36Mg, but still considerably underestimate them for 37,38Mg. The large matter radii suggest that 37,38Mg are candidates for deformed halo nucleus. AMD also reproduces other existing measured ground-state properties (spin-parity, total binding energy, and one-neutron separation energy) of Mg isotopes. Neutron-number (N) dependence of deformation parameter is predicted by AMD. Large deformation is seen from 31Mg with N = 19 to a drip-line nucleus 40Mg with N = 28, indicating that both the N = 20 and 28 magicities disappear. N dependence of neutron skin thickness is also predicted by AMD.Comment: 15 pages, 13 figures, to be published in Phys. Rev.