Discontinuous Galerkin Methods for Extended Hydrodynamics.

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dc.contributor.author Suzuki, Yoshifumi en_US
dc.date.accessioned 2008-05-08T19:01:58Z
dc.date.available NO_RESTRICTION en_US
dc.date.available 2008-05-08T19:01:58Z
dc.date.issued 2008 en_US
dc.identifier.uri http://hdl.handle.net/2027.42/58411
dc.description.abstract 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. en_US
dc.format.extent 2975863 bytes
dc.format.extent 1373 bytes
dc.format.mimetype application/pdf
dc.format.mimetype text/plain
dc.language.iso en_US en_US
dc.subject Discontinuous Galerkin Method en_US
dc.subject Extended Hydrodynamics en_US
dc.subject High Order Method en_US
dc.subject Hyperbolic-relaxation Equation en_US
dc.subject Hancock Method en_US
dc.subject Space-time Discretization Method en_US
dc.title Discontinuous Galerkin Methods for Extended Hydrodynamics. en_US
dc.description.thesisdegreename Ph.D. en_US
dc.description.thesisdegreediscipline Aerospace Engineering and Scientific Computing en_US
dc.description.thesisdegreegrantor University of Michigan, Horace H. Rackham School of Graduate Studies en_US
dc.contributor.committeemember Van Leer, Bram en_US
dc.contributor.committeemember Huynh, Hung T. en_US
dc.contributor.committeemember Larsen, Edward W. en_US
dc.contributor.committeemember Powell, Kenneth G. en_US
dc.contributor.committeemember Roe, Philip L. en_US
dc.subject.hlbsecondlevel Aerospace Engineering en_US
dc.subject.hlbtoplevel Engineering en_US
dc.description.bitstreamurl http://deepblue.lib.umich.edu/bitstream/2027.42/58411/4/ysuzuki_1.pdf
dc.owningcollname Dissertations and Theses (Ph.D. and Master's)
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