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A kinetic scheme for the Navier-Stok...

May, Georg.

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A kinetic scheme for the Navier-Stokes equations and high-order methods for hyperbolic conservation laws.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A kinetic scheme for the Navier-Stokes equations and high-order methods for hyperbolic conservation laws./
作者:	May, Georg.
面頁冊數:	136 p.
附註:	Source: Dissertation Abstracts International, Volume: 67-09, Section: B, page: 5222.
Contained By:	Dissertation Abstracts International67-09B.
標題:	Engineering, Aerospace. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3235284
ISBN:	9780542895012

A kinetic scheme for the Navier-Stokes equations and high-order methods for hyperbolic conservation laws.
May, Georg.

A kinetic scheme for the Navier-Stokes equations and high-order methods for hyperbolic conservation laws. - 136 p.

Source: Dissertation Abstracts International, Volume: 67-09, Section: B, page: 5222.

Thesis (Ph.D.)--Stanford University, 2006.

This dissertation revolves around algorithm development in the context of numerical methods for hyperbolic conservation laws and the compressible Navier-Stokes equations, with particular emphasis on unstructured meshes. Three distinct topics may be identified: Firstly, a new kinetic scheme for the compressible Navier-Stokes equations is developed. Kinetic numerical schemes are based on the discretization of a probability density function. In the context of fluid flow such schemes have a natural basis rooted in the kinetic theory of gases. A significant advantage of kinetic schemes is that they allow a compact, completely mesh-independent discretization of the Navier-Stokes equations, which makes them well suited for next-generation solvers on general unstructured meshes. The new kinetic scheme is based on the Xu-Prenderaast BGK scheme, and achieves a dramatic reduction in computational cost, while also improving and clarifying the formulation with respect to the underlying kinetic gas theory.

ISBN: 9780542895012Subjects--Topical Terms:

1018395
Engineering, Aerospace.

A kinetic scheme for the Navier-Stokes equations and high-order methods for hyperbolic conservation laws.
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245 1 2 $a A kinetic scheme for the Navier-Stokes equations and high-order methods for hyperbolic conservation laws.
300 $a 136 p.
500 $a Source: Dissertation Abstracts International, Volume: 67-09, Section: B, page: 5222.
500 $a Adviser: Anthony Jameson.
502 $a Thesis (Ph.D.)--Stanford University, 2006.
520 $a This dissertation revolves around algorithm development in the context of numerical methods for hyperbolic conservation laws and the compressible Navier-Stokes equations, with particular emphasis on unstructured meshes. Three distinct topics may be identified: Firstly, a new kinetic scheme for the compressible Navier-Stokes equations is developed. Kinetic numerical schemes are based on the discretization of a probability density function. In the context of fluid flow such schemes have a natural basis rooted in the kinetic theory of gases. A significant advantage of kinetic schemes is that they allow a compact, completely mesh-independent discretization of the Navier-Stokes equations, which makes them well suited for next-generation solvers on general unstructured meshes. The new kinetic scheme is based on the Xu-Prenderaast BGK scheme, and achieves a dramatic reduction in computational cost, while also improving and clarifying the formulation with respect to the underlying kinetic gas theory.
520 $a The second topic addresses high-order numerical methods for conservation laws on unstructured meshes. High-order methods potentially produce higher accuracy with fewer degrees of freedom, compared to standard first or second order accurate schemes, while formulation for unstructured meshes makes complex computational domains amenable. The Spectral Difference Method offers a remarkably simple alternative to such high-order schemes for unstructured meshes as the Discontinuous Galerkin and Spectral Volume Methods. Significant contributions to the development of the Spectral Difference Method are presented, including stability analysis, viscous formulation, and h/p-multigrid convergence acceleration.
520 $a Finally, the theory of Gibbs-complementary reconstruction is utilized in the context of high-order numerical methods for hyperbolic equations. Gibbs-complementary reconstruction makes it possible to extract pointwise high-order convergence in the spectral approximation of non-smooth functions, despite the presence of the Gibbs phenomenon. Information is extracted from the spectral coefficients of the solution by reprojection onto a functional space endowed with certain properties, called a Gibbs-complementary space. This dissertation includes a proof of concept validating the technique on discontinuous solutions to nonlinear hyperbolic PDE, such as the Burgers equation and the Euler equations.
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