博碩士論文 93221006 詳細資訊




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姓名 賴家駿(Chia-chun Lai)  查詢紙本館藏   畢業系所 數學系
論文名稱 對接近音速流量可壓縮尤拉方程式的柯西問題去架構區間逼近解
(The Construction of Local Approximate Solutions to The Cauchy Problem of Compressible Euler Equations in Transonic Flow.)
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摘要(中) 在這篇文章我們考慮尤拉方程式在接近音速流量無變化可壓縮的管,在方程式出現的壓力項和管的位置有關。我們對這柯西問題的方程式,去架構一個區間的逼近解,這個逼近解是由黎曼問題的基本波和線性化方程式的逼近解所組合架構,線性化方程式的逼近解藉由使用”operator splitting”來架構。
摘要(英) In this paper we consider the compressible Euler equations of uniform duct in transonic flow. The pressure term appearing in the equations is also dependent on the location of the duct, which is considered as the product of the density of flow and a function of space. We construct a local approximate solution for the Cauchy problem of equations. This approximate solution is constructed as a combination of homogeneous elementary waves to the Riemann problem and an approximate solution of the linearized equations. The approximate solution of the linearized equations is constructed by the scheme of the
operator splitting.
關鍵字(中) ★ 對接近音速流量
★ 可壓縮尤拉方程式
★ 黎曼問題.
關鍵字(英) ★ hyperbolic systems of conservation laws.
★ transonic flow
★ Riemann problem
★ operator splitting method
★ Compressible Euler equations
論文目次 1.Introduction………………………………………………………………………2
2.The Riemann problem of the homogeneous system ( 1.8 )..…………………...5
3.Operator splitting scheme to the linearized system……………………………..14
4.References……………………………………………………………………….23
參考文獻 [1] J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equa-
tions, Comm. Pure Appl. Math., 18 (1956), 697-715.
[2] J. M. Hong, An extension of Glimm's method to inhomogeneous strictly
hyperbolic systems of conservation laws by weaker than wealer" solutions
of the Riemann problem, J. Di®. Equations, (2005), to appear.
[3] J. M. Hong and B. Temple, The generic solution of the Riemann problem
in a neighborhood of a point of resonance for systems of nonlinear balance
laws, Methods Appl. Anal., 10 (2003), 279-294.
[4] J. M. Hong and B. Temple, A bound on the total variation of the conserved
quantities for solutions of a general resonant nonlinear balance law, SIAM
J. Appl. Math., 64 (2004), 819-857.
[5] E. Isaacson and B. Temple, Nonlinear resonant in inhomogenous systems of
conservation laws, Contemporary Mathematics, vol. 108, 1990.
[6] P. D. Lax, Hyperbolic system of conservation laws, II, Comm. Pure Appl.
Math., 10 (1957), 537-566.
[7] P. G. LeFloch, Shock waves for nonlinear hyperbolic systems in nonconser-
vative form, Institute for Mathematics and its Applications, Minneapolis,
Preprint 593, 1989.
[8] T. P. Liu, Quasilinear hyperbolic systems, Comm. Math. Phys., bf 68 (1979),
141-172.
[9] J. A. Smoller, On the solution of the Riemann problem with general stepdata
for an extended class of hyperbolic system, Mich. Math. J., 16, 201-210.
[10] J. Smoller, Shock waves and reaction-d®usion equations, Springer, New York,
1983.
[11] B. Temple, Global solution of the Cauchy problem for a class of 2£2 non-
strictly hyperbolic conservation laws, Adv. Appl. Math. 3 (1982), 335-375.
[12] B. Temple, Global solution of the Cauchy problem for a class of 2 £ 2
nonstrictly hyperbolic conservation laws, Adv. Appl. Math., 3 (1982), 335-
375.
指導教授 洪盟凱(John M .Hong) 審核日期 2007-7-3
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