Patent ID: 6516292
Filing Date: 2003-02-04
Classification: G06F

Abstract:
A method of providing information useful in designing a solid body past which a compressible fluid flows, comprising the steps of:(a) providing an equation of state for the fluid; (b) formulating the fluid flow in terms of a potential functional &Integral;v&it;[12&it;(Î±&it;&Del;&RightArrow;&it;Î²+&Del;&RightArrow;&it;v)2+&varepsilon;&it;(Ï )+Î¦]&it;Ï &it;â€ƒ&it;d3&it;x-Î²1&it;(&Integral;v&it;Î±&it;â€ƒ&it;Ï &it;â€ƒ&it;d3&it;x-Î±&RightArrow;&it;M0)-v1&it;(&Integral;v&it;Ï &it;â€ƒ&it;d3&it;x-M0)â€ƒwherein &agr;, &bgr; and &ngr; are Clebsch scalar fields, &rgr; is a density field, &bgr;1 and &ngr;1 are scalar variables, &egr; is a specific internal energy that is related to &rgr; via said equation of state, &PHgr; is a potential of an external force, {overscore (&agr;)} and M0 are constants and V is a volume of integration exclusive of the body; (c) forming a numerical representation of said potential functional external to the body; (d) extremizing said numerical representation of said potential functional with respect to &agr;, &bgr;, &ngr;, &rgr;, &bgr;1 and &ngr;1; and (e) computing a velocity vector field as &agr;{right arrow over (âˆ‡)}&bgr;+{right arrow over (âˆ‡)}&ngr;, said velocity vector field being the information useful in designing the solid body.