The Euler Equations of Steady Flow in Terms of New Dependent and Independent Variables
Authors: Peiangpob Monnuanprang
In this paper we study the transformation of Euler equations 1 , u u u Pf t (ρ ∂) + ⋅∇ = − ∇ + ∂ G G G G ∇⋅ = u 0, G where (ux, t) G G is the velocity of a fluid, P(x, t) G is the pressure of a fluid andρ (x, t) G is density. First of all, we rewrite the Euler equations in terms of new unknown functions. Then, we introduce new independent variables and transform it to a new curvilinear coordinate system. We obtain the Euler equations in the new dependent and independent variables. The governing equations into two subsystems, one is hyperbolic and another is elliptic.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1334528Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1394
 P.J. Roache, Computational Fluid Dynamics. Hermosa Publishers, Albuquerque, 1976.
 L. Quartapelle, . Numerical Solution of the Incompressible Navier Stokes Equations. Berlin. Germany,1993.
 I.L Osipov, V.P. Pashenko, and A.V. Shippillin, "Calculation of inviiscous gas flow within channel with essential change of geometry,"J.Comm. Math. Phy, vol 18,1978, pp. 964-973.
 P.Monnuanprang, "Numerical Method For The Incompressible Euler Equations," IAENG International Journal of .Applied Mathematics, vol.38, Sep. 2008, pp. 125-128.
 C.K. Batchelor, An Introduction to Fluid Dynamics. Cambridge: Cambridge University , 1970.