Notes on the Euler Equations

Notes on the Euler EquationsThese Notes describe how to do a piecewise linear or piecewise parabolic method for the Euler Euler equation propertiesThe Euler Equations in one dimension appear as: t+ ( u) x=0(1) ( u) t+ ( uu+p) x=0(2) ( E) t+ ( uE+up) x=0(3)These represent conservation of mass, momentum, and is the density,uis the one-dimensional velocity,pis the pressure, andEis the total energy / mass, and can be expressed in terms ofthe specific internal energy and kinetic energies as:E=e+12u2(4)The Equations are closed with the addition of an equation of state :p= e( 1)(5)where is the ratio of specific heats for the gas/fluid (for an ideal , monatomic gas, =5/3).In this form, the Equations are said to be inconservative form.

Apr 16, 2013 · The equations are closed with the addition of an equation of state: p =ρe(γ −1) (5) where γ is the ratio of specific heats for the gas/fluid (for an ideal, monatomic gas, γ =5/3). In this form, the equations are said to be in conservative form. They can be written as: Ut +[F(U)] x =0 (6) with U = ρ ρu ρE F(U)= ρu ρuu+p ρuE+up (7)

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  States, Equations, Ideal, Equation of state

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