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Quasi-1D Euler Equations

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Old   March 20, 2007, 20:24
Default Quasi-1D Euler Equations
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I am having problems with the Quasi-1D Euler Equations. I am trying to covert the equations written in primitive variables to conserved variables. My starting equation set it written as: (drho/dt) + (1/A)(d/dx)(rho u A) = 0

(du/dt) + u(du/dx) + (1/rho)(dp/dx) = 0

(dp/dt) + (1/A)(d/dx)(puA) + [( (y-1)p)/A] d/dx(uA) = 0

I have found that this is not the normal formulation. I am trying to write them in the form of: dQ/dt + dF/dx + S = 0, where Q is the vector of conserved variables, F is the flux vector, and S becomes the source term. Q will be {rho, rho*u, Et}, F = {rho*u, rho*uČ + p, u(Et+p)

Where y is the ratio of specific heats (gamma) and Et is the total energy, where: Et = (p / y-1) + 1/(2rho)[(rho u)^2]

I have found source term for the continuity equation as: S_1 = (rho u / A)(dA/dx)

and the second source term (for momentum) as: S_2 = (rho uČ / A)(dA/dx)

I am however having a very hard time transforming the final energy equation into its proper form. Can anyone give me some references or anything that might help me out.

I would greatly appreciate it, thanks,
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