CAN YOU FIND JACOBIAN ?????

Yogesh Talekar

Gurus,

I have a set a 1-D flow given in a book "Computaional Flud Dynamics" by John D. Anderson page number 339,

dU1/dt = - dF1/dx

dU2/dt = -dF2/dx + J2 and

dU3/dt = - dF3/dx

Where, 'd' above means "partial derivative".

U1 = (Rho) * A

U2 = Rho * A * v

U3 = Rho * (e/gamma -1 + gamma/2 * v^2) * A

F1 = Rho * v * A

F2 = Rho * A * v^2 + 1/gamma * p * A

F3 = Rho * (e/gamma-1 + gamma/2 * v^2) * v*A + p * A *v

J2 = 1/gamma * p * dA/dx

Where v is velocity and A is area is function of x.

Can you find the jacobian of 'dF/dU's as per the procedure given on pages 482-487 of the above book.

Please help

YOgesh