Question

The Tricomi equation YUxx+Uyy = 0 is a simple and useful PDE that captures the key...

The Tricomi equation YUxx+Uyy = 0 is a simple and useful PDE that captures the key characterisitics of transonic flow, where the supersonic and subsonic flows are present in flow field simultaneously.

(a) Show that the Tricomi equation is of mixed type. Identify the regions on the x−y plane where the PDE becomes elliptic, parabolic, and hyperbolic.

(b) Assuming U(0, y) = U(L, y) = 0, obtain the Airy equation G''(y) − k^(2)yG(y) = 0 from the Tricomi equation by separation of variables. Note, you are not required to solve this equation.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The Tricomi equation yuxx+uyy = 0 is a simple and useful PDE that captures the key...
The Tricomi equation yuxx+uyy = 0 is a simple and useful PDE that captures the key characterisitics of transonic flow, where the supersonic and subsonic flows are present in flow field simultaneously. (a) Show that the Tricomi equation is of mixed type. Identify the regions on the x−y plane where the PDE becomes elliptic, parabolic, and hyperbolic. (b) Assuming u(0, y) = u(L, y) = 0, obtain the Airy equation G′′(y) − k2yG(y) = 0 from the Tricomi equation by...
To write Laplace’s equation, Uxx + Uyy = 0, in polar coordinates, we begin with Ux...
To write Laplace’s equation, Uxx + Uyy = 0, in polar coordinates, we begin with Ux = (∂U/∂r)(∂r/∂x) + (∂U/∂θ)(∂θ/∂x) where r = √(x2+y2), θ = arctan (y/x), x = r cos θ, y = r sin θ. We get Ux = (cos θ) Ur – (1/r)(sin θ) Uθ , Uxx = [∂(Ux)/∂r] (∂r/∂x) + [∂(Ux)/∂θ](∂θ/∂x) Carry out this computation, as well as that for Uyy. Since Uxx and Uyy are both expressed in polar coordinates, their sum gives Laplace...
Consider the second order linear partial differential equation a(x, y)uxx + 2b(x, y)uxy + c(x, y)uyy...
Consider the second order linear partial differential equation a(x, y)uxx + 2b(x, y)uxy + c(x, y)uyy + d(x, y)ux + e(x, y)uy + f(x, y)u = 0. (1) a). Show that under a coordinate transformation ξ = ξ(x, y), η = η(x, y) the PDE (1) transforms into the PDE α(ξ, η)uξξ + 2β(ξ, η)uξη + γ(ξ, η)uηη + δ(ξ, η)uξ + (ξ, η)uη + ψ(ξ, η)u = 0, (2) where α(ξ, η) = aξ2 x + 2bξxξy + cξ2...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT