[pswpswpsw]

For 2D steady non-viscous flow, we often solve the Laplace equation of potential function. But, 2D unsteady euler equation can be applied to any kind of unsteady nonviscous flow. Why no one use that equation to solve?

I would be very happy to know if I made any mistakes above

Best,
Shawn

First I give my own reasons.

1) Taken this problem as hyperbolic would be highly tough. Because the boundary layer condition would be trouble because we first need an initial condition, whose velocity direction on the boundary will affect the number of boundary conditions on the boundary condition.

[FMDenaro]

Originally Posted by pswpswpsw

For 2D steady non-viscous flow, we often solve the Laplace equation of potential function. But, 2D unsteady euler equation can be applied to any kind of unsteady nonviscous flow. Why no one use that equation to solve?

I would be very happy to know if I made any mistakes above

Best,
Shawn

First I give my own reasons.

1) Taken this problem as hyperbolic would be highly tough. Because the boundary layer condition would be trouble because we first need an initial condition, whose velocity direction on the boundary will affect the number of boundary conditions on the boundary condition.

Who told you that unsteady Euler equations are not used??? The literature is full of that...

[robo]

The potential flow equations can only be used if the flow is irrotational in addition to being inviscid and incompressible. They are not restricted to the steady or unsteady case; you can solve unsteady problems with potential flow. An example of an unsteady potential flow would be the inviscid flow around an oscillating airfoil.

The advantage of the potential flow formulation is that the dimensionality of the problem is reduced. A potential flow only requires the solution of the potential on the boundaries; ie a surface integration, whereas a solution of the Euler equations will require a volume integration of the whole domain of interest.