Numerical solution of a Rayleigh-Taylor instability problem

The numerical solution of a Rayleigh-Taylor instability problem where an inviscid liquid of finite depth is accelerated into a gas of semi-infinite extent is obtained by transforming the irregular flow domain into a rectangular domain by a coordinate transformation. The free surface equation is solved by a Crank-Nicolson procedure. The boundary condition at the free surface for the velocity potential ø which contains the time derivative of ø is also treated by an implicit scheme. The numerical results agree well with those obtained by higher order perturbation analysis.