AN ACCURATE SEMI-LAGRANGIAN SCHEME DESIGNED FOR INCOMPRESSIBLE NAVIER-STOKES EQUATIONS WRITTEN IN GENERALIZED COORDINATES

An accurate Semi-Lagrangian (SL) scheme for incompressible Navier-Stok es equations written in generalized coordinates was developed. The sch eme explicitly calculates the advection phase of the governing equatio ns by a newly developed SL transport model and the viscous term by a m odified Crank-Nicholson method. Several numerical schemes approximatin g the trajectory and the unknowns at the upstream departure point have been verified to construct a well-balanced, totally accurate numerica l solver. Employing the contravariant velocity, the scheme directly pr edicates the generalized coordinates of the upstream departure point b y the four-stage fourth order Runge-Kutta method. The velocity at the departure point is interpolated with the third order accuracy. Unlike the traditional Eulerian schemes, the scheme allows a large time step length free from the CFL condition while keeping accuracy. The unstead y flows around a 2D circular cylinder are accurately predicted in 1/6 to 1/3 of the CPU times required for the traditional Eulerian solvers. The proposed scheme is expected to replace the traditional Eulerian s olvers to quickly investigate the practical flow problems.