A diagonalized diagonal dominant alternating direction implicit (D3ADI) scheme and subiteration correction

A diagonal form of the recently developed diagonal dominant alternating direction implicit scheme for solving the Navier-Stokes equations is presented. The diagonally dominant scheme with a subiteration procedure eliminates the factorization error and therefore the scheme is more robust. The diagonalization uncouples the system of equations so that only scalar tridiagonal or pentadiagonal matrix inversions are required; thus avoiding the block tridiagonal matrix inversions of the original scheme. For total diagonalization, a scalar approximation to the diagonal matrix is needed and several variations are investigated. Flows over a compression ramp and an ONER A M6 wing are employed to validate the scheme. They demonstrate that the scheme is efficient and stable for very large CFL numbers.