Unsteady Navier–Stokes solvers using hybrid spectral/hp element methods Original Research Article

A domain decomposition unsteady Stokes solver has been implemented in a hybrid spectral/hp element solver. To extend the algorithm to solve the Navier–Stokes equations the non-linear terms are explicitly advanced in time and treated as a forcing function to the Stokes solver. This scheme is compared with the computationally efficient high order splitting method and it is found that for polynomial orders typically used in practice that the Stokes scheme is approximately 4/3 times more expensive in two-dimensions. A preliminary result for the Oseen problem using an analytic solution due to Kovasznay is also presented.