An approximate projection scheme based on the pressure correction method is proposed to solve the Navier–Stokes equations for incompressible flow. The algorithm is applied to the continuous equations; however, there are no problems concerning the choice of boundary conditions of the pressure step. The resulting velocity and pressure are consistent with the original system. For the spatial discretization a high‐order spectral element method is chosen. The high‐order accuracy allows the use of a diagonal mass matrix, resulting in a very efficient algorithm. The properties of the scheme are extensively tested by means of an analytical test example. The scheme is further validated by simulating the laminar flow over a backward‐facing step.

. (1995). A second order splitting algorithm for thermally-driven flow problems.

SUMMARYSeveral explicit Taylor-Galerkin-based time integration schemes are proposed for the solution of both linear and non-linear convection problems with divergence-free velocity. These schemes are based on second-order Taylor series of the time derivative. The spatial discretization is performed by a high-order Galerkin spectral element method. For convection-diffusion problems an operator-splitting technique is given that decouples the treatment of the convective and diffusive terms. Both problems are then solved using a suitable time scheme. The Taylor-Galerkin methods and the operator-splitting scheme are tested numerically for both convection and convection-diffusion problems.

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