A stabilized incremental projection scheme for the incompressible Navier-Stokes equations (Q2747790)

The paper describes the numerical solution of time-dependent incompressible Navier-Stokes equations. The focus lies on equal order approximations for velocity and pressure, and on splitting schemes for computing the discrete solution. At the beginning, two types of splitting schemes are presented and their advantages and drawbacks are discussed. The violation of LBB condition for equal order approximations requires an additional stabilization which contains a parameter. Using such a stabilization and based on the observation that the splitting schemes can be considered as the first step of a preconditioned iteration for solving the pressure Schur complement equation, the so-called stabilized incremental projection scheme is derived. On the one hand, the stabilization parameter must be large enough to ensure sufficient stabilization. On the other hand, it must be sufficiently small such that the order of discretization is not deteriorated. An analysis presented in the paper leads to a stabilization parameter which fulfills both requirements. The behavior of the stabilized incremental projection scheme is demonstrated in three-dimensional test examples, such as driven cavity problem and the flow over a backward facing step. The numerical tests show the predicted order of convergence, and they reveal that, in contrast to a non-stabilized splitting scheme, the solutions computed with stabilized incremental projection scheme do not possess spurious pressure oscillations.