An efficient and modular grad–div stabilization

Abstract This paper presents two modular grad–div algorithms for calculating solutions to the Navier–Stokes equations (NSE). These algorithms add to an NSE code a minimally intrusive module that implements grad–div stabilization. The algorithms do not suffer from either solver breakdown or debilitating slow down for large values of grad–div parameters. Stability and optimal-order convergence of the methods are proven. Numerical tests confirm the theory and illustrate the benefits of these algorithms over a fully coupled grad–div stabilization.

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