A Modular Voigt Regularization of the Crank-Nicolson Finite Element Method for the Navier-Stokes Equations

We study a modular Crank-Nicolson based Voigt regularization algorithm for the Navier-Stokes equations. This algorithm adds a minimally intrusive module that not only implements Voigt regularization but also adds some numerical dissipation which is not existent in the monolithic algorithms. The additional dissipation induced by the method could act to dampen spurious oscillations, improve stability of numerical solutions, and yield improved accuracy with large-scale dynamics. Within, we prove that the algorithm is unconditionally stable. A convergence analysis is provided whereby O(Δ t^2 + α ^2 + h^k) convergence is proven for velocity solutions. Numerical tests illustrate both the proven stability and convergence properties and the benefit of modular Voigt regularization over the monolithic implementation.