SIAM Journal on Mathematical Analysis
Review of incompressible fluid flow computations using the vorticity-velocity formulation
Applied Numerical Mathematics
Effective vorticity-velocity formulations for three-dimensional incompressible viscous flows
Journal of Computational Physics
A penalty method for the vorticity-velocity formulation
Journal of Computational Physics
A compact-difference scheme for the Navier-Stokes equations in vorticity-velocity formulation
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Introduction to the Numerical Analysis of Incompressible Viscous Flows
Introduction to the Numerical Analysis of Incompressible Viscous Flows
On the accuracy of the rotation form in simulations of the Navier-Stokes equations
Journal of Computational Physics
Velocity-vorticity-helicity formulation and a solver for the Navier-Stokes equations
Journal of Computational Physics
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We present a rigorous numerical analysis and computational tests for the Galerkin finite element discretization of the velocity-vorticity-helicity formulation of the equilibrium Navier-Stokes equations (NSEs). This formulation, recently derived by the authors, is the first NSE formulation that directly solves for helicity and the first velocity-vorticity formulation to naturally enforce incompressibility of the vorticity, and preliminary computations confirm its potential. We present a numerical scheme; prove stability, existence of solutions, uniqueness under a small data condition, and convergence; and provide numerical experiments to confirm the theory and illustrate the effectiveness of the scheme on a benchmark problem.