Weak Versus Strong Wall Boundary Conditions for the Incompressible Navier-Stokes Equations

Abstract The pressure-velocity formulation of the incompressible Navier-Stokes equations is solved using high-order finite difference operators satisfying a summation-by-parts property. Two methods for imposing Dirichlet boundary conditions (one strong and one weak) are presented proven stable energy method. Additionally, novel diagonal-norm second-derivative derived with highly improved accuracy. Accuracy convergence measurements verified against theoretical expectations. Numerical experiments also show that subtle effects close to solid walls more efficiently captured condition imposition rather than weak (less degrees freedom required).