Wall-compatibility condition for the solution of the Navier-Stokes equations (Q794842)

The authors suggest to use the continuity equation for time-dependent compressible flow for computation of the density \(\phi\) or the pressure p on solid walls in finite-difference solutions. The advantage offered in this approach is that one-sided second-order finite-difference formulation can be avoided, which is necessary, when the momentum equation for the direction normal to the wall is used for density or pressure calculations. The formulation proposed requires only evaluation of first-order time and space-derivatives.