Accurate solutions of the Navier-Stokes equations despite unknown outflow boundary data
The paper deals with calculating the solutions of the Navier-Stokes equations with outflow boundary operators of extrapolation type on artificial boundaries, with errors in the boundary data of order one. Both the problems when the artificial outflow boundary is located in essentially uniform flow and when the artificial outflow boundary is located in a flow field with large gradients are discussed. A linear model problem, where the effect of large gradients in the basic flow field is included, is studied. Appropriate bounds on the solution to the model problem are also derived. In the subsonic outflow case, one obtains accurate solutions of the nonlinear problem if and only if large transversal gradients are present in the basic flow field. In the supersonic outflow case, one can always obtain accurate solutions by using derivative boundary conditions. Numerical experiments support the theoretical conclusions drawn from the model problem.
scientific article; zbMATH DE number 818551