Optimal coordinates for higher-order boundary-layer theory

The optimal coordinates for higher-order boundary-layer theory are derived using an extension of Kaplun’s approach. They are applicable to any approximation order and become small-parameter dependent beginning with the second-order boundary-layer problem. The new result is consistent with an earlier methodology that led to the same results. Two boundary-layer solutions from the literature confirm the new rule. The optimal coordinates will be valuable for analytical investigations of the Navier–Stokes equations as well as for new approaches to developing grid schemes for CFD.