A new method for solution of viscous shock-layer equations

Abstract

A new method is presented that considerably improves the computational efficiency of the viscous shock-layer technique. This approach can solve both subsonic and supersonic regions of the shock layer without a starting solution for the shock shape, and the global iterations are limited only to the nose region. In the nose region, the shock shape is specified from an algebraic expression and corrected through global passes through that region. The shock shape is computed as part of the solution beyond the nose region and requires only a single global pass. Under the high Reynolds number (at low altitudes), the Cebeci—Smith (CS) turbulent model has been analysed with the present numerical technique for application to long slender bodies. The surface-slip and the currently corrected shock-slip boundary conditions are employed to account for the low-density effects. The method of solution is a spatial-marching, implicit, finite-difference technique, which includes coupling of the normal momentum and continuity equations and uses a simple relation instead of Vigneron pressure condition in the subsonic nose region for instability. Comparisons are made with available experiment data and other solutions. The comparisons demonstrated that accurate solutions are obtained.