Higher-order accurate Osher schemes with application to compressible boundary layer stability

Two fourth order accurate Osher schemes are presented which maintain higher order accuracy on nonuniform grids. They use either a conservative finite difference or finite volume discretization. Both methods are successfully used for direct numerical simulations of flat plate boundary layer instability at different Mach numbers. Results of growth rates of Tollmien-Schlichting waves compare well with direct simulations of incompressible flow and for compressible flow with results obtained by solving the parabolic stability equations.