A Fourth-Order Scheme for the Compressible Navier-Stokes Equations

This study focuses on a fourth-order nite-volume scheme to solve the compressible Navier-Stokes equations on a Cartesian grid. Two approaches for handling boundary conditions are presented, one approach employs one-sided-di erence methods and the other approach almost completely supports using centered-di erence methods everywhere. Both approaches are genuinely fourth-order in space and time for the treatment of viscous terms. For time integration, a fourth-order Runge-Kutta method is used. The fourth-order scheme was applied to an unsteady boundary layer at plate ow and the solution accuracy was qualitatively veri ed.