A fourth-order boundary treatment for viscous fluxes on Cartesian grid finite-volume methods

This study focuses on a fourth-order boundary treatment for nite-volume schemes to solve the compressible Navier-Stokes equations on a Cartesian grid. A fourth-order nite-volume stencil is derived for the viscous stress tensor operator and the modi ed fourth-order stencil near the physical boundary is developed. Fourier error analysis and stability analysis are performed for the fourth-order elliptic operator. For time integration, we use the fourth-order Runge-Kutta method. The fourth-order scheme was applied to the transient Couette ow and the solution accuracy was veri ed.