Finite volume formulation of compact upwind and central schemes with artificial selective damping

Abstract

This chapter discusses the formulation allowing the use of central and upwind compact schemes in the finite volume context on arbitrary meshes. A formulation of artificial selective damping needed to ensure the stability and monotonicity of central schemes applicable on nonuniform meshes is also reviewed. The results for a variety of test cases ranging from one-dimensional model equation to large-eddy simulation of turbulent flows for both central and upwind compact schemes are compared. One-dimensional convection of a Gaussian pulse compares the accuracy of the upwind schemes and purely central scheme without artificial selective damping (ASD). The compact central schemes may suffer from stability problems or produce spurious numerical oscillations arising from the lack of built-in numerical dissipation.