Chapter 7 - Unstructured finite volume approaches for turbulence

Abstract

Unstructured finite volume methods represent a common discretization technique exercised in practical turbulence flow modeling and simulation studies. This is particularly true when resolving complex geometries. An efficient meshing process must be deployed, especially when simulations are expected to support decisions in a timely manner. This drives one towards unstructured meshes that allow for both efficient meshing, and the resolution of flow features. In this chapter, the primary goal is to introduce low-dissipation, unstructured finite volume discretization techniques for turbulent flow applications. Although the discretization approach provided is applicable to direct numerical simulation (DNS), the chapter will focus on the suitability of unstructured finite volume discretizations for large-eddy simulation (LES). Emphasis will be placed on the low-Mach regime where explicit pressure stabilization is commonplace. Both cell- and vertex-centered schemes will be reviewed in the high-Peclet number, advectively-dominated regime. Extension to higher-order is provided within a class of hybrid discretizations known as the control volume finite element method (CVFEM). The chapter will focus on establishing design-order numerical methods by the extensive usage of formal code verification using analytical and manufactured solutions. Finally, an LES case study is provided to demonstrate the effective usage of finite volume discretization on unstructured meshes.