Finite element methods for turbulence

Finite element methods provide very low dissipation, higher order accurate discretizations for use in scale resolving simulations of turbulence. Their ability to use unstructured grids to match grid resolution to the local needs of the scale resolving simulation makes them particularly attractive and efficient for complex geometry flows and more fundamental flows with a large spatial variation in the smallest required scale that must be resolved. This chapter provides the background for the basis functions that will be used with the finite element method to convert partial differential equation into ordinary differential equations which are then integrated in time by either explicit or implicit methods. The chapter also provides a contrast of classical and newer approaches to equation formation, assembly, and solution that accounts for emerging hardware and closes with a demonstration of the method's application to flow over a vertical tail rudder assembly where the methods ability to support grid adaptivity provides additional computational efficiency.