This contribution is a tribute to the foresight of Paolo Orlandi who demonstrated and advocated the suitability of second-order discretization methods for turbulent flow simulations. His pioneering work has shown how to combine cost effective and relatively easy to implement, central, second-order accurate finite difference schemes with the appropriate variable discretization and time integration methods to efficiently solve complex turbulent flows. In this communication, we first compare the cost and accuracy of Fourier-spectral methods and second order finite difference discretization for the solution of a simple variable coefficient convection problem. We then extend our analysis to the inviscid Taylor Green vortex. We conclude with a discussion of related findings from the literature including the accuracy requirements for large eddy simulation (LES) of turbulent flows.
- Energy conserving schemes
- Second-order finite-differences
- Staggered grids