Development of High-Order Taylor–Galerkin Schemes for LES

In this paper we describe the implementation and development of a new Taylor–Galerkin finite-element scheme within an unstructured/hybrid, parallel solver. The scheme has been specifically conceived for unsteady LES: it is third-order in space and time and has a low dissipative error. Minimal additional CPU costs are achieved by using a new approximation of the finite-element integrals and a simple iterative method for the approximate inversion of the modified mass matrix. Basic convective tests are carried out in 2 and 3 dimensions for arbitrary elements. Numerical estimates of the order of convergence are presented on regular and perturbed grids. Finally, test cases that are relevant to LES are carried out, and these clearly demonstrate the important improvements that our new scheme offers relative to a selection of existing methods.