Development of high-order Taylor-Galerkin schemes for LES

In this paper we describe the implementation and development of a new Taylo r-Galerkin finite-element scheme within an unstructured/hybrid, parallel so lver. The scheme has been specifically conceived for unsteady LES: it is th ird-order in space and time and has a low dissipative error. Minimal additi onal CPU costs are achieved by using a new approximation of the finite-elem ent integrals and a simple iterative method for the approximate inversion o f the modified mass matrix. Basic convective tests are carried out in 2 and 3 dimensions for arbitrary elements. Numerical estimates of the order of c onvergence are presented on regular and perturbed grids. Finally, test case s that are relevant to LES are carried out, and these clearly demonstrate t he important improvements that our new scheme offers relative to a selectio n of existing methods. (C) 2000 Academic Press.