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Development of an efficient Navier-Stokes/LES solver on unstructured grids for highorder accurate schemes

Tuesday, 23 November, 2010 - 16:30
Campus: Brussels Humanities, Sciences & Engineering campus
Matteo Parsani
phd defence

The main goal of this thesis is to develop an efficient Navier-Stokes/LES solver on unstructured grids for high-order
accurate spatial discretizations, and build up the necessary know-how to make a high-order accurate solver for
industrial purposes. In the field of the computational fluid dynamics, the expectation is that an efficient higher-order
discretization may provide an alternate path for achieving high accuracy in a flow with a wide disparity of length
scales at reduced cost, by avoiding the use of excessive grid resolution. However, the development of optimal, or
near optimal solution strategies for higher-order discretizations and implicit time integration strategies, remains then
one of the key determining factors in devising higher-order methods. In addition, although spatially high-order
accurate numerical schemes guarantee the accurate resolution of small scales, their application to the simulation of
general turbulent flows implies that particular attention has still to be paid to subgrid models. In this framework, two
spatially high-order accurate methods for unstructured grids are considered, namely the spectral volume and the
spectral difference methods. To fully exploit the potential benefits of such high-order operators, an efficient nonlinear
algebraic solver, denoted as non-linear LU-SGS algorithm, is investigated. This solver is used to invert the
non-linear algebraic systems arising from implicit time discretizations with the backward Euler scheme and the
second-order backward difference formula. Several test cases are used to demonstrate the potential benefits of the
implicit time integration/algebraic solver technique. In addition, the need for paying particular attention to subgrid
models for the simulation of general turbulent is recognized. A high-order spectral difference scheme is coupled
with a subgrid model to perform LES. A new procedure to calculate the filter width is proposed. The accuracy and
the reliability of the method are tested by solving 2D and 3D turbulent test cases. A good agreement between the
present numerical results and reference solutions is observed, showing the capability and the quality of the new
coupling approach.