Scientific and Technical Aerospace Reports Volume 39 April 6, 2001

widely considered as the most cost-effective method for solving the Navier-Stokes equations. Indeed, they provide a maximum
decoupling of the velocity and the pressure so that only sparse elliptic problems need to be solved at each time-cycle.
Author
Navier-Stokes Equation; Collocation; Numerical Analysis; Computerized Simulation; Spline Functions; Incompressible Flow
20010022646 Stanford Univ., Center for Turbulence Research, Stanford, CA USA
Construction of Cummutative Filters for LES on Unstructured Meshes
Marsden, Alison L., Stanford Univ., USA; Vailyev, Oleg V., Missouri Univ., USA; Moin, Parvis, Stanford Univ., USA; Annual
Research Briefs - 2000: Center for Turbulence Research; December 2000, pp. 179-192; In English; See also 20010022631; No
Copyright; Avail: CASI; A03, Hardcopy; A03, Microfiche
Application of large eddy simulation (LES) to flows with increasingly complex geometry necessitates the extension of LES
to unstructured meshes. A desirable feature for LES on unstructured meshes is that the filtering operation used to remove small
scale motions from the flow commutes with the differentiation operator. If this commutation requirement is satisfied, the LES
equations have the same structure as the unfiltered Navier Stokes equations. Commutation is generally satisfied if the filter has
a constant width. However, in inhomogeneous turbulent flows, the minimum size of eddies that need to be resolved varies throughout
the flow. Thus, the filter width should also vary accordingly. Given these challenges, the objective of this work is to develop
a general theory for constructing discrete variable width commutative filters for LES on unstructured meshes. Variable width filters
and their commuting properties have been the focus of several recent works. Van der Ven constructed a family of continuous
filters which commute with differentiation up to arbitrary order in the filter width. However, this set of filters applies only to an
infinite domain without addressing the practical issue of boundary conditions in a finite domain. More recently, a class of discrete
commutative filters was developed by Vasilyev et al. for use on nonuniform structured meshes. Their formulation uses a mapping
function to perform the filtering in the computational domain. Although this type of mapping is impossible for the unstructured
case, the theory developed in Vasilyev et al. was used as a starting point for the present work. In this paper we present a theory
for constructing discrete commutative filters for unstructured meshes in two and three dimensions. In addition to commutation,
other issues such as control of filter width and shape in wavenumber space are also considered. In particular, we wish to specify
a desired filter width at each point in space and obtain a discrete filter which satisfies this requirement regardless of the choice
of the computational mesh.
Author
Large Eddy Simulation; Turbulent Flow; Unstructured Grids (Mathematics); Mathematical Models; Nonlinear Filters
20010022647 Stanford Univ., Center for Turbulence Research, Stanford, CA USA
Shock-Capturing in LES of High-Speed Flows
Martin, M. P., Stanford Univ., USA; Annual Research Briefs - 2000: Center for Turbulence Research; December 2000, pp.
193-198; In English; See also 20010022631; No Copyright; Avail: CASI; A02, Hardcopy; A03, Microfiche
The bursting events that are present in a turbulent boundary layer bring low-momentum fluid from the near wall region into
the boundary layer edge. In high-speed boundary layers, shocks form where the low-momentum fluid meets the incoming freestream.
Thus, to perform accurate large-eddy simulations (LES) of these flows, shock-capturing techniques are necessary. There
are two types of shock-capturing techniques: (1) total variation diminishing (TVD) and (2) essentially nonoscillatory (ENO)
schemes. TVD shock-capturing techniques reduce to first-order accuracy near shocks and damp the small-scale flow features.
Thus, this type of technique is not desired for turbulent flows. ENO schemes are designed to maintain high accuracy but not highbandwidth,
which is necessary for performing accurate numerical simulations of turbulent flows. Also, ENO schemes are inherently
dissipative due to the upwinded, optimal difference stencils and the smoothness measurement. Recently, Weirs and Candler
designed an optimized ENO scheme for simulating compressible turbulent flows based on the weighted essentially nonoscillatory
(WENO) scheme of Jiang and Shu. Weirs and Candler used bandwidth optimization techniques and developed symmetric optimal
stencils with reduced dissipation and greater resolving efficiency than those provided by typical ENO schemes. Martin and Candler
show that this WENO scheme gives good results for the direct numerical simulation (DNS) of supersonic turbulent boundary
layers. In the present work, the presence of shock waves in high-speed boundary layers is illustrated and the results from the LES
of a supersonic boundary layer using the WENO scheme are assessed.
Author
TVD Schemes; Essentially Non-Oscillatory Schemes; Large Eddy Simulation; Shock Waves; Turbulent Boundary Layer
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