Scientific and Technical Aerospace Reports Volume 39 April 6, 2001

undertaken to isolated it are described next. The results are then discussed, with emphasis on the low-dimensional behavior of
the structures in the simplified flows and on how they evolve into a fully turbulent flow once the constraints are removed.
Author
Numerical Analysis; Turbulence; Turbulent Flow; Wall Flow
20010022643 Stanford Univ., Center for Turbulence Research, Stanford, CA USA
Mapping Closure Approximation to Conditional Dissipation Rate for Turbulent Scalar Mixing
He, Guowei, Stanford Univ., USA; Rubenstein, R., Institute for Computer Applications in Science and Engineering, USA; Annual
Research Briefs - 2000: Center for Turbulence Research; December 2000, pp. 141-147; In English; See also 20010022631; No
Copyright; Avail: CASI; A02, Hardcopy; A03, Microfiche
The probability density function (PDF) approach has been shown to be a useful tool in turbulence research. The systematic
approach for determining PDFs is by means of solving the transport equations for PDFs. In the PDF equations for turbulent scalar
fields, conditional dissipation rate (CDR) appears as the only unclosed term. Recently developed large-eddy simulation schemes
for turbulent reactive flow, such as the filtered PDF approach, the conditional moment closure, and the Lagrangian flamelet model,
also require models for the CDR. No satisfactory closure model for CDR had been constructed until the mapping closure approach
was formulated. Amplitude mapping closure suggests a CDR model whose form is separable in scalar and time variables. The
model is in good agreement with direct numerical simulation (DNS) for initially symmetric binary mixing but fails in describing
asymptotic behavior of the CDR for initially unsymmetric binary mixing has developed a novel amplitude mapping closure
approach in which the reference fields are time-dependent. The CDR model obtained from a time-evolving Gaussian reference
field still fails to describe-the asymptotic behavior, but the one from a time-evolving Beta reference field can successfully describe
the asymptotic behavior. This strongly suggests that the amplitude mapping closure is inadequate to describe the asymptotic
behavior by itself. In the present research, we will develop a novel mapping closure approximation (MCA) to make successive
approximations to statistics of a scalar in homogeneous turbulence. This technique will be used to construct a CDR model which
accounts for the asymptotic behavior of the CDR. In Section 2.1, we will investigate the asymptotic behavior of the CDR model
from amplitude mapping closure and explain the reason why it fails to describe the asymptotic behavior correctly. In Section 2.2,
we will outline the MCA technique for successive approximation. In Section 2.3, we will use the MCA technique to formulate
a novel CDR model and compare it with DNS results. We will conclude with a summary in Section 3.
Author
Asymptotic Properties; Mathematical Models; Probability Density Functions; Turbulent Mixing; Dissipation; Turbulent Flames
20010022645 Stanford Univ., Center for Turbulence Research, Stanford, CA USA
A High-Order Approximate-Mass Spline Collocation Scheme for Incompressible Flow Simulations
Botella, Olivier, Stanford Univ., USA; Annual Research Briefs - 2000: Center for Turbulence Research; December 2000, pp.
159-177; In English; See also 20010022631; No Copyright; Avail: CASI; A03, Hardcopy; A03, Microfiche
The development of numerical methods based on B-spline methodology is motivated by the substantial computational cost
of large-eddy simulations (LES) of complex turbulent flows. Indeed, the large number of grid points needed in turbulent boundary
layers remains one of the principle obstacles to a wider application of LES to flows of engineering interest. An active part of
research in LES is devoted to reducing these resolution requirements by the formulation of approximate wall conditions and by
the development of highly accurate numerical methods for the precise representation of near-wall structures. Several works have
been devoted to the development of B-spline methods on semi-structured embedded meshes. This technique allows a substantial
reduction in the computational cost of a simulation by using fine grids in physically significant flow regions only. The use of
B-splines is motivated by the development of robust and non-dissipative LES schemes on arbitrary meshes. The conservation of
physical invariants such as kinetic energy is highly desirable for the simulation of turbulent flows, and these requirements are
difficult to reproduce by finite-difference schemes on non-uniform meshes. Moreover, the resolution power of B-splines of maximum
continuity allows the representation of a broad range of scales of a turbulent flow. The work of Kravchenko et al. and Kravchenko
and Moin has shown the high suitability of B-spline methods for the computation of complex turbulent flows. However,
the Galerkin approximation that is employed is too CPU intensive. The method is burdened by the cost of evaluating nonlinear
terms where, as observed in Kravchenko et al., 50% of the computational time is spent on their evaluation. This report represents
a follow-up to the work initiated in Botella for developing a cost-effective B-spline Navier-Stokes solver. The equations are discretized
with the collocation method, which allows a drastic reduction of the cost of evaluating nonlinearities. A stable approximation
of the pressure is obtained by constructing staggered bases for the velocity and pressure which are, in a sense, the B-spline equivalent
to the popular staggered finite-difference discretization. The time-discretization employs a fractional step scheme. In association
with ’local’ (or ’explicit’) discretizations such as finite-difference or finite-volume approaches, fractional step techniques are
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