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ABSTRACT: In a conventional numerical scheme, the computational domain is truncated from a large physical system, leaving the inflow/outflow
boundary conditions difficult to specify. In this study, a “spatial window function” is introduced to truncate the computational
domain from the physical domain in the streamwise direction. The standard compressible Navier-Stokes equations are transformed
into a set of equations which can be solved efficiently by Fourier spectral methods in the nonperiodic streamwise direction.
No numerical inflow/outflow boundary conditions are needed. The accuracy of the scheme is shown to be mainly related to the
window function. By properly designing the window function, spectral accuracy can be achieved. Issues concerning the numerical
implementation of this scheme are also discussed. Numerical validation has been carried out extensively. The results are in
good agreement with those from linear stability theory (LST), parabolized stability equations (PSE), and other spatial DNS
codes.
06/2011: pages 249-259;
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ABSTRACT: A short review of numerical simulation approaches for transitional and turbulent shear flows is presented. Some results using
large-eddy simulation (LES) are for canonical turbulent and transitional flows obtained with different subgrid-scale (SGS)
models such as a variant of the approximate deconvolution (ADM) and high-pass-filtered (HPF) eddy-viscosity model. Special
focus is the LES of transition in incompressible flow.
12/2004: pages 207-214;
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ABSTRACT: A formulation of the approximate deconvolution model (ADM) for the large-eddy simulation of flows in complex geometries is
detailed and applied to compressible turbulent flows. The paper considers two different issues. First, we study the feasibility
of low-order schemes with ADM for large-eddy simulation. As test case compressible decaying isotropic turbulence is considered.
Results obtained with low-order finite difference schemes and a pseudospectral scheme are compared with filtered well-resolved
direct numerical simulation (DNS) data. It is found that even for low-order schemes very good results can be obtained if the
cutoff wavenumber of the filter is adjusted to the modified wavenumber of the differentiation scheme. Second, we consider
the application of ADM to large-eddy simulation of the turbulent supersonic boundary layer along a compression ramp, which
exhibits considerable physical complexity due to the interaction of shock, separation, and turbulence in an ambient inhomogeneous
shear flow. The results compare very well with filtered DNS data and the filtered shock solution is correctly predicted by
the ADM procedure, demonstrating that turbulent and non-turbulent subgrid-scales are properly modeled. We found that a computationally
expensive shock-capturing technique as used in the DNS was not necessary for stable integration with the LES.
12/2003: pages 33-47;
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Physics of Fluids. 01/2001; 13(4):997.
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Physics of Fluids. 01/2001; 13(4):997.
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ABSTRACT: The subharmonic transition process of a flat-plate boundary layer at a free-stream Mach number of M[infty infinity] = 4.5 and a Reynolds number of 10000 based on free-stream velocity and initial displacement thickness is investigated by direct numerical simulation up to the beginning of turbulence. A second-mode instability superimposed with random noise of low amplitude is forced initially. The secondary subharmonic instability evolves from the noise in accordance with theory and leads to a staggered Λ-vortex pattern. Finite-amplitude Λ-vortices initiate the build-up of detached high-shear layers below and above the critical layer. The detached shear-layer generation and break-up are confined to the relative-subsonic part of the boundary layer. The breakdown to turbulence can be separated into two phases, the first being the break-up of the lower shear layer and the second being the break-up of the upper shear layer. Four levels of subsequent roll-up of the lower, Y-shaped shear layer have been observed, leading to new vortical structures which are unknown from transition at low Mach numbers. The upper shear layer behaviour is similar to that of the well-known high-shear layer in incompressible boundary-layer transition. It is concluded that, as in incompressible flow, turbulence is generated via a cascade of vortices and detached shear layers with successively smaller scales. The different phases of shear-layer break-up are also reflected in the evolution of averaged quantities. A strong decrease of the shape factor, as well as an increase of the skin friction coefficient, and a gradual loss of spanwise symmetry indicate the final breakdown to turbulence, where the mean velocity and temperature profiles approach those measured in fully turbulent flow.
Journal of Fluid Mechanics 06/1996; 317:301 - 335. · 2.46 Impact Factor
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ABSTRACT: The late stages of transition to turbulence in a Mach two boundary layer are investigated by direct numerical simulation of the compressible Navier-Stokes equations. The primary instability at this Mach number consists of oblique waves, which are known to form a pattern of quasi-streamwise vortices. It is found that breakdown does not follow immediately from these vortices, which decay in intensity. The generation of new vortices is observed by following the evolution of the pressure and vorticity in the simulation, and analysed by consideration of vorticity stretching. It is found that the slight inclined and skewed nature of the quasi-streamwise vortices leads to a production of oppositely signed streamwise vorticity, which serves as a strong localised forcing of the shear layer alongside the original vortices, formed by convection and stretching of spanwise vorticity. The shear layer rolls up into many new vortices, and is followed by a sharp increase in the energy of higher frequencies and in the skin friction.
Applied Scientific Research 03/1995; 54(3):223-234.
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ABSTRACT: One important alternative to spatial direct numerical simulation (SDNS) of a growing boundary-layer transition is a temporal direct numerical simulation (TDNS), where the flow is assumed to be locally parallel and the transition develops in time. To model nonparallel effects of a growing boundary layer, the TDNS allows the boundary layer to grow in time. This approach has been shown to be effective for an incompressible boundary layer. For a compressible boundary layer, however, a simple application of this approach has been found to be insufficient. To investigate this issue, we first split the variation of the flow field in the streamwise direction into a slowly evolving part and a fast and small-scale fluctuation part. By Taylor-expanding the slowly evolving large-scale part, this study shows that the Navier-Stokes operator can be reformulated as a power series of the perturbation parameter (x–x
0), yielding one set of equations for each power. Each set of these equations has a periodic solution in the streamwise direction, and therefore a modified TDNS method can be employed to solve these equations. Only the first set of the equations is considered in the applications presented. During the linear stage of transition, the results from this extended formulation show a significant improvement over those from the previous parallel flow formulation, especially for second modes which have short wavelengths. The results are well comparable with those from parabolized stability equations (PSE) and SDNS. A good agreement between this extended formulation and SDNS results is also demonstrated at the nonlinear stage.
Theoretical and Computational Fluid Dynamics 01/1995; 7(2):141-157. · 1.03 Impact Factor
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ABSTRACT: The present contribution reviews some of the recent progress obtained at our group in the direct numerical simulation (DNS) of compressible boundary layer transition. Elements of the different simulation approaches and numerical techniques employed are surveyed. Temporal and spatial simulations, as well as comparisons with results obtained from Parabolized Stability Equations, are discussed. DNS results are given for flat plate boundary layers in the Mach number range 1.6 to 4.5. A temporal DNS at Mach 4.5 has been continued through breakdown all the way to the turbulent stage. In addition results obtained with a recently developed extended temporal DNS approach are presented, which takes into account some nonparallel effects of a growing boundary layer. Results from this approach are quite close to those of spatial DNS, while preserving the efficiency of the temporal DNS.
01/1995;
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ABSTRACT: An inflow/outflow boundary treatment procedure is described for the numerical computation of non-periodic flows which allows for the use of periodic spatial boundary conditions. Due to this periodicity, e.g. efficient and accurate Fourier spectral methods can be applied. The governing equations of the flow are modified using window functions as known from signal processing. Thereby, the windowed solution is forced to zero to high order at the artificial boundaries. The physical solution near the boundaries is obtained by a regularised dewindowing operation and boundary conditions are imposed with the help of a suitable base flow which needs to be defined only within the window-boundary regions. On the inner domain, the unmodified flow equations are solved. The base flow can contain spatially and temporally varying disturbances. Hence it is possible to employ transitional and turbulent inflow conditions using the windowing technique.By properly designing the window function, spectral accuracy of a Fourier discretisation can be obtained. The performance of this scheme is analysed theoretically, verified numerically and compared to the more widely used fringe region technique. It is found that the accuracy of imposing the boundary conditions is similar for both techniques. Furthermore, for flow problems with a spatially evolving base flow, the windowing method does not require the base flow to be periodic.In this paper, the implementation of the windowing method in a two-dimensional incompressible Navier–Stokes code is examined and compared in detail to the fringe region technique for two test cases: The convection of a localised disturbance and a stationary, spatially evolving jet.
Journal of Computational Physics.
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ABSTRACT: Asymptotic stability of high-order finite-difference schemes for linear hyperbolic systems is investigated using the Nyquist criterion of linear-system theory. This criterion leads to a sufficient stability condition which is evaluated numerically. A fifth-order compact upwind-biased finite-difference scheme is developed which is asymptotically stable, according to the Nyquist criterion, for linear 2 × 2 systems. Moreover, this scheme is optimised with respect to its dispersion properties. The suitability of the scheme for discretisation of the compressible Navier–Stokes equations is demonstrated by computing inviscid and viscous eigensolutions of compressible Couette flow.
Journal of Computational Physics. 208(2):435-454.
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ABSTRACT: Evidence is presented that a two-dimensional saddle-point instability
mechanism is present in strictly two-dimensional Poiseuille flows, which
results in vorticity being ejected away from the wall, in a fashion that
recalls the ejections in natural turbulent channels. It is then shown
that the sublayer of natural wall turbulent flows contains structures
that have many features in common with the two-dimensional phenomena,
and that also appear to be responsible for at least some of the
vorticity ejections.
Near-Wall Turbulence. -1:7-27.
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ABSTRACT: The late stages of transition, from the Lambda-vortex stage up to
turbulence, are investigated by postprocessing data from a direct
numerical simulation of the complete Kappa-type transition process in
plane channel flow. The process by which the shear layer associated with
the Lambda-vortices rolls up into vortices is examined in detail.
Interactions between the different vortices, and between the two channel
halves, are found to be important. After breakup of the hairpin vortex a
sequence of events is observed, which includes the formation and roll-up
of a new shear layer, and results in the local appearance of 'wall
turbulence', characterized by high wall shear, sublayer streaks and
ejections. The generality of the findings are discussed with reference
to data from simulations of H-type and mixed-type transition.
-1:26.
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5. STAB-Workshop, Göttingen, 13.-15. Nov. 1991;
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AIAA/DGLR Fifth International Aerospace Planes and Hypersonics Technologies Conference;
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8. DGLR Fach-Symposium Strömung mit Ablösung;
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Cambridge, 8.-12. April 1991;
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Deutscher Luft- und Raumfahrtkongress, DGLR-Jahrestagung, Goettingen, 28.9.-1.10.1993;
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11th Canadian Symposium on Fluid Dynamics, Edmonton, Canada, June 10-12, 1994;
