A three-dimensional meshless fluid-shell interaction framework based on smoothed particle hydrodynamics coupled with semi-meshless thin shell

A new targeted essentially non-oscillatory (TENO) limiter with adaptive dissipation has been developed for the 3rd- and 4th-order spectral difference method. This limiter can potentially be useful for other nodal-based discontinuous high-order methods as well. Unlike traditional WENO limiters for these methods which limit low-order moments one by one, the new limiter is based on a direct convex combination of reconstruction polynomial candidates. This strategy ensures the good computational efficiency for high order reconstructions. The reconstruction stencils only involve nodal values from the target cell and its neighbors sharing faces with it. The reconstruction employs Hermite polynomials, making the new limiter compact. It can be implemented in a dimension-by-dimension manner for multi-dimensional problems, which is consistent with the spectral difference method. To further enhance efficiency, a TENO-based troubled-cell indicator is also developed to only activate limiters in troubled cells. Extensive one-dimensional and two-dimensional numerical experiments validate the performance of the new TENO-based limiter and indicator. In summary, the limiter is much less dissipative than WENO limiters and can resolve richer small-scale flow structures on coarse meshes. The indicator precisely marks out troubled cells, slightly improving over the KXRCF indicator.

Efficient dimension-by-dimension adaptive TENO-based limiter and troubled-cell indicator for nodal-based high-order spectral difference method

A new targeted essentially non-oscillatory (TENO) limiter with adaptive dissipation has been
developed for the 3rd- and 4th-order spectral difference method. This limiter can potentially be useful
for other nodal-based discontinuous high-order methods as well. Unlike traditional WENO limiters for
these methods which limit low-order moments one by one, the new limiter is based on a direct convex combination of reconstruction polynomial candidates. This strategy ensures the good computational efficiency for high order reconstructions. The reconstruction stencils only involve nodal values
from the target cell and its neighbors sharing faces with it. The reconstruction employs Hermite polynomials, making the new limiter compact. It can be implemented in a dimension-by-dimension manner for multi-dimensional problems, which is consistent with the spectral difference method. To further enhance efficiency, a TENO-based troubled-cell indicator is also developed to only activate limiters in troubled cells. Extensive one-dimensional and two-dimensional numerical experiments validate the performance of the new TENO-based limiter and indicator. In summary, the limiter is much less dissipative than WENO limiters and can resolve richer small-scale flow structures on coarse meshes. The indicator precisely marks out troubled cells, slightly improving over the KXRCF indicator.

Mean temperature scalings in compressible wall turbulence

In the present study, we report a new Mach number invariant function ($\phi_{S}$) for the mean temperature field in compressible wall turbulence. We demonstrate its validation by comparing it with the invariant functions derived in the previous studies, i.e., the semi-local-type ($\phi_{SL}$) and van-Driest-type ($\phi_{VD}$) scalings, case by case. To be specific, $\phi_{SL}$ works well in the inner layer of compressible channel flows with isothermal walls; $\phi_{S}$ works well in the inner layer of compressible channel flows with adiabatic walls, and supersonic/hypersonic turbulent boundary layers with cold walls; $\phi_{VD}$ does not work the best among all three functions in the flows under consideration. The newly proposed temperature transformations based on $\phi_{S}$ show an improvement in channel flows over adiabatic walls and supersonic/hypersonic turbulent boundary layers with cold walls. The effects of the generated high-order terms during derivation are also clarified. These findings may be revealing for the development of the near-wall model in high-speed aerodynamics.

A new high-order shock-capturing TENO scheme combined with skew-symmetric-splitting method for compressible gas dynamics and turbulence simulation

The high-order shock-capturing scheme is one of the main building blocks for the simulation of the compressible fluid characterized by strong shockwaves and broadband length scales. However, the classical shock-capturing scheme fails to perform long-time stable and non-dissipative simulations since the quadratic invariants associated with the conservation equations cannot be conserved as a result of the inherent numerical dissipation. Additionally, the overall computational cost for classical shock-capturing schemes is quite expensive as a result of the time-consuming local characteristic decomposition and the nonlinear-weights computing process. In this work, based on a new efficient discontinuity indicator, which distinguishes the non-smooth high-wavenumber fluctuations and discontinuities from smooth scales in the wavenumber space, a paradigm of high-order shock-capturing scheme by recasting the non-dissipative skew-symmetric-splitting method with newly optimized dispersion property for smooth flow scales and invoking the nonlinear targeted ENO (TENO) schemes for non-smooth discontinuities is proposed. The resulting TENO-S scheme not only successfully performs long-time stable computations for smooth flows without numerical dissipation, but also recovers the robust shock-capturing capabilities with adaptive numerical dissipation. Without the necessity of parameter tuning case by case, extensive benchmark simulations involving a wide range of flow length scales and strong discontinuities demonstrate that the proposed TENO-S scheme performs significantly better than the straightforward deployment of WENO/TENO-family schemes with better spectral property and higher computational efficiency.

An improved Baldwin-Lomax algebraic wall model for high-speed canonical turbulent boundary layers using established scalings

In this work, well-established relations for compressible turbulent mean flows, including the velocity transformation and algebraic temperature–velocity relation, are utilized for an improved algebraic Baldwin–Lomax (BL) wall model for high-speed zero-pressure-gradient boundary layers. Any new functions or coefficients fitted by ourselves are avoided. Twelve published direct numerical simulation (DNS) datasets are employed for a priori inspiration and a posteriori examination, with edge Mach numbers up to 14 under adiabatic, cold and heated walls. The baseline BL model is the widely used one with semi-local scaling. Three targeted modifications are made. First, the GFM transformation (Griffin et al., Proc. Natl. Acad. Sci., vol.118, 2021, p.34) is applied to the inner-layer eddy viscosity for improved scaling up to the logarithmic region. Second, the van Driest transformation is utilized in the outer layer based on compressible defect velocity scaling. Third, considering the difficulty in modelling the rapidly varying and singular turbulent Prandtl number near the temperature peak in cold-wall cases, the quadratic temperature–velocity relation is used to formulate the inner-layer temperature. Numerical results prove that the modifications take effect as designed. The prediction accuracy for mean streamwise velocity is notably improved for diabatic cases, especially in the logarithmic region. Moreover, a significant improvement in mean temperature is realized for both adiabatic and diabatic cases. The mean relative errors of temperature to DNS for all cases are down to 0.4% in logarithmic wall-normal coordinate and 3.4% in the normal coordinate, around one-third of those in the baseline model.

Multi-scale analysis of the space-time properties in incompressible wall-bounded turbulence

It is believed that the space-time correlation is a fundamental statistical theory for analyzing the dynamic coupling between spatial and temporal scales of the motions in turbulent flows. In this paper, by coupling the inner-outer interaction model (IOIM) with attached-eddy hypothesis, the space-time correlations of both wall-shear fluctuations and the streamwise velocity fluctuations carried by wall-attached eddies at a given length-scale are investigated. The present results demonstrate that the space-time correlations for the wall-shear stress fluctuation are mainly dominated by near-wall small-scale motions, and the superposition effects generated by wall-attached eddies are only reflected in the weakly correlated regions with large space separations and/or time delays. Furthermore, the findings in the present study demonstrate that, for the first time, wall-attached eddies at a given length scale feature distinctly different space-time properties as compared to that of ensembled eddies with multiple length scales, which provides a new perspective for analyzing the decorrelation mechanisms in turbulence theory and developing an advanced space-time correlation model.

Finite-volume TENO scheme with a new cell-interface flux evaluation strategy for unstructured meshes

The development of high-order shock-capturing schemes is critical for compressible fluid simulations, in particular for cases where both shock waves and small-scale turbulence structures present. As one of the state-of-the-art high-order numerical schemes, the family of high-order targeted ENO (TENO) schemes proposed by Fu et al. [Journal of Computational Physics 305 (2016): 333-359] has been demonstrated to perform well for compressible gas dynamics on structured meshes and recently extended to unstructured meshes by Ji et al. [Journal of Scientific Computing 92(2022): 1-39]. In this paper, with the observation that the TENO scheme not only provides the high-order reconstructed data at the cell interface but also features the potential to separate the local flow scales in the wavenumber space, we propose a low-dissipation finite-volume TENO scheme with a new cell-interface flux evaluation strategy for unstructured meshes. The novelty originates from the fact that the local flow scales are classified, following a strong scale separation in the reconstruction process, as “very smooth” or not. When the corresponding large central-biased stencil for the targeted cell interface is judged to be “very smooth”, a low-dissipation Riemann solver, even the non-dissipative central flux scheme, is employed for the cell-interface flux computing. Otherwise, a dissipative approximate Riemann solver is employed to avoid spurious oscillations and achieve stable shock-capturing. Such a strategy provides separate control over the numerical dissipation of the high-order reconstruction process and the cell-interface flux calculation within a unified framework and leads to a resultant finite-volume method with extremely low-dissipation properties and good numerical robustness. Without parameter tuning case by case, a set of canonical benchmark simulations has been conducted to assess the performance of the proposed scheme.

Resolvent analyses of incompressible turbulent channel, pipe and boundary-layer flows

This work investigates the linear responses of turbulent mean flow to harmonic forcing in incompressible channel, pipe, and zero-pressure-gradient boundary-layer flows. Employing established universal relations, the mean flow and associated eddy viscosity at Re_{\tau}=8000 are obtained. This research reveals that the most amplified perturbations in all three flows are streamwise uniform, corresponding to streamwise streaks originating from streamwise vortices. With the low-rank nature of the resolvent analysis, the streamwise energy density subject to harmonic forcings in a broad parameter space is examined. The greatest energy amplification occurs near the critical wall-normal location where the turbulent mean velocity matches the wave speed, aligning with Taylor’s frozen-turbulence hypothesis. Analysis centered on resolvent modes, where wave speeds match the mean velocity, uncovers that the coherent structures related to these modes are geometrically self-similar. The spanwise dimensions of these structures are proportional to their distance from the wall, thereby providing robust evidence supporting the attached-eddy model. Furthermore, the constructed premultiplied energy spectra based on the linear operator can identify large-scale motions and very-large-scale motions in wall-bounded turbulent flows, suggesting their capacity to be amplified by the mean flow.

Investigation on the inclination angles of wall-attached eddies for streamwise velocity and temperature fields in compressible turbulent channel flows

The attached eddy hypothesis (AEH) (Townsend, Cambridge University Press, 1976), as one of the most elegant models in incompressible wall turbulence, has been recently applied to compressible wall turbulence to explain the numerical observations and predict the scaling laws. Before a more profound extension can be established, a comprehensive investigation of the features of wall-attached eddies for streamwise velocity and temperature fields in compressible wall-bounded turbulence is required. In this work, the AEH and the inner-outer interaction model (Marusic et al., Science, vol. 329, 2010, pp. 193–196) are combined to isolate the signature of attached eddies at a targeted length scale and then assess their inclination angles statistically based on the Direct Numerical Simulation (DNS) database. The inclination angle obtained in the streamwise velocity fluctuating fields, which approaches $45^\circ$ as the Reynolds number increases, shows a minor Mach-number influence within the Mach-number range included in this work. As for those in temperature fluctuations, a high statistical similarity can be seen to streamwise velocity fluctuations. This slight Mach-number effect indicates that a uniform model can be potentially developed for compressible wall-bounded turbulence with different Mach numbers in the future.

On the streamwise velocity, temperature and passive scalar fields in compressible turbulent channel flows: a viewpoint from multi-physics couplings

It is generally believed that the velocity and passive scalar fields share many similarities and differences in wall-bounded turbulence. In the present study, we conduct a series of direct numerical simulations of compressible channel flows with passive scalars and employ the two-dimensional spectral linear stochastic estimation and the correlation function as diagnostic tools to shed light on these aspects. Particular attention is paid to the relevant multi-physics couplings in the spectral domain, i.e., the velocity-temperature (u-T), scalar-temperature (g-T), and velocity-scalar (u-g) couplings. These couplings are found to be utterly different at a given wall-normal position in the logarithmic and outer regions. Specifically, in the logarithmic region, the u-T and u-g couplings are tight at the scales that correspond to the attached eddies and the very large-scale motions (VLSMs), whereas the g-T coupling is robust in the whole spectral domain. In the outer region, u-T and u-g couplings are only active at the scales corresponding to the VLSMs, whereas the g-T coupling is diminished but still strong at all scales. Further analysis indicates that although the temperature field in the vast majority of zones in a channel can be roughly treated as a passive scalar, its physical properties gradually deviate from those of a pure passive scalar as the wall-normal height increases due to the enhancement of the acoustic mode. Furthermore, the deep involvement of the pressure field in the self-sustaining process of energy-containing motions also drives the streamwise velocity fluctuation away from a passive scalar. The current work is an extension of our previous study (Cheng, C. & Fu, L., J. Fluid Mech., vol. 964, 2023, A15), and further uncovers the details of the multi-physics couplings in compressible wall turbulence.