We analyse the low-frequency dynamics of a high Reynolds number impinging shock-wave/turbulent boundary-layer interaction (SWBLI) with strong mean-flow separation. The flow configuration for our ...grid-converged large-eddy simulations (LES) reproduces recent experiments for the interaction of a Mach 3 turbulent boundary layer with an impinging shock that nominally deflects the incoming flow by
$19.6^{\circ }$
. The Reynolds number based on the incoming boundary-layer thickness of
$Re_{\unicodeSTIX{x1D6FF}_{0}}\approx 203\times 10^{3}$
is considerably higher than in previous LES studies. The very long integration time of
$3805\unicodeSTIX{x1D6FF}_{0}/U_{0}$
allows for an accurate analysis of low-frequency unsteady effects. Experimental wall-pressure measurements are in good agreement with the LES data. Both datasets exhibit the distinct plateau within the separated-flow region of a strong SWBLI. The filtered three-dimensional flow field shows clear evidence of counter-rotating streamwise vortices originating in the proximity of the bubble apex. Contrary to previous numerical results on compression ramp configurations, these Görtler-like vortices are not fixed at a specific spanwise position, but rather undergo a slow motion coupled to the separation-bubble dynamics. Consistent with experimental data, power spectral densities (PSD) of wall-pressure probes exhibit a broadband and very energetic low-frequency component associated with the separation-shock unsteadiness. Sparsity-promoting dynamic mode decompositions (SPDMD) for both spanwise-averaged data and wall-plane snapshots yield a classical and well-known low-frequency breathing mode of the separation bubble, as well as a medium-frequency shedding mode responsible for reflected and reattachment shock corrugation. SPDMD of the two-dimensional skin-friction coefficient further identifies streamwise streaks at low frequencies that cause large-scale flapping of the reattachment line. The PSD and SPDMD results of our impinging SWBLI support the theory that an intrinsic mechanism of the interaction zone is responsible for the low-frequency unsteadiness, in which Görtler-like vortices might be seen as a continuous (coherent) forcing for strong SWBLI.
Although classical WENO schemes have achieved great success and are widely accepted, they exhibit several shortcomings. They are too dissipative for direct simulations of turbulence and lack ...robustness when very-high-order versions are applied to complex flows. In this paper, we propose a family of high-order targeted ENO schemes which are applicable for compressible-fluid simulations involving a wide range of flow scales. In order to increase the numerical robustness as compared to very-high-order classical WENO schemes, the reconstruction dynamically assembles a set of low-order candidate stencils with incrementally increasing width. While discontinuities and small-scale fluctuations are efficiently separated, the numerical dissipation is significantly diminished by an ENO-like stencil selection, which either applies a candidate stencil with its original linear weight, or removes its contribution when it is crossed by a discontinuity. The background linear scheme is optimized under the constraint of preserving an approximate dispersion–dissipation relation. By means of quasi-linear analyses and practical numerical experiments, a set of case-independent parameters is determined. The general formulation of arbitrarily high-order schemes is presented in a straightforward way. A variety of benchmark-test problems, including broadband waves, strong shock and contact discontinuities are studied. Compared to well-established classical WENO schemes, the present schemes exhibit significantly improved robustness, low numerical dissipation and sharp discontinuity capturing. They are particularly suitable for DNS and LES of shock–turbulence interactions.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
•Derivation of a centralized flux formulation for the HLLC solver.•Dissipation control in transverse direction to shock propagation.•Smooth reduction of nonlinear signal speeds suppresses shock ...instability.•HLLC-LM proves stable for extreme resolutions also in three dimensions.
The purpose of this paper is twofold. First, the application of high-order methods in combination with the popular HLLC Riemann solver demonstrates that the grid-aligned shock instability can strongly affect simulation results when the grid resolution is increased. Beyond the well-documented two-dimensional behavior, the problem is particularly troublesome with three-dimensional simulations. Hence, there is a need for shock-stable modifications of HLLC-type solvers for high-speed flow simulations.
Second, the paper provides a stabilization of the popular HLLC flux based on a recently proposed mechanism for grid aligned-shock instabilities Fleischmann et al. (2020) 8. The instability was found to be triggered by an inappropriate scaling of acoustic and advection dissipation for local low Mach numbers. These low Mach numbers occur during the calculation of fluxes in transverse direction of the shock propagation, where the local velocity component vanishes. A centralized formulation of the HLLC flux is provided for this purpose, which allows for a simple reduction of nonlinear signal speeds. In contrast to other shock-stable versions of the HLLC flux, the resulting HLLC-LM flux reduces the inherent numerical dissipation of the scheme.
The robustness of the proposed scheme is tested for a comprehensive range of cases involving strong shock waves. Three-dimensional single- and multi-component simulations are performed with high-order methods to demonstrate that the HLLC-LM flux also copes with latest challenges of compressible high-speed computational fluid dynamics.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
We develop a mesoscopic lattice Boltzmann model for liquid-vapor phase transition by handling the microscopic molecular interaction. The short-range molecular interaction is incorporated by ...recovering an equation of state for dense gases, and the long-range molecular interaction is mimicked by introducing a pairwise interaction force. Double distribution functions are employed, with the density distribution function for the mass and momentum conservation laws and an innovative total kinetic energy distribution function for the energy conservation law. The recovered mesomacroscopic governing equations are fully consistent with kinetic theory, and thermodynamic consistency is naturally satisfied.
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CMK, CTK, FMFMET, IJS, NUK, PNG, UL, UM
The standard smoothed particle hydrodynamics (SPH) method suffers from tensile instability. In fluid-dynamics simulations this instability leads to particle clumping and void regions when negative ...pressure occurs. In solid-dynamics simulations, it results in unphysical structure fragmentation. In this work the transport-velocity formulation of Adami et al. (2013) 14 is generalized for providing a solution of this long-standing problem. Other than imposing a global background pressure, a variable background pressure is used to modify the particle transport velocity and eliminate the tensile instability completely. Furthermore, such a modification is localized by defining a shortened smoothing length. The generalized formulation is suitable for fluid and solid materials with and without free surfaces. The results of extensive numerical tests on both fluid and solid dynamics problems indicate that the new method provides a unified approach for multi-physics SPH simulations.
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•The new framework establishes a unified concept of TENO schemes with classical nonlinear limiters for shock-capturing.•In smooth regions, all candidate stencils are identified as smooth by the TENO ...stencil selection procedure and TENO-M recovers to TENO.•The present framework can be applied to a wide range of limiters, such as TVD and MP.•The results show that adapting nonlinear numerical dissipation in nonsmooth regions can be controlled by the choice of limiter function.
In this work, a framework to construct arbitrarily high-order low-dissipation shock-capturing schemes with flexible and controllable nonlinear dissipation for convection-dominated problems is proposed. While a set of candidate stencils of incremental width is constructed, each one is indicated as smooth or nonsmooth by the ENO-like stencil selection procedure proposed in the targeted essentially non-oscillatory (TENO) scheme (Fu et al. 2016 9). Rather than being discarded directly as with TENO schemes, the nonsmooth candidates are filtered by an extra nonlinear limiter, such as a monotonicity-preserving (MP) limiter or a total variation diminishing (TVD) limiter. Consequently, high-order reconstruction is achieved by assembling candidate fluxes with optimal linear weights since they are either smooth reconstructions or filtered ones which feature good non-oscillation property. A weight renormalization procedure as with the standard TENO paradigm is not necessary. This new framework concatenates the concepts of TENO, WENO and other nonlinear limiters for shock-capturing, and provides a new insight to designing low-dissipation nonlinear schemes. Through the adaptation of nonlinear limiters, nonlinear dissipation in the newly proposed framework can be controlled separately without affecting the performance in smooth regions. Based on the proposed framework, a family of new six- and eight-point nonlinear schemes with controllable dissipation is proposed. A set of critical benchmark cases involving strong discontinuities and broadband fluctuations is simulated. Numerical results reveal that the proposed new schemes capture discontinuities sharply and resolve the high-wavenumber fluctuations with low dissipation, while maintaining the desired accuracy order in smooth regions.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
In Fu et al. 23, a family of high-order targeted ENO (TENO) schemes with a new nonlinear weighting strategy has been proposed. Building upon this strategy, in the current paper, a new class of ...adaptive TENO schemes for hyperbolic conservation laws is proposed based on three new concepts: (1) a hierarchical voting strategy is proposed to improve the ENO-like stencil selection; (2) the TENO weighting strategy is extended to function as a built-in discontinuity-location detector. Since the reconstruction scheme must not cross any discontinuity, corresponding target schemes are selected from a set of predefined linear schemes which are optimized towards maximum accuracy order or spectral resolution; (3) based on the observation that the cut-off parameter CT in the TENO weighting strategy determines nonlinear dissipation, a CT adaptation strategy is developed to minimize numerical dissipation for high-wavenumber fluctuations while maintaining robustness for shock-capturing. Six-point and eight-point TENO schemes are constructed, and their spectral properties are analyzed by the ADR analysis. A set of benchmark cases is considered to demonstrate the performance of proposed adaptive TENO schemes. Numerical results suggest that the proposed TENO schemes preserve the accuracy order at first and second order critical points and show less numerical dissipation compared with typical WENO schemes. Moreover, the TENO8-NA scheme exhibits good results for both highly compressible flows and nearly incompressible turbulence.
•A hierarchical voting strategy to improve the ENO-like stencil selection.•Targeted ENO weighting strategy extended as a built-in discontinuity-location detector.•New adaptation strategy for resolving high-wavenumber fluctuations and shock-capturing.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
This work presents a data-driven approach to the identification of spatial and temporal truncation errors for linear and nonlinear discretization schemes of Partial Differential Equations (PDEs). ...Motivated by the central role of truncation errors, for example in the creation of implicit Large Eddy schemes, we introduce the Sparse Identification of Truncation Errors (SITE) framework to automatically identify the terms of the modified differential equation from simulation data. We build on recent advances in the field of data-driven discovery and control of complex systems and combine it with classical work on modified differential equation analysis of Warming, Hyett, Lerat and Peyret. We augment a sparse regression-rooted approach with appropriate preconditioning routines to aid in the identification of the individual modified differential equation terms. The construction of such a custom algorithm pipeline allows attenuating of multicollinearity effects as well as automatic tuning of the sparse regression hyperparameters using the Bayesian information criterion (BIC). As proof of concept, we constrain the analysis to finite difference schemes and leave other numerical schemes open for future inquiry. Test cases include the linear advection equation with a forward-time, backward-space discretization, the Burgers' equation with a MacCormack predictor-corrector scheme and the Korteweg-de Vries equation with a Zabusky and Kruska discretization scheme. Based on variation studies, we derive guidelines for the selection of discretization parameters, preconditioning approaches and sparse regression algorithms. The results showcase highly accurate predictions underlining the promise of SITE for the analysis and optimization of discretization schemes, where analytic derivation of modified differential equations is infeasible.
•Sparse regression based framework to automatically identify truncation error terms.•Proving modified differential equations can be identified from simulation data.•Preconditioning at multiple stages attenuates multicollinearity effects.•Highly accurate results for test cases with main limit being machine precision.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
Modern applications of computational fluid dynamics involve complex interactions across scales such as shock interactions with turbulent structures and multiphase interfaces. Such phenomena, which ...occur at very small physical viscosity, require high-resolution and low-dissipation compressible flow solvers. Many recent publications have focused on the design of high-order accurate numerical schemes and provide e.g. weighted essentially non-oscillatory (WENO) stencils up to 17th order for this purpose. As shown in detail by different authors, such schemes tremendously decrease adverse effects of numerical dissipation. However, such schemes are prone to numerically induced symmetry breaking which renders validation for the targeted problem range problematic.
In this paper, we show that symmetry-breaking relates to vanishing numerical viscosity and is driven systematically by algorithmic floating-point effects which are no longer hidden by numerical dissipation. We propose a systematic procedure to deal with such errors by numerical and algorithmic formulations which respect floating-point arithmetic. We show that by these procedures inherent symmetries are preserved for a broad range of test cases with high-order shock-capturing schemes in particular in the high-resolution limit for both 2D and 3D.
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The surface thermodynamics and wetting condition are investigated for the recent multiphase lattice Boltzmann model with a self-tuning equation of state (EOS), where the multiphase EOS is specified ...in advance and the reduced temperature is set to a relatively low value. The surface thermodynamics is first explored starting from the free-energy functional of a multiphase system and a theoretical expression for the contact angle is derived for the general multiphase EOS. The conventional free-energy density for the solid surface, which is in linear form, is analysed, and it is found that the fluid density on the solid surface significantly deviates from that in the bulk phase when the reduced temperature is relatively low. A new free-energy density for the solid surface, which is in hyperbolic tangent form, is then proposed. Two independent parameters are introduced, which can dramatically reduce the density deviation and effectively adjust the contact angle, respectively. Meanwhile, the contact angle, surface tension and interface thickness can be independently adjusted in the present theoretical framework. Based on the analysed surface thermodynamics, a thermodynamically consistent treatment for the wetting condition is proposed for both straight and curved walls. Numerical tests of droplets on straight and curved walls validate the theoretical analysis of the surface thermodynamics and the present wetting condition treatment. As further applications, a moving droplet on an inclined wall, which is vertically and sinusoidally oscillated, and the evaporation of a droplet on an adiabatic substrate are simulated, and satisfying results consistent with previous studies are obtained.
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