Cover page of review paper on compressible wall-bounded turbulence

A semi-meshless Lagrangian finite-volume framework based on Voronoi diagram for general elastoplastic Reissner-Mindlin shell

In this study, a semi-meshless Lagrangian finite-volume (FV) framework based on the Voronoi diagram is proposed for the Reissner–Mindlin shell considering general elastoplastic deformations. The governing equations of the strong form are derived rigorously based on Hamilton’s principle. For elastoplastic deformations, an incremental nonlinear elastoplasticity algorithm of stress update is developed for the Reissner–Mindlin shell. Based on the general governing equations of the strong form, a novel semi-meshless finite-volume framework for the Reissner–Mindlin shell is developed, and the local control volume is constructed via a local Voronoi diagram through the local material point and its neighboring stress points. At the stress points, the stress state is calculated with a kernel function method. The compensation terms are devised for further suppressing the zero-energy modes in mid-surface and the rotational motions of the shell, ensuring high numerical robustness. A set of challenging cases is simulated by the present method, with which the geometrically nonlinear and elastoplastic behaviors are validated with reliable accuracy and high stability.

A new troubled cell indicator and a new limiter based on TENO schemes for RKDG methods

Runge-Kutta discontinuous Galerkin (RKDG) methods are widely used for solving hyperbolic conservation laws, supplemented with troubled cell indicators and limiters to capture discontinuous solutions. However, traditional troubled cell indicators, such as the total variation bounded (TVB) minmod indicator and KXRCF indicator, generally rely on a critical parameter that is dependent on the solution of PDEs and needs tuning in a case-by-case manner. Moreover, the weighted essentially non-oscillatory (WENO) scheme, widely deployed as a limiter in RKDG methods to capture shock discontinuities, is highly dissipative and may substantially smear the small-scale flow structures. In this work, a new troubled cell indicator and a new limiter for RKDG methods based on targeted essentially non-oscillatory (TENO) scheme are proposed to overcome the above limitations. The proposed new troubled cell indicator adopts a uniform parameter for different cases, while the new limiter deploys a distinct smoothness indicator for enhancing robustness and a TENO stencil selection strategy to achieve a significantly lower numerical dissipation. A set of benchmark cases including strong shockwaves and a broad range of flow length scales is simulated to demonstrate the performance of the new scheme. The smooth accuracy test cases demonstrate that the new troubled cell indicator does not activate the nonlinear limiter, indicating its ability to accurately identify smooth regions without misjudging critical points as troubled cells. Additionally, more cases with discontinuities show the accuracy of the new troubled cell indicator and the low-dissipation property of the new limiter in comparison to the KXRCF indicator and the WENO limiter.

High-fidelity Reconstruction of Large-area Damaged Turbulent Fields with Physically-constrained Generative Adversarial Network

The reconstruction of incomplete information in flow fields is a pervasive challenge in numerous turbulence-related applications. This paper proposes a novel framework for the high-fidelity reconstruction of large-area damaged turbulent fields with high resolution based on a physically-constrained generative adversarial network. The network incorporates some special designs, such as leveraging complete/sparse fields of velocity components as physical constraints, employing a ResNet-like network with a fast Fourier convolution module, and adopting a PatchGAN discriminator network. To train the network, we employ a combination of loss functions, which comprise mean absolute error, network-level loss, and feature matching loss. We validate our method on a dataset of compressible isotropic turbulent flow and investigate three distinct damaged distributions with gap ratios of 39.06% and 56.25%. The proposed reconstruction framework has been shown to achieve excellent reconstruction performance. The reconstructed flow fields are consistent with the raw flow fields in terms of magnitude, power spectrum, and two-point correlation function. We also provide extensive ablation studies to validate our approach. The results indicate that the utilization of physical constraints significantly improves the reconstruction performance in damaged regions, particularly in cases that involve a large damaged area. Furthermore, in the proposed reconstruction framework, the size of patch in the PatchGAN discriminator network can be flexibly adjusted according to the scale of turbulence structures, and the perceptual loss function plays a crucial role in evaluating differences between feature maps of flow fields at network levels based on a pre-trained network. These special designs ensure consistency across diverse scales of turbulence structures and improve the accuracy and efficiency of network training.

A high-order diffuse-interface method with TENO-THINC scheme for compressible multiphase flows

High-fidelity numerical simulation of compressible multi-phase flows is of great challenge due to its competing requirements for resolving complex flow structures with low dissipation and capturing moving interfaces as well as other discontinuities sharply. Recently, a novel hybrid scheme, combining the standard targeted essentially non-oscillatory (TENO) scheme with Tangent of Hyperbola for INterface Capturing (THINC) scheme as two building blocks for smooth and non-smooth regions respectively and thus named as TENO-THINC, has been proposed and shows great potential for resolving complex single-phase fluids. In this work, a high-order finite-volume method, based on the TENO-THINC scheme for spatial reconstruction and the Harten-Lax-van Leer contact (HLLC) approximate Riemann solver for flux evaluation, is developed for simulating compressible multi-phase flows with a reduced five-equation formulation of the diffuse-interface model. The TENO-THINC scheme deploys the THINC reconstruction to resolve the physical discontinuities as well as the material interfaces within a few cells, and is desired to resolve the interface evolution more reliably in multi-phase flow simulations. Several algorithms have been implemented and elaborated for ensuring the numerical robustness of extreme simulations with high density and pressure ratios. Numerical results of the 1D and 2D challenging benchmark tests show that the TENO-THINC scheme is more robust than the standard TENO scheme and less dissipative than both the TENO and WENO-JS schemes. This property is essential for the long-term simulations of compressible multi-phase flows.

Progress in physical modeling of compressible wall-bounded turbulent flows

Understanding, modeling and control of the high-speed wall-bounded transition and turbulence not only receive wide academic interests but also are vitally important for high-speed vehicle design and energy saving because transition and turbulence can induce significant surface drag and heat transfer. The high-speed flows share some fundamental similarities with the incompressible counterparts according to Morkovin’s hypothesis, but there are also significant distinctions resulting from multi-physics coupling with thermodynamics, shocks, high-enthalpy effects and so on. In this paper, the recent advancements on the physics and modeling of high-speed wall-bounded transitional and turbulent flows are reviewed; most parts are covered by turbulence studies. For integrity of the physical process, we first briefly review the high-speed flow transition, with the main focus on aerodynamic heating principles and passive control strategies for transition delay. Afterward, we summarize recent encouraging findings on turbulent mean flow scaling laws for streamwise velocity and temperature, based on which a series of unique wall models are constructed to improve the simulation accuracy. As one of the foundations for turbulence modeling, the research survey on turbulent structures is also included, with particular focus on the scaling and modeling of energy-containing motions in the logarithmic region of boundary layers. Besides, we review a variety of linear models for predicting wall-bounded turbulence, which have achieved a great success over the last two decades, though turbulence is generally believed to be highly nonlinear. In the end, we conclude the review and outline future works.