The robustness issue on multigrid schemes applied to the Navier–Stokes equations for laminar and turbulent,incompressible and compressible flows

The paper's leitmotiv is condensed in one word: robustness. This is a real hindrance for the successful implementation of any multigrid scheme for solving the Navier–Stokes set of equations. In this paper, many hints are given to improve this issue. Instead of looking for the best possible speed‐up rate for a particular set of problems, at a given regime and in a given condition, the authors propose some ideas pursuing reasonable speed‐up rates in any situation. In a previous paper, the authors presented a multigrid method for solving the incompressible turbulent RANS equations, with particular care in the robustness and flexibility of the solution scheme. Here, these concepts are further developed and extended to compressible laminar and turbulent flows. This goal is achieved by introducing a non‐linear multigrid scheme for compressible laminar (NS equations) and turbulent flow (RANS equations), taking benefit of a convenient master–slave implementation strategy. Copyright © 2004 John Wiley & Sons, Ltd.     

A reformulated synthetic turbulence generation method for a zonal RANS–LES method and its application to zero-pressure gradient boundary layers

A synthetic turbulence generation (STG) method for subsonic and supersonic flows at low and moderate Reynolds numbers to provide inflow distributions of zonal Reynolds-averaged Navier–Stokes (RANS) – large-eddy simulation (LES) methods is presented. The STG method splits the LES inflow region into three planes where a local velocity signal is decomposed from the turbulent flow properties of the upstream RANS solution. Based on the wall-normal position and the local flow Reynolds number, specific length and velocity scales with different vorticity content are imposed at the inlet plane of the boundary layer. The quality of the STG method for incompressible and compressible zero-pressure gradient boundary layers is shown by comparing the zonal RANS–LES data with pure LES, pure RANS, and direct numerical simulation (DNS) solutions. The distributions of the time and spanwise wall-shear stress, Reynolds stress distributions, and two point correlations of the zonal RANS–LES simulations are smooth in the transition region and in good agreement with the pure LES and reference DNS findings. The STG approach reduces the RANS-to-LES transition length to less than four boundary-layer thicknesses.     

Numerical simulations of non‐equilibrium turbulent boundary layer flowing over a bump

Large‐eddy simulation (LES) and Reynolds‐averaged Navier–Stokes simulation (RANS) with different turbulence models (including the standard k?ε, the standard k?ω, the shear stress transport k?ω (SST k?ω), and Spalart–Allmaras (S–A) turbulence models) have been employed to compute the turbulent flow of a two‐dimensional turbulent boundary layer over an unswept bump. The predictions of the simulations were compared with available experimental measurements in the literature. The comparisons of the LES and the SST k?ω model including the mean flow and turbulence stresses are in satisfied agreements with the available measurements. Although the flow experiences a strong adverse pressure gradient along the rear surface, the boundary layer is unique in that intermittent detachment occurring near the wall. The numerical results indicate that the boundary layer is not followed by mean‐flow separation or incipient separation as shown from the numerical results. The resolved turbulent shear stress is in a reasonable agreement with the experimental data, though the computational result of LES shows that its peak is overpredicted near the trailing edge of the bump, while the other used turbulence models, except the standard k?ε, underpredicts it. Analysis of the numerical results from LES confirms the experimental data, in which the existence of internal layers over the bump surface upstream of the summit and along the downstream flat plate. It also demonstrates that the quasi‐step increase in skin friction is due to perturbations in pressure gradient. The surface curvature enhances the near‐wall shear production of turbulent stresses, and is responsible for the formation of the internal layers. The aim of the present work is to examine the response and prediction capability of LES with the dynamic eddy viscosity model as a sub‐grid scale to the complex turbulence structure with the presence of streamline curvature generated by a bumpy surface. Aiming to reduce the computational costs with focus on the mean behavior of the non‐equilibrium turbulent boundary layer of flow over the bump surface, the present investigation also explains the best capability of one of the used RANS turbulence models to capture the driving mechanism for the surprisingly rapid return to equilibrium over the trailing flat plate found in the measurements. Copyright © 2010 John Wiley & Sons, Ltd.     

Mesh adaptation framework for embedded boundary methods for computational fluid dynamics and fluid-structure interaction

Embedded Boundary Methods (EBMs) are often preferred for the solution of Fluid-Structure Interaction (FSI) problems because they are reliable for large structural motions/deformations and topological changes. For viscous flow problems, however, they do not track the boundary layers that form around embedded obstacles and therefore do not maintain them resolved. Hence, an Adaptive Mesh Refinement (AMR) framework for EBMs is proposed in this paper. It is based on computing the distance from an edge of the embedding computational fluid dynamics mesh to the nearest embedded discrete surface and on satisfying the y⁺ requirements. It is also equipped with a Hessian-based criterion for resolving flow features such as shocks, vortices, and wakes and with load balancing for achieving parallel efficiency. It performs mesh refinement using a parallel version of the newest vertex bisection method to maintain mesh conformity. Hence, while it is sufficiently comprehensive to support many discretization methods, it is particularly attractive for vertex-centered finite volume schemes where dual cells tend to complicate the mesh adaptation process. Using the EBM known as FIVER, this AMR framework is verified for several academic FSI problems. Its potential for realistic FSI applications is also demonstrated with the simulation of a challenging supersonic parachute inflation dynamics problem.     

An immersed boundary-lattice Boltzmann flux solver and its applications to fluid–structure interaction problems

An immersed boundary-lattice Boltzmann flux solver (IB–LBFS) for the simulation of two-dimensional fluid–structure interaction (FSI) problems is presented in this paper. The IB–LBFS applies the fractional-step method to split the overall solution process into the predictor step and the corrector step. In the predictor step, the intermediate flow field is predicted by applying the LBFS (lattice Boltzmann flux solver) without considering the presence of immersed object. The LBFS applies the finite volume method to solve N–S (Navier–Stokes) equations for the flow variables at cell centers. At each cell interface, the LBFS evaluates its viscous and inviscid fluxes simultaneously through local reconstruction of the LBE (lattice Boltzmann equation) solutions. In the corrector step, the intermediate flow field is corrected by the implicit boundary condition-enforced immersed boundary method (IBM) so that the no-slip boundary conditions can be accurately satisfied. The IB–LBFS effectively combines the advantages of the LBFS in solving the flow field and the flexibility of the IBM in dealing with boundary conditions. Consequently, the IB–LBFS presents a much simpler and more effective approach for simulating complex FSI problems on non-uniform grids. Several test cases, including flows past one and two cylinders with prescribed motions, are firstly simulated to examine the accuracy of present solver. After that, two strongly coupled fluid–structure interaction problems, i.e., particle sedimentations and vortex-induced vibrations of a circular cylinder are investigated. Good agreements between the present results and those in literature verify the capability and flexibility of IB–LBFS for simulating FSI problems.     

Parallel finite element computation of missile aerodynamics

A flow simulation tool, developed by the authors at the Army HPC Research Center, for compressible flows governed by the Navier–Stokes equations is used to study missile aerodynamics at supersonic speeds, high angles of attack and for large Reynolds numbers. The goal of this study is the evaluation of this Navier–Stokes computational technique for the prediction of separated flow fields around high-length-to-diameter (L/D) bodies. In particular, this paper addresses two issues: (i) turbulence modelling with a finite element computational technique and (ii) efficient performance of the computational technique on two different multiprocessor mainframes, the Thinking Machines CM-5 and CRAY T3D. The paper first provides a discussion of the Navier–Stokes computational technique and the algorithm issues for achieving efficient performance on the CM-5 and T3D. Next, comparisons are shown between the computation and experiment for supersonic ramp flow to evaluate the suitability of the turbulence model. Following that, results of the computations for missile flow fields are shown for laminar and turbulent viscous effects. © 1997 John Wiley & Sons, Ltd.     

Algorithms for interface treatment and load computation in embedded boundary methods for fluid and fluid–structure interaction problems

Embedded boundary methods for CFD (computational fluid dynamics) simplify a number of issues. These range from meshing the fluid domain, to designing and implementing Eulerian‐based algorithms for fluid–structure applications featuring large structural motions and/or deformations. Unfortunately, embedded boundary methods also complicate other issues such as the treatment of the wall boundary conditions in general, and fluid–structure transmission conditions in particular. This paper focuses on this aspect of the problem in the context of compressible flows, the finite volume method for the fluid, and the finite element method for the structure. First, it presents a numerical method for treating simultaneously the fluid pressure and velocity conditions on static and dynamic embedded interfaces. This method is based on the exact solution of local, one‐dimensional, fluid–structure Riemann problems. Next, it describes two consistent and conservative approaches for computing the flow‐induced loads on rigid and flexible embedded structures. The first approach reconstructs the interfaces within the CFD solver. The second one represents them as zero level sets, and works instead with surrogate fluid/structure interfaces. For example, the surrogate interfaces obtained simply by joining contiguous segments of the boundary surfaces of the fluid control volumes that are the closest to the zero level sets are explored in this work. All numerical algorithms presented in this paper are applicable with any embedding CFD mesh, whether it is structured or unstructured. Their performance is illustrated by their application to the solution of three‐dimensional fluid–structure interaction problems associated with the fields of aeronautics and underwater implosion. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical study of an oscillatory turbulent flow over a flat plate

Oscillatory turbulent flow over a flat plate is studied using large eddy simulation (LES) and Reynolds-average Navier-Stokes (RANS) methods. A dynamic subgrid-scale model is employed in LES and Saffman's turbulence model is used in RANS. The flow behaviors are discussed for the accelerating and decelerating phases during the oscillating cycle. The friction force on the wall and its phase shift from laminar to turbulent regime are also investigated for different Reynolds numbers. The project supported by the Youngster Funding of Academia Sinica and by the National Natural Science Foundation of China     

A stabilized Nitsche‐type extended embedding mesh approach for 3D low‐ and high‐Reynolds‐number flows

This paper presents a stabilized extended finite element method (XFEM) based fluid formulation to embed arbitrary fluid patches into a fixed background fluid mesh. The new approach is highly beneficial when it comes to computational grid generation for complex domains, as it allows locally increased resolutions independent from size and structure of the background mesh. Motivating applications for such a domain decomposition technique are complex fluid‐structure interaction problems, where an additional boundary layer mesh is used to accurately capture the flow around the structure. The objective of this work is to provide an accurate and robust XFEM‐based coupling for low‐ as well as high‐Reynolds‐number flows. Our formulation is built from the following essential ingredients: Coupling conditions on the embedded interface are imposed weakly using Nitsche's method supported by extra terms to guarantee mass conservation and to control the convective mass transport across the interface for transient viscous‐dominated and convection‐dominated flows. Residual‐based fluid stabilizations in the interior of the fluid subdomains and accompanying face‐oriented fluid and ghost‐penalty stabilizations in the interface zone stabilize the formulation in the entire fluid domain. A detailed numerical study of our stabilized embedded fluid formulation, including an investigation of variants of Nitsche's method for viscous flows, shows optimal error convergence for viscous‐dominated and convection‐dominated flow problems independent of the interface position. Challenging two‐dimensional and three‐dimensional numerical examples highlight the robustness of our approach in all flow regimes: benchmark computations for laminar flow around a cylinder, a turbulent driven cavity flow at Re = 10000 and the flow interacting with a three‐dimensional flexible wall. Copyright © 2016 John Wiley & Sons, Ltd.     

Status of turbulence modeling for hypersonic propulsion flowpaths

This report provides an assessment of current turbulent flow calculation methods for hypersonic propulsion flowpaths, particularly the scramjet engine. Emphasis is placed on Reynolds-averaged Navier–Stokes (RANS) methods, but some discussion of newer methods such as large eddy simulation (LES) is also provided. The report is organized by considering technical issues throughout the scramjet-powered vehicle flowpath, including laminar-to-turbulent boundary layer transition, shock wave/turbulent boundary layer interactions, scalar transport modeling (specifically the significance of turbulent Prandtl and Schmidt numbers), and compressible mixing. Unit problems are primarily used to conduct the assessment. In the combustor, results from calculations of a direct connect supersonic combustion experiment are also used to address the effects of turbulence model selection and in particular settings for the turbulent Prandtl and Schmidt numbers. It is concluded that RANS turbulence modeling shortfalls are still a major limitation to the accuracy of hypersonic propulsion simulations, whether considering individual components or an overall system. Newer methods such as LES-based techniques may be promising, but are not yet at a maturity to be used routinely by the hypersonic propulsion community. The need for fundamental experiments to provide data for turbulence model development and validation is discussed.     

Joint RANS/LES Approach to Premixed Flame Modelling in the Context of the TFC Combustion Model

We present an original timesaving joint RANS/LES approach to simulate turbulent premixed combustion. It is intended mainly for industrial applications where LES may not be practical. It is based on successive RANS/LES numerical modelling, where turbulent characteristics determined from RANS simulations are used in LES equations for estimation of the subgrid chemical source and viscosity. This approach has been developed using our TFC premixed combustion model, which is based on a generalization of the Kolmogorov’s ideas. We assume existence of small-scale statistically equilibrium structures not only of turbulence but also of the reaction zones. At the same time, non-equilibrium large-scale structures of reaction sheets and turbulent eddies are described statistically by model combustion and turbulence equations in RANS simulations or follow directly without modelling in LES. Assumption of small-scale equilibrium gives an opportunity to express the mean combustion rate (controlled by small-scale coupling of turbulence and chemistry) in the RANS and LES sub-problems in terms of integral or subgrid parameters of turbulence and the chemical time, i.e. the definition of the reaction rate is similar to that of the mean dissipation rate in turbulence models where it is expressed in terms of integral or subgrid turbulent parameters. Our approach therefore renders compatible the combustion and turbulent parts of the RANS and LES sub-problems and yields reasonable agreement between the RANS and averaged LES results. Combining RANS simulations of averaged fields with LES method (and especially coupled and acoustic codes) for simulation of corresponding nonstationary process (and unsteady combustion regimes) is a promising strategy for industrial applications. In this work we present results of simulations carried out employing the joint RANS/LES approach for three examples: High velocity premixed combustion in a channel, combustion in the shear flow behind an obstacle and the impinging flame (a premixed flame attached to an obstacle).     

Implementation and Evaluation of an Embedded LES-RANS Solver

In the current work, we present the development and application of an embedded large-eddy simulation (LES) - Reynolds-averaged Navier Stokes (RANS) solver. The novelty of the present work lies in fully embedding the LES region inside a global RANS region through an explicit coupling at the arbitrary mesh interfaces, exchanging flow and turbulence quantities. In particular, a digital filter method (DFM) extracting mean flow, turbulent kinetic energy and Reynolds stress profiles from the RANS region is used to provide meaningful turbulent fluctuations to the LES region. The framework is developed in the open-source computational fluid dynamics software OpenFOAM. The embedding approach is developed and validated by simulating a spatially developing turbulent channel flow. Thereafter, flow over a surface mounted spanwise-periodic vertical fence is simulated to demonstrate the importance of the DFM and the effect of the location of the RANS-LES interface. Mean and second-order statistics are compared with direct numerical simulation (DNS) data from the literature. Results indicate that feeding synthetic turbulence at the LES interface is essential to achieve good agreement for the mean flow quantities. However, in order to obtain a good match for the Reynolds stresses, the LES interface needs to be placed sufficiently far upstream, which in the present case was six spoiler heights before the fence. Further, a realistic spoiler configuration with finite-width in the spanwise direction and inclined at 30 degrees was simulated using the embedding approach. As opposed to the vertical fence case this is a genuinely (statistically) three-dimensional case and a very good match with mean and second-order statistics was obtained with the experimental data. Finally, in order to test the present solver for high sub-sonic speed flows the flow over an open cavity was simulated. A good match with reference data is obtained for mean and turbulence profile comparisons. Tones in the pressure spectra were predicted reasonably well and an overall sound pressure level with a maximum deviation of 2.6 d B was obtained with the present solver when compared with the experimental data.     

Investigation of three-dimensional effects on a cavitating Venturi flow

A numerical investigation of the behaviour of a cavitation pocket developing along a Venturi geometry has been performed using a compressible one-fluid hybrid RANS/LES solver. The interplay between turbulence and cavitation regarding the unsteadiness and structure of the flow is complex and not well understood. This constitutes a determinant point to accurately simulate the dynamic of sheet cavities. Various turbulent approaches are tested: a new Scale-Adaptive model and the Detached Eddy Simulation. 2D and 3D simulations are compared with the experimental data. An oblique mode of the sheet is put in evidence.     

Numerical solution of single and multi‐phase internal transonic flow problems

This paper presents numerical methods for solving turbulent and two‐phase transonic flow problems. The Navier–Stokes equations are solved using cell‐vertex Lax–Wendroff method with artificial dissipation or cell‐centred upwind method with Roe's Riemann solver and linear reconstruction. Due to a big difference of time scales in two‐phase flow of condensing steam a fractional step method is used. Test cases including 2D condensing flow in a nozzle and one‐phase transonic flow in a turbine cascade with transition to turbulence are presented. Copyright © 2005 John Wiley & Sons, Ltd.     

DNS,LES and RANS of turbulent heat transfer in boundary layer with suddenly changing wall thermal conditions

The objectives of this study are to investigate a thermal field in a turbulent boundary layer with suddenly changing wall thermal conditions by means of direct numerical simulation (DNS), and to evaluate predictions of a turbulence model in such a thermal field, in which DNS of spatially developing boundary layers with heat transfer can be conducted using the generation of turbulent inflow data as a method. In this study, two types of wall thermal condition are investigated using DNS and predicted by large eddy simulation (LES) and Reynolds-averaged Navier–Stokes equation simulation (RANS). In the first case, the velocity boundary layer only develops in the entrance of simulation, and the flat plate is heated from the halfway point, i.e., the adiabatic wall condition is adopted in the entrance, and the entrance region of thermal field in turbulence is simulated. Then, the thermal boundary layer develops along a constant temperature wall followed by adiabatic wall. In the second case, velocity and thermal boundary layers simultaneously develop, and the wall thermal condition is changed from a constant temperature to an adiabatic wall in the downstream region. DNS results clearly show the statistics and structure of turbulent heat transfer in a constant temperature wall followed by an adiabatic wall. In the first case, the entrance region of thermal field in turbulence can be also observed. Thus, both the development and the entrance regions in thermal fields can be explored, and the effects upstream of the thermal field on the adiabatic region are investigated. On the other hand, evaluations of predictions by LES and RANS are conducted using DNS results. The predictions of both LES and RANS almost agree with the DNS results in both cases, but the predicted temperature variances near the wall by RANS give different results as compared with DNS. This is because the dissipation rate of temperature variance is difficult to predict by the present RANS, which is found by the evaluation using DNS results.     

A Rapid and Accurate Switch from RANS to LES in Boundary Layers Using an Overlap Region

An efficient recycling algorithm is developed for injecting resolved turbulent content in a boundary layer as it switches from a Reynolds Averaged Navier-Stokes (RANS) type treatment to a Large Eddy Simulation (LES) type treatment inside a generalized Detached-Eddy Simulation (DES). The motivation is to use RANS in the thinnest boundary-layer area, following the original argument in favour of DES, and LES in the thicker boundary-layer areas especially approaching separation, to improve accuracy and possibly obtain unsteady outputs. The algorithm relies on an overlap of the RANS and LES domains and, therefore, the availability of both RANS and LES solutions in the recycling region, which is about 5 boundary-layer thicknesses long. This permits a smooth transfer of the turbulent stresses from this section to the LES inflow. The continuity of the skin-friction distribution is very good, reflecting the excellent viability of the resolved turbulence. The approach is validated in a flat-plate boundary layer and an airfoil near stall, with mild pressure gradient near the interface, and then applied to the compressible flow over an idealized airliner windshield wiper. The pressure fluctuations at reattachment are 12dB more intense than under a simple boundary layer at the same speed, and the output contains all the quantities needed to calculate the transmission of sound through the glass.     

气体动理学格式与多尺度流动模拟

介绍了气体动理学格式(GKS)的基本构造原理及其在两种典型多尺度流动模拟中的应用。GKS利用介观BGK方程的跨尺度演化解来构造网格界面上的数值通量,从而发展出能随计算网格尺度变化自动切换物理模型的多尺度方法。对湍流这种宏观多尺度流动,发展了高精度GKS方法并成功用于低雷诺数湍流的直接数值模拟;为实现对高雷诺数湍流的高效精细模拟,基于拓展BGK方程和已有的RANS,LES模型建立了新型多尺度模拟框架。对跨流域稀薄流动,发展了适合大规模并行的三维统一气体动理学格式(UGKS),并建立了适合轴对称稀薄流动的UGKS。研究表明,GKS在多尺度流动高效模拟中的优异性能,具有很好的发展前景。     

Numerical simulation of compressible turbulent flow via improved gas‐kinetic BGK scheme

In order to solve compressible turbulent flow problems, this study focuses on incorporating the Spalart–Allmaras turbulence model into gas‐kinetic BGK (Bhatnagar–Gross–Krook) scheme. The Spalart–Allmaras turbulence model is solved using finite difference discretization. The variables on the cell interface are interpolated via the van Leer limiter in the reconstruction stage. Simulation of subsonic and transonic flow over a NACA0012 airfoil has been implemented using two‐dimensional body‐fitted grids. The numerical results obtained appear in good agreement with the AGARD results, demonstrating the effectiveness and usefulness of the strategy of coupling the Spalart–Allmaras turbulence model with the BGK scheme for compressible turbulent flow simulation. Copyright © 2010 John Wiley & Sons, Ltd.     

On the performance of WENO/TENO schemes to resolve turbulence in DNS/LES of high‐speed compressible flows

High‐speed compressible turbulent flows typically contain discontinuities and have been widely modeled using Weighted Essentially Non‐Oscillatory (WENO) schemes due to their high‐order accuracy and sharp shock capturing capability. However, such schemes may damp the small scales of turbulence and result in inaccurate solutions in the context of turbulence‐resolving simulations. In this connection, the recently developed Targeted Essentially Non‐Oscillatory (TENO) schemes, including adaptive variants, may offer significant improvements. The present study aims to quantify the potential of these new schemes for a fully turbulent supersonic flow. Specifically, DNS of a compressible turbulent channel flow with M = 1.5 and Re_τ = 222 is conducted using OpenSBLI, a high‐order finite difference computational fluid dynamics framework. This flow configuration is chosen to decouple the effect of flow discontinuities and turbulence and focus on the capability of the aforementioned high‐order schemes to resolve turbulent structures. The effect of the spatial resolution in different directions and coarse grid implicit LES are also evaluated against the WALE LES model. The TENO schemes are found to exhibit significant performance improvements over the WENO schemes in terms of the accuracy of the statistics and the resolution of the three‐dimensional vortical structures. The sixth‐order adaptive TENO scheme is found to produce comparable results to those obtained with nondissipative fourth‐ and sixth‐order central schemes and reference data obtained with spectral methods. Although the most computationally expensive scheme, it is shown that this adaptive scheme can produce satisfactory results if used as an implicit LES model.