A methodology for high performance computation of fully inhomogeneous turbulent flows

A large‐eddy simulation methodology for high performance parallel computation of statistically fully inhomogeneous turbulent flows on structured grids is presented. Strategies and algorithms to improve the memory efficiency as well as the parallel performance of the subgrid‐scale model, the factored scheme, and the Poisson solver on shared‐memory parallel platforms are proposed and evaluated. A novel combination of one‐dimensional red–black/line Gauss–Seidel and two‐dimensional red–black/line Gauss–Seidel methods is shown to provide high efficiency and performance for multigrid relaxation of the Poisson equation. Parallel speedups are measured on various shared‐distributed memory systems. Validations of the code are performed in large‐eddy simulations of turbulent flows through a straight channel and a square duct. Results obtained from the present solver employing a Lagrangian dynamic subgrid‐scale model show good agreements with other available data. The capability of the code for more complex flows is assessed by performing a large‐eddy simulation of the tip‐leakage flow in a linear cascade. Copyright © 2006 John Wiley & Sons, Ltd.     

Large eddy simulation of turbulent incompressible flows by a three‐level finite element method

The variational multiscale method provides a methodical framework for large eddy simulation of turbulent flows. In this work, a particular implementation in the form of a three‐level finite element method separating large resolved, small resolved, and unresolved scales is proposed. Residual‐free bubbles are used for the numerical approximation of the small‐scale momentum equation. A stabilizing term is added, in order to take into account the effect of the small‐scale continuity equation. This implementation guarantees the stability of the method without further provisions and offers substantial computational savings on the small‐scale level. Furthermore, it is accounted for the unresolved scales by a specific dynamic modelling procedure. The method is tested for two different turbulent flow situations. Copyright © 2005 John Wiley & Sons, Ltd.     

Wall‐stress boundary conditions for variational‐multiscale LES

Two methods are introduced for the implementation of wall‐stress boundary conditions in variational‐multiscale large‐eddy simulations. In both methods, the boundary conditions are applied weakly using an interior‐penalty approach, where the discretization parameters are determined using information from a wall‐stress model. The performance of the methods is compared with that of hard Dirichlet boundary conditions for turbulent channel flows. A convergence study is performed for the second of the methods, which is found to be the most viable for practical application. Sources of error affecting the convergence study are discussed and quantified. Copyright © 2010 John Wiley & Sons, Ltd.     

An immersed boundary method wall model for high‐Reynolds‐number channel flow over complex topography

High‐Reynolds‐number channel flows regularly encounter topographies composed of multiple length scales and that protrude into the boundary layer. Physically, the presence of immersed obstacles leads to increased velocity gradients, turbulence production, and manifestation of wakes. Considerable challenges are associated with numerically describing the presence of obstacles in channel flows. Common approaches include generation of a computational mesh that is uniquely designed for the flow and obstacle, the immersed boundary method, and terrain‐following coordinates. There are challenges and limitations associated with each of these techniques. Specification of boundary conditions representing the perimeter of solid obstacles is a primary challenge of the immersed boundary method. In this document, a simplistic canopy stress‐like wall model is used to impose boundary conditions. The model isolates aerodynamically relevant local frontal areas through evaluation of the gradient of the topographic height field. The gradient of the height field describes both the surface‐normal direction and the frontal area, making it ideal for detecting areas on which the flow impinges. The model is tested in numerical simulations of turbulent half‐channel flow over topographies with different obstacles affixed–right prisms, rectangular prisms, ellipsoidal mounds, and sinusoids. In all cases, the performance is strong relative to datasets presented in the literature. Results are finally presented for numerical simulation of flow over complex synthetic fractal‐like topography and a synthetic city. These results show interesting trends in how the turbulent multiscale flow field responds to multiscale topography. Copyright © 2012 John Wiley & Sons, Ltd.     

Large eddy simulations of wall‐bounded flows using a simplified immersed boundary method and high‐order compact schemes

This paper presents a solution algorithm based on an immersed boundary (IB) method that can be easily implemented in high‐order codes for incompressible flows. The time integration is performed using a predictor‐corrector approach, and the projection method is used for pressure‐velocity coupling. Spatial discretization is based on compact difference schemes and is performed on half‐staggered meshes. A basic algorithm for body‐fitted meshes using the aforementioned solution method was developed by A. Tyliszczak (see article “A high‐order compact difference algorithm for half‐staggered grids for laminar and turbulent incompressible flows” in Journal of Computational Physics) and proved to be very accurate. In this paper, the formulated algorithm is adapted for use with the IB method in the framework of large eddy simulations. The IB method is implemented using its simplified variant without the interpolation (stepwise approach). The computations are performed for a laminar flow around a 2D cylinder, a turbulent flow in a channel with a wavy wall, and around a sphere. Comparisons with literature data confirm that the proposed method can be successfully applied for complex flow problems. The results are verified using the classical approach with body‐fitted meshes and show very good agreement both in laminar and turbulent regimes. The mean (velocity and turbulent kinetic energy profiles and drag coefficients) and time‐dependent (Strouhal number based on the drag coefficient) quantities are analyzed, and they agree well with reference solutions. Two subfilter models are compared, ie, the model of Vreman (see article “An eddy‐viscosity subgrid‐scale model for turbulent shear flow: algebraic theory and applications” in Physics and Fluids) and σ model (Nicoud et al, see article “Using singular values to build a subgrid‐scale model for large eddy simulations” in Physics and Fluids). The tests did not reveal evident advantages of any of these models, and from the point of view of solution accuracy, the quality of the computational meshes turned out to be much more important than the subfilter modeling.     

Residual‐based variational multiscale methods for laminar,transitional and turbulent variable‐density flow at low Mach number

In the present study, residual‐based variational multiscale methods are developed for and applied to variable‐density flow at low Mach number. In particular, two different formulations are considered in this study: a standard stabilized formulation featuring SUPG/PSG/grad‐div terms and a complete residual‐based variational multiscale formulation additionally containing cross‐ and Reynolds‐stress terms as well as subgrid‐scale velocity terms in the energy‐conservation equation. The proposed methods are tested for various laminar flow test cases as well as a test case at laminar via transitional to turbulent flow stages. Stable and accurate results are obtained for all numerical examples. Substantial differences in the results between the two approaches do not become notable until a high temperature gradient is applied and the flow reaches a turbulent flow stage. The more pronounced influence of adding subgrid‐scale velocity terms to the energy‐conservation equation on the results than adding analogous terms to the momentum‐conservation equation in this situation appears particularly noteworthy. Copyright © 2009 John Wiley & Sons, Ltd.     

Projection‐based variational multiscale method for incompressible Navier–Stokes equations in time‐dependent domains

A variational multiscale method for computations of incompressible Navier–Stokes equations in time‐dependent domains is presented. The proposed scheme is a three‐scale variational multiscale method with a projection‐based scale separation that uses an additional tensor valued space for the large scales. The resolved large and small scales are computed in a coupled way with the effects of unresolved scales confined to the resolved small scales. In particular, the Smagorinsky eddy viscosity model is used to model the effects of unresolved scales. The deforming domain is handled by the arbitrary Lagrangian–Eulerian approach and by using an elastic mesh update technique with a mesh‐dependent stiffness. Further, the choice of orthogonal finite element basis function for the resolved large scale leads to a computationally efficient scheme. Simulations of flow around a static beam attached to a square base, around an oscillating beam and around a plunging aerofoil are presented. Copyright © 2016 John Wiley & Sons, Ltd.     

On parallel pre‐conditioners for pressure Poisson equation in LES of complex geometry flows

This paper presents an assessment of fast parallel pre‐conditioners for numerical solution of the pressure Poisson equation arising in large eddy simulation of turbulent incompressible flows. Focus is primarily on the pre‐conditioners suitable for domain decomposition based parallel implementation of finite volume solver on non‐uniform structured Cartesian grids. Bi‐conjugate gradient stabilized method has been adopted as the Krylov solver for the linear algebraic system resulting from the discretization of the pressure Poisson equation. We explore the performance of multigrid pre‐conditioner for the non‐uniform grid and compare its performance with additive Schwarz pre‐conditioner, Jacobi and SOR(k) pre‐conditioners. Numerical experiments have been performed to assess the suitability of these pre‐conditioners for a wide range of non‐uniformity (stretching) of the grid in the context of large eddy simulation of a typical flow problem. It is seen that the multigrid preconditioner shows the best performance. Further, the SOR(k) preconditioner emerges as the next best alternative. Copyright © 2016 John Wiley & Sons, Ltd.     

Multiple semi‐coarsened multigrid method with application to large eddy simulation

The Multiple Semi‐coarsened Grid (MSG) multigrid method of Mulder (J. Comput. Phys. 1989; 83 :303–323) is developed as a solver for fully implicit discretizations of the time‐dependent incompressible Navier–Stokes equations. The method is combined with the Symmetric Coupled Gauss–Seidel (SCGS) smoother of Vanka (Comput. Methods Appl. Mech. Eng. 1986; 55 :321–338) and its robustness demonstrated by performing a number of large‐eddy simulations, including bypass transition on a flat plate and the turbulent thermally‐driven cavity flow. The method is consistently able to reduce the non‐linear residual by 5 orders of magnitude in 40–80 work units for problems with significant and varying coefficient anisotropy. Some discussion of the parallel implementation of the method is also included. Copyright © 2005 John Wiley & Sons, Ltd.     

Investigation of the sensitivity of turbulent closures and coupling of hybrid RANS‐LES models for predicting flow fields with separation and reattachment

Hybrid models have found widespread applications for simulation of wall‐bounded flows at high Reynolds numbers. Typically, these models employ Reynolds‐averaged Navier–Stokes (RANS) and large eddy simulation (LES) in the near‐body and off‐body regions, respectively. A number of coupling strategies between the RANS and LES regions have been proposed, tested, and applied in the literature with varying degree of success. Linear eddy‐viscosity models (LEVM) are often used for the closure of turbulent stress tensor in RANS and LES regions. LEVM incorrectly predicts the anisotropy of Reynolds normal stress at the RANS‐LES interface region. To overcome this issue, use of non‐linear eddy‐viscosity models (NLEVM) have started receiving attention. In this study, a generic non‐linear blended modeling framework for performing hybrid simulations is proposed. Flow over the periodic hills is used as the test case for model evaluation. This case is chosen due to complex flow physics with simplified geometry. Analysis of the simulations suggests that the non‐linear hybrid models show a better performance than linear hybrid models. It is also observed that the non‐linear closures are less sensitive to the RANS‐LES coupling and grid resolution. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical simulation of particle‐laden flows by the residual‐based variational multiscale method

We present a finite element residual‐based variational multiscale formulation applied to the numerical simulation of particle‐laden flows. We employ a Eulerian–Eulerian framework to describe the flows in which the mathematical model results from the incompressible Navier–Stokes equation combined with an advection–diffusion transport equation. Special boundary conditions at the bottom are introduced to take into account sediments deposition. Computational experiments are organized in two examples. The first example deals with the well‐known gravity current benchmark, the lock‐exchange configuration. The second also employs for the current initiation the lock configuration, but the sediment particles are endowed with a deposition velocity and are allowed to leave the domain in the moment they reach the bottom. This is intended to mimic, partially, as the bed morphology is not allowed to change, the deposition process, in which sediment deposits are no longer carried by the flow. The spatial pattern of the deposition and its correlation with flow structures are the main focus of this analysis. Numerical experiments have shown that the present formulation captures most of the relevant turbulent flow features with reasonable accuracy, when compared with highly resolved numerical simulations and experimental data. Copyright © 2013 John Wiley & Sons, Ltd.     

A semi‐implicit scheme for large Eddy simulation of piston engine flow and combustion

A semi‐implicit scheme is presented for large eddy simulation of turbulent reactive flow and combustion in reciprocating piston engines. First, the governing equations in a deforming coordinate system are formulated to accommodate the moving piston. The numerical scheme is made up of a fourth‐order central difference for the diffusion terms in the transport equations and a fifth‐order weighted essentially nonoscillatory (WENO) scheme for the convective terms. A second‐ order Adams–Bashforth scheme is used for time integration. For higher density ratios, it is combined with a predictor–corrector scheme. The numerical scheme is explicit for time integration of the transport equations, except for the continuity equation which is used together with the momentum equation to determine the pressure field and velocity field by using a Poisson equation for the pressure correction field. The scheme is aimed at the simulation of low Mach number flows typically found in piston engines. An efficient multigrid method that can handle high grid aspect ratio is presented for solving the pressure correction equation. The numerical scheme is evaluated on two test engines, a laboratory four‐stroke engine with rectangular‐shaped engine geometry where detailed velocity measurements are available, and a modified truck engine with practical cylinder geometry where lean ethanol/air mixture is combusted under a homogeneous charge compression ignition (HCCI) condition. Copyright © 2012 John Wiley & Sons, Ltd.     

Treatment of the small time instability in the finite element analysis of fluid structure interaction problems

In this paper, the fluid–structure interaction problem in mechanical systems in which a high frequency vibrating solid structure interacts with the surrounding fluid flow is considered. Such a situation normally appears in many microelectromechanical systems like a wide variety of microfluidic devices. A different implementation of the residual‐based variational multiscale flow method is employed within the arbitrary Lagrangian–Eulerian formulation. The combination of the variational multiscale method with appropriate stabilization parameters is used to handle the so‐called small time step instability in the finite element analysis of the fluid part in the coupled fluid–structure interaction problem. The capability of the employed approach has been demonstrated through finite element study of a benchmark example and FEM simulation of two different mechanical micropumping devices. High frequency vibrations of the solid membrane are used to derive the fluid flow in these micropumps. Results of FEM simulations are shown to be in good agreement with available experimental data.Copyright © 2012 John Wiley & Sons, Ltd.     

Calculation of three‐dimensional turbulent flow with a finite volume multigrid method

A numerical method for the efficient calculation of three‐dimensional incompressible turbulent flow in curvilinear co‐ordinates is presented. The mathematical model consists of the Reynolds averaged Navier–Stokes equations and the k–ε turbulence model. The numerical method is based on the SIMPLE pressure‐correction algorithm with finite volume discretization in curvilinear co‐ordinates. To accelerate the convergence of the solution method a full approximation scheme‐full multigrid (FAS‐FMG) method is utilized. The solution of the k–ε transport equations is embedded in the multigrid iteration. The improved convergence characteristic of the multigrid method is demonstrated by means of several calculations of three‐dimensional flow cases. Copyright © 1999 John Wiley & Sons, Ltd.     

Usability of explicit filtering in large eddy simulation with a low‐order numerical scheme and different subgrid‐scale models

Based on a priori tests, in large eddy simulation (LES) of turbulent fluid flow, the numerical error related to low‐order finite‐difference‐type methods can be large in comparison with the effect of subgrid‐scale (SGS) model. Explicit filtering has been suggested to reduce the error, and it has shown promising results in a priori studies and in some simulations with fourth‐order method. In this paper, the effect of explicit filtering on the total simulation error is studied together with a second‐order scheme, where the numerical error should be even larger. The fully developed turbulent channel flow between two parallel walls is used as a test case. Rather simple SGS models are applied, because these models are most likely used in practical applications of LES. Explicit filtering is here applied to the non‐linear convection term of the Navier–Stokes equations, four three‐dimensional filter functions are applied, and the effect of filtering is separated from the effect of SGS modelling. It is shown that the effect of filtering is rather large and smooth filters introduce an additional error component that increases the total simulation error. Finally, filtering via subfilter‐scale modelling is applied, and it is shown that this approach performs better. However, the large‐frequency components of the resolved flow field are not as effectively damped as when the non‐linear convection term is filtered. Copyright © 2007 John Wiley & Sons, Ltd.     

Validation of a novel very large eddy simulation method for simulation of turbulent separated flow

The paper describes the validation of a newly developed very LES (VLES) method for the simulation of turbulent separated flow. The new VLES method is a unified simulation approach that can change seamlessly from Reynolds‐averaged Navier–Stokes to DNS depending on the numerical resolution. Four complex test cases are selected to validate the performance of the new method, that is, the flow past a square cylinder at Re = 3000 confined in a channel (with a blockage ratio of 20%), the turbulent flow over a circular cylinder at Re = 3900 as well as Re = 140,000, and a turbulent backward‐facing step flow with a thick incoming boundary layer at Re = 40,000. The simulation results are compared with available experimental, LES, and detached eddy simulation‐type results. The new VLES model performs well overall, and the predictions are satisfactory compared with previous experimental and numerical results. It is observed that the new VLES method is quite efficient for the turbulent flow simulations; that is, good predictions can be obtained using a quite coarse mesh compared with the previous LES method. Discussions of the implementation of the present VLES modeling are also conducted on the basis of the simulations of turbulent channel flow up to high Reynolds number of Re_τ = 4000. The efficiency of the present VLES modeling is also observed in the channel flow simulation. From a practical point of view, this new method has considerable potential for more complex turbulent flow simulations at relative high Reynolds numbers. Copyright © 2013 John Wiley & Sons, Ltd.     

Turbulent flow calculations using unstructured and adaptive meshes

A method of efficiently computing turbulent compressible flow over complex two-dimensional configurations is presented. The method makes use of fully unstructured meshes throughout the entire flow field, thus enabling the treatment of arbitrarily complex geometries and the use of adaptive meshing techniques throughout both viscous and inviscid regions of the flow field. Mesh generation is based on a locally mapped Delaunay technique in order to generate unstructured meshes with highly stretched elements in the viscous regions. The flow equations are discretized using a finite element Navier-Stokes solver, and rapid convergence to steady state is achieved using an unstructured multigrid algorithm. Turbulence modelling is performed using an inexpensive algebraic model, implemented for use on unstructured and adaptive meshes. Compressible turbulent flow solutions about multiple-element aerofoil geometries are computed and compared with experimental data.     

High‐order stable interpolations for immersed boundary methods

The analysis and improvement of an immersed boundary method (IBM) for simulating turbulent flows over complex geometries are presented. Direct forcing is employed. It consists in interpolating boundary conditions from the solid body to the Cartesian mesh on which the computation is performed. Lagrange and least squares high‐order interpolations are considered. The direct forcing IBM is implemented in an incompressible finite volume Navier–Stokes solver for direct numerical simulations (DNS) and large eddy simulations (LES) on staggered grids. An algorithm to identify the body and construct the interpolation schemes for arbitrarily complex geometries consisting of triangular elements is presented. A matrix stability analysis of both interpolation schemes demonstrates the superiority of least squares interpolation over Lagrange interpolation in terms of stability. Preservation of time and space accuracy of the original solver is proven with the laminar two‐dimensional Taylor–Couette flow. Finally, practicability of the method for simulating complex flows is demonstrated with the computation of the fully turbulent three‐dimensional flow in an air‐conditioning exhaust pipe. Copyright © 2006 John Wiley & Sons, Ltd.     

A time‐implicit high‐order compact differencing and filtering scheme for large‐eddy simulation

This work investigates a high‐order numerical method which is suitable for performing large‐eddy simulations, particularly those containing wall‐bounded regions which are considered on stretched curvilinear meshes. Spatial derivatives are represented by a sixth‐order compact approximation that is used in conjunction with a tenth‐order non‐dispersive filter. The scheme employs a time‐implicit approximately factored finite‐difference algorithm, and applies Newton‐like subiterations to achieve second‐order temporal and sixth‐order spatial accuracy. Both the Smagorinsky and dynamic subgrid‐scale stress models are incorporated in the computations, and are used for comparison along with simulations where no model is employed. Details of the method are summarized, and a series of classic validating computations are performed. These include the decay of compressible isotropic turbulence, turbulent channel flow, and the subsonic flow past a circular cylinder. For each of these cases, it was found that the method was robust and provided an accurate means of describing the flowfield, based upon comparisons with previous existing numerical results and experimental data. Published in 2003 by John Wiley & Sons, Ltd.