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.     

Parallel large eddy simulation of turbulent flow around MIRA model using linear equal‐order finite element method

A parallel large eddy simulation code that adopts domain decomposition method has been developed for large‐scale computation of turbulent flows around an arbitrarily shaped body. For the temporal integration of the unsteady incompressible Navier–Stokes equation, fractional 4‐step splitting algorithm is adopted, and for the modelling of small eddies in turbulent flows, the Smagorinsky model is used. For the parallelization of the code, METIS and Message Passing Interface Libraries are used, respectively, to partition the computational domain and to communicate data between processors. To validate the parallel architecture and to estimate its performance, a three‐dimensional laminar driven cavity flow inside a cubical enclosure has been solved. To validate the turbulence calculation, the turbulent channel flows at Re_τ = 180 and 1050 are simulated and compared with previous results. Then, a backward facing step flow is solved and compared with a DNS result for overall code validation. Finally, the turbulent flow around MIRA model at Re = 2.6 × 10⁶ is simulated by using approximately 6.7 million nodes. Scalability curve obtained from this simulation shows that scalable results are obtained. The calculated drag coefficient agrees better with the experimental result than those previously obtained by using two‐equation turbulence models. Copyright © 2007 John Wiley & Sons, Ltd.     

可压缩流体流动多尺度混合有限元数值方法研究

可压缩流体是天然油藏中广泛存在的一种流体,研究其在多孔介质中的渗流规律对于油藏开发具有重要意义。本文采用多尺度混合有限元方法,对可压缩流体渗流问题进行了研究。考虑流体的可压缩性以及介质形变,推导得到了可压缩流体渗流问题的多尺度计算格式。数值计算结果表明,多尺度混合有限元适于求解非均质性和可压缩流问题,具有节省计算量、计算精度高等优势,对于实际大规模油藏模拟具有重要意义。     

Large eddy simulation in a turbulent channel flow using exit boundary conditions

The influence of the exit boundary conditions on the vanishing first derivative of the velocity components and constant pressure on the large eddy simulation of the fully developed turbulent channel flow has been investigated for equidistant and stretched grids at the channel exit. Results show that the chosen exit boundary conditions introduce some small disturbances that are mostly damped by the grid stretching. The difference of rms values between the fully developed turbulent channel flow with periodicity conditions and the fully developed channel flow using inlet and the exit boundary conditions is less than 10% for the equidistant grids and less than 5% for the stretched grids. The chosen boundary conditions are of interest because they may be used in complex problems with back flow at the exit. Copyright © 1999 John Wiley & Sons, Ltd.     

Spectral-finite element method for compressible fluid flow

In this paper, a combined Fourier spectral-finite element method is proposed for solving n-dimensional (n=2, 3), semi-periodio compressible fiuid flow problems. The strict error estimation as well as the convergence rate, is presented.     

A finite point method for adaptive three‐dimensional compressible flow calculations

The finite point method (FPM) is a meshless technique, which is based on both, a weighted least‐squares numerical approximation on local clouds of points and a collocation technique which allows obtaining the discrete system of equations. The research work we present is part of a broader investigation into the capabilities of the FPM to deal with 3D applications concerning real compressible fluid flow problems. In the first part of this work, the upwind‐biased scheme employed for solving the flow equations is described. Secondly, with the aim of exploiting the meshless capabilities, an h‐adaptive methodology for 2D and 3D compressible flow calculations is developed. This adaptive technique applies a solution‐based indicator in order to identify local clouds where new points should be inserted in or existing points could be safely removed from the computational domain. The flow solver and the adaptive procedure have been evaluated and the results are encouraging. Several numerical examples are provided in order to illustrate the good performance of the numerical methods presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Shear‐improved Smagorinsky modeling of turbulent channel flow using generalized Lattice Boltzmann equation

Generalized Lattice Boltzmann equation (GLBE) was used for computation of turbulent channel flow for which large eddy simulation (LES) was employed as a turbulence model. The subgrid‐scale turbulence effects were simulated through a shear‐improved Smagorinsky model (SISM), which is capable of predicting turbulent near wall region accurately without any wall function. Computations were done for a relatively coarse grid with shear Reynolds number of 180 in a parallelized code. Good numerical stability was observed for this computational framework. The results of mean velocity distribution across the channel showed good correspondence with direct numerical simulation (DNS) data. Negligible discrepancies were observed between the present computations and those reported from DNS for the computed turbulent statistics. Three‐dimensional instantaneous vorticity contours showed complex vortical structures that appeared in such flow geometries. It was concluded that such a framework is capable of predicting accurate results for turbulent channel flow without adding significant complications and the computational cost to the standard Smagorinsky model. As this modeling was entirely local in space it was therefore adapted for parallelization. Copyright © 2010 John Wiley & Sons, Ltd.     

Simple lattice Boltzmann approach for turbulent buoyant flow simulation

In the present work, a simple large eddy simulation （LES）-based lattice Boltz- mann model （LBM） is developed for thermal turbulence research. This model is validated by some benchmark tests. The numerical results demonstrate the good performance of the present model for turbulent buoyant flow simulation.     

An improved near‐wall modeling for large‐eddy simulation using immersed boundary methods

An improved near‐wall modeling for large‐eddy simulation using the immersed boundary method is proposed. It is shown in this study that the existing near‐wall modeling for the immersed boundary (IB) methods that imposes the velocity boundary condition at the IB node is not sufficient to enforce a correct wall shear stress at the IB node. A new method that imposes a shear stress condition through the modification of the subgrid scale‐eddy viscosity at the IB node is proposed. In this method, the subgrid eddy viscosity at the IB node is modified such that the viscous flux at the face adjacent to the IB node correctly approximates the total shear stress. The method is applied to simulate the fully developed turbulent flows in a plane channel and a circular pipe. It is demonstrated that the new method improves the prediction of the mean velocity and turbulence stresses in comparison with the existing wall modeling based solely on the velocity boundary condition. Copyright © 2015 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.     

Large eddy simulation and a simple wall model for turbulent flow calculation by a particle method

A turbulent channel flow and the flow around a cubic obstacle are calculated by the moving particle semi‐implicit method with the subparticle‐scale turbulent model and a wall model, which is based on the zero equation RANS (Reynolds Averaged Navier‐Stokes). The wall model is useful in practical problems that often involve high Reynolds numbers and wall turbulence, because it is difficult to keep high resolution in the near‐wall region in particle simulation. A turbulent channel flow is calculated by the present method to validate our wall model. The mean velocity distribution agrees with the log‐law velocity profile near the wall. Statistical values are also the same order and tendency as experimental results with emulating viscous layer by the wall model. We also investigated the influence of numerical oscillations on turbulence analysis in using the moving particle semi‐implicit method. Finally, the turbulent flow around a cubic obstacle is calculated by the present method to demonstrate capability of calculating practical turbulent flows. Three characteristic eddies appear in front of, over, and in the back of the cube both in our calculation and the experimental result that was obtained by Martinuzzi and Tropea. Mean velocity and turbulent intensity profiles are predicted in the same order and have similar tendency as the experimental result. Copyright © 2012 John Wiley & Sons, Ltd.     

A stabilized finite element formulation for high‐speed inviscid compressible flows using finite calculus

This paper aims at the development of a new stabilization formulation based on the finite calculus (FIC) scheme for solving the Euler equations using the Galerkin FEM on unstructured triangular grids. The FIC method is based on expressing the balance of fluxes in a space–time domain of finite size. It is used to prevent the creation of instabilities typically present in numerical solutions due to the high convective terms and sharp gradients. Two stabilization terms, respectively called streamline term and transverse term, are added via the FIC formulation to the original conservative equations in the space–time domain. An explicit fourth‐order Runge–Kutta scheme is implemented to advance the solution in time. The presented numerical test examples for inviscid flows prove the ability of the proposed stabilization technique for providing appropriate solutions especially near shock waves. Although the derived methodology delivers precise results with a nearly coarse mesh, a mesh refinement technique is coupled to the solution process for obtaining a suitable mesh particularly in the high‐gradient zones. Copyright © 2014 John Wiley & Sons, Ltd.     

Anisotropic multistage finite element method for two dimensional viscous transonic flow in turbomachinery

A new method based on the anisotropic tensor force finite element and Taylor-Galerkin finite element is presented in the present paper. Its application to two-dimensional viscous transonic flow in turbomachinery improves the convergence rate and stability of calculation, and the results obtained agree well with the experimental measurements.     

Dilation‐based shock capturing for high‐order methods

In this paper, we introduce a shock‐capturing artificial viscosity technique for high‐order unstructured mesh methods. This artificial viscosity model is based on a non‐dimensional form of the divergence of the velocity. The technique is an extension and improvement of the dilation‐based artificial viscosity methods introduced in Premasuthan et al., 15 and further extended in Nguyen and Peraire 27 . The approach presented has a number attractive properties including non‐dimensional analytical form, sub‐cell resolution, and robustness for complex shock flows on anisotropic meshes. We present extensive numerical results to demonstrate the performance of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

A finite element method for compressible viscous fluid flows

This work presents a mixed three‐dimensional finite element formulation for analyzing compressible viscous flows. The formulation is based on the primitive variables velocity, density, temperature and pressure. The goal of this work is to present a ‘stable’ numerical formulation, and, thus, the interpolation functions for the field variables are chosen so as to satisfy the inf–sup conditions. An exact tangent stiffness matrix is derived for the formulation, which ensures a quadratic rate of convergence. The good performance of the proposed strategy is shown in a number of steady‐state and transient problems where compressibility effects are important such as high Mach number flows, natural convection, Riemann problems, etc., and also on problems where the fluid can be treated as almost incompressible. Copyright © 2010 John Wiley & Sons, Ltd.     

GPU‐accelerated direct numerical simulations of decaying compressible turbulence employing a GKM‐based solver

Gas Kinetic Method‐based flow solvers have become popular in recent years owing to their robustness in simulating high Mach number compressible flows. We evaluate the performance of the newly developed analytical gas kinetic method (AGKM) by Xuan et al. in performing direct numerical simulation of canonical compressible turbulent flow on graphical processing unit (GPU)s. We find that for a range of turbulent Mach numbers, AGKM results shows excellent agreement with high order accurate results obtained with traditional Navier–Stokes solvers in terms of key turbulence statistics. Further, AGKM is found to be more efficient as compared with the traditional gas kinetic method for GPU implementation. We present a brief overview of the optimizations performed on NVIDIA K20 GPU and show that GPU optimizations boost the speedup up‐to 40x as compared with single core CPU computations. Hence, AGKM can be used as an efficient method for performing fast and accurate direct numerical simulations of compressible turbulent flows on simple GPU‐based workstations. Copyright © 2016 John Wiley & Sons, Ltd.     

A control-volume based finite element method for three-dimensional incompressible turbulent fluid flow,heat transfer,and related phenomena

A control-volume based finite element method of equal-order type for three-dimensional incompressible turbulent fluid flow, heat transfer, and related phenomena is presented. The discretization equations are based mainly on the physics of the phenomena under consideration, more than on mathematical arguments. Special emphasis is devoted to the discretization of the convective terms and the continuity equation, and to the treatment of the boundary conditions imposed by the use of a high Reynolds k-?, type turbulence model. The pressure-velocity coupling in the fluid flow calculation is made from a derivative of the original SIMPLER method, without pressure correction. The discretized equations are solved in a sequential, rather than a coupled, form with significant advantage in the required computer time and storage. The method is an extension of a former version proposed by us for two-dimensional, laminar problems, and is here successfully applied to the following situations: three-dimensional deflected turbulent jet, and flows in 90° and 45° junctions of ducts with rectangular cross sections. The calculated results are in very good agreement with the experimental and numerical (obtained with the well established finite difference method) data available in the literature.