Methods for parallel computation of complex flow problems

This paper is an overview of some of the methods developed by the Team for Advanced Flow Simulation and Modeling (TAFSM) [http://www.mems.rice.edu/TAFSM/] to support flow simulation and modeling in a number of “Targeted Challenges”. The “Targeted Challenges” include unsteady flows with interfaces, fluid–object and fluid–structure interactions, airdrop systems, and air circulation and contaminant dispersion. The methods developed include special numerical stabilization methods for compressible and incompressible flows, methods for moving boundaries and interfaces, advanced mesh management methods, and multi-domain computational methods. We include in this paper a number of numerical examples from the simulation of complex flow problems.     

Conceptual design of aeroelastic structures by topology optimization

A topology optimization methodology is presented for the conceptual design of aeroelastic structures accounting for the fluid–structure interaction. The geometrical layout of the internal structure, such as the layout of stiffeners in a wing, is optimized by material topology optimization. The topology of the wet surface, that is, the fluid–structure interface, is not varied. The key components of the proposed methodology are a Sequential Augmented Lagrangian method for solving the resulting large-scale parameter optimization problem, a staggered procedure for computing the steady-state solution of the underlying nonlinear aeroelastic analysis problem, and an analytical adjoint method for evaluating the coupled aeroelastic sensitivities. The fluid–structure interaction problem is modeled by a three-field formulation that couples the structural displacements, the flow field, and the motion of the fluid mesh. The structural response is simulated by a three-dimensional finite element method, and the aerodynamic loads are predicted by a three-dimensional finite volume discretization of a nonlinear Euler flow. The proposed methodology is illustrated by the conceptual design of wing structures. The optimization results show the significant influence of the design dependency of the loads on the optimal layout of flexible structures when compared with results that assume a constant aerodynamic load.     

The stability of an oceanic structure with T–S fuzzy models

In this study we construct and derive analytical solutions for a mathematical model of an oceanic environment in which wave-induced flow fields cause structural surge motion after which a fuzzy control technique is developed to alleviate structural vibration. Specifically the Takagi–Sugeno (T–S) fuzzy model is employed to approximate the oceanic structure and a parallel-distributed-compensation (PDC) scheme is utilized in a control procedure designed to reduce the structural response. All local state feedback controllers are integrated to construct a global fuzzy logic controller. The Lyapunov method is used to achieve structural stability. The interaction between the wave motion and the structural response is explained using the separation of variables method. The surge motion is related to the characteristics of the wave and the structure. A parametric approach is utilized to show these effects. Other parameters remain constant. In an oceanic structural system, platform migration is often caused by the wave force. The stability of an oceanic structure can be proven theoretically based on stability analysis. The decay of the displacement and velocity due to the use of the proposed fuzzy controllers is demonstrated by a numerical simulation.     

Simulation of spilling breaking waves using a two phase flow CFD model

A two phase flow CFD model has been developed for 2D spilling breaking wave simulations. A mass conservative level set method similar to Olsson and Kreiss [Olsson E, Kreiss G. A conservative level set method for two phase flow. J Comput Phys 2005;210(1):225–46] is implemented for capturing the air–water interface. The solver is discretised using a finite volume method based on a curvilinear coordinate system. A fully implicit fractional step method is used to advance simulations in time. The solver has been tested and validated by repeating benchmark results of dam breaking simulation and travelling solitary wave simulation. Finally, we employ this solver to simulate spilling breaking waves in the surf zone. Our results show that surface elevations, the location of the breaking point and undertow profiles can generally be well captured. We have also found that temporal and spatial schemes may have significant impacts on computational results.     

Numerical simulation of ground water mounding and its verification by Hele–Shaw model

Ground water mounding is the rise of the water table above its regional level in a local area of an aquifer in order to provide sufficient head to distribute the water supplied by a localized source to that area. The shape and height of the mound depend on many factors including recharge rate and distribution, geology, hydraulic conductivity, flow/head control locations, saturated thickness and regional flow in the aquifer in that area. In this work, an accurate and efficient numerical model for calculating ground water mounding was developed. Numerical calculations were done on a uniform rectangular grid, obtained by a transformation of the physical domain. Grid for computation were generated by a grid generation code, EagleView, which is developed by the Mississippi State University. Model predictions were verified with tests in a Hele–Shaw model for situations with and without a regional flow, with and without heterogeneity, and for two recharge rates. SAE#50 oil was used as the fluid in the Hele–Shaw. A peristaltic pump was used to supply the constant (and adjustable) recharge rate from the reservoir below the Hele–Shaw model. The results of experiments of estimating mounds and the numerical mounding model are in good agreement. However, mound height of the region below recharge of Hele–Shaw model can not be observed because the flow of this region combines vertical flow from recharge and the rising of the free surface (horizontal flow). Hence, an emulated perched aquifer was used so that mound height of the recharge region can be observed.     

Flow analysis of a ribbed helix lip seal with consideration of fluid–structure interaction

Ribbed helix lip seals for rotating shafts have been widely used to retain oil and exclude contaminants in many applications throughout the industry. The objective of this study is to better understand the basic flow behavior associated with the pumping process of a ribbed helix lip seal. The theoretical model consists of a flow analysis of the lubricating film of the hydraulic fluid in conjunction with a stress analysis of the lip seal distortion. The complicated mechanical interaction between the oil flow and rubber deformation was simulated using a coupled fluid–structure approach implemented in a commercial computational fluid dynamics (CFD) code ESI-CFD, ACE+®. The flow characteristics and rubber deformation around a ribbed helix lip seal were fully resolved in a pumping-rate test environment, where both air and oil sides were filled with oil initially. The three-dimensional pressure field solved by the model via the coupled flow-stress analysis was compared with the predictions obtained from the model via the nondeformable rubber assumption to elucidate the significant effect of the fluid–structure interaction on accurate simulation of the oil pumping behavior. In the rotating speed ranging from 1000 to 6000 rpm, both measured and calculated pumping rates increase with the shaft speed for a ribbed helix lip seal. As compared to the baseline case, calculations with considering the fluid–structure interaction at higher rotary speeds can result in thicker oil films, and in turn produce greater pumping rates.     

Numerical simulation of patient-specific left ventricular model with both mitral and aortic valves by FSI approach

Intraventricular flow is important in understanding left ventricular function; however, relevant numerical simulations are limited, especially when heart valve function is taken into account. In this study, intraventricular flow in a patient-specific left ventricle has been modelled in two-dimension (2D) with both mitral and aortic valves integrated. The arbitrary Lagrangian–Eulerian (ALE) approach was employed to handle the large mesh deformation induced by the beating ventricular wall and moving leaflets. Ventricular wall deformation was predefined based on MRI data, while leaflet dynamics were predicted numerically by fluid–structure interaction (FSI). Comparisons of simulation results with in vitro and in vivo measurements reported in the literature demonstrated that numerical method in combination with MRI was able to predict qualitatively the patient-specific intraventricular flow. To the best of our knowledge, we are the first to simulate patient-specific ventricular flow taking into account both mitral and aortic valves.     

Fully Lagrangian and Lattice Boltzmann Methods for the Advection-Diffusion Equation

In the last decade or so, the Lattice–Boltzmann method (LBM) has achieved great success in computational fluid dynamics. The Fully–Lagrangian method (FLM) is the generalization of LBM for conservation systems. LBM can also be developed from FLM. In this paper a FL model and a LB model are developed for D-dimensional advection-diffusion equation. The LB model can be viewed as an improved version of the FL model. Numerical results of simulation of 1-dimensional advection-diffusion equation are presented. The numerical results are found to be in good agreement with the analytic solution.     

A comparison of analytical–numerical models for nonlinear vibrations of cylindrical shells

The nonlinear flexural vibration behaviour of cylindrical shells has received considerable attention to date. It is pointed out that, although in a well-known reference case there seems to be a reasonable agreement, there are unresolved discrepancies between the results obtained by different authors. In the present paper, the problem is studied using various analytical–numerical models with different levels of accuracy and complexity. The frequency–amplitude curves from the different analysis models developed are compared both for isotropic shells and for an orthotropic composite shell. Secondary modes can play an important role. In more complicated cases modal interactions may significantly influence the nonlinear vibration behaviour, and the results obtained strongly depend on the analysis model chosen.     

Inter-spike-intervals analysis of AER Poisson-like generator hardware

Address–Event–Representation (AER) is a communication protocol for transferring images between chips, originally developed for bio-inspired image-processing systems. Such systems may consist of a complicated hierarchical structure with many chips that transmit images among them in real time, while performing some processing (for example, convolutions). In developing AER-based systems it is very convenient to have available some means of generating AER streams from on-computer stored images. Rank order coding (ROC) and Poisson rate coding are the extremes of spikes coding. In this paper, we present a pseudo-random hardware method for generating AER streams in real time from a sequence of images stored in a computer's memory. The Kolmogorov–Smirnov test has been applied to quantify that this method follows a Poisson distribution of the spikes. A USB–AER board, developed by our RTCAR group, have been used for the measurements. An example scenario of use under the EU CAVIAR project is presented.     

Numerical Convergence Study of Nearly Incompressible,Inviscid Taylor–Green Vortex Flow

A spectral method and a fifth-order weighted essentially non-oscillatory method were used to examine the consequences of filtering in the numerical simulation of the three-dimensional evolution of nearly-incompressible, inviscid Taylor–Green vortex flow. It was found that numerical filtering using the high-order exponential filter and low-pass filter with sharp high mode cutoff applied in the spectral simulations significantly affects the convergence of the numerical solution. While the conservation property of the spectral method is highly desirable for fluid flows described by a system of hyperbolic conservation laws, spectral methods can yield erroneous results and conclusions at late evolution times when the flow eventually becomes under-resolved. In particular, it is demonstrated that the enstrophy and kinetic energy, which are two integral quantities often used to evaluate the quality of numerical schemes, can be misleading and should not be used unless one can assure that the solution is sufficiently well-resolved. In addition, it is shown that for the Taylor–Green vortex (for example) it is useful to compare the predictions of at least two numerical methods with different algorithmic foundations (such as a spectral and finite-difference method) in order to corroborate the conclusions from the numerical solutions when the analytical solution is not known.     

Optimal design of an aircraft engine mount via bit-masking oriented genetic algorithms

In this paper a geometric–topologic structural optimisation procedure for a transport aircraft engine mount is shown. In order to achieve the minimum structural weight under some functional and operative constraints, both static and dynamic aspects have been treated. A parametric FEM model with extended self-consistent controls on topology has been developed. The genetic algorithm used for the optimisation procedure was based on a specific bit-masking oriented data structure able to handle properly both continuous and discrete design variables requested by the hybrid geometric–topological model of the structure.     

Unsteady analysis of the six DOF motion of a buoyantly rising submarine

The roll instability observed in buoyantly rising small to medium sized submarines is analyzed in this work using a computational fluid dynamics (CFD) RANS solver coupled to the six degree of freedom (DOF) solid body equations of motion for the submarine. The theoretical framework and the numerical implementation, in particular the fluid–rigid-body interaction methodology, are outlined in detail in conjunction with models for control, propulsion, and ballast blowing. The submarine-specific models are conventional while the RANS flow field predictions are compared with a coefficient-based model and validated against steady state wind tunnel data spanning the onset flow conditions of interest. Detailed analyses of full-scale rising stability scenarios identify the magnitude and onset behavior of contributing moments to the instability. The rolling moment generated by the sail was found to be the primary cause of the instability. Simulation results confirm the finding from a previous study that the emergence roll angle of the submarine is very sensitive to the initial heel (roll) angle. When the initial heel angle is a fraction of a degree, the emergence roll angle is too small to be of concern but an initial heel angle of 2° results in a significant emergence roll angle of 10°. Unsteady viscous effects due to vorticity trailing from the sail were observed but they were found to have an insignificant impact on roll instability for the scenarios investigated.     

Numerical simulation of a plate-gap biosensor with an outer porous membrane

A plate-gap model of a porous enzyme doped electrode covered by a porous membrane has been proposed and analyzed. The two-dimensional-in-space mathematical model of the plate-gap biosensor is based on the reaction–diffusion equations containing a nonlinear term related to Michaelis–Menten kinetics of the enzymatic reaction. The model involves four regions: the enzyme-filled gaps where the enzymatic reaction as well as the mass transport by diffusion take place, the porous membrane, a diffusion limiting region where only the mass transport by diffusion takes place, and a convective region where the analyte concentration is maintained constant. Using numerical simulation, the effect of the biosensor geometry on the biosensor response was investigated. The simulation was carried out using the finite difference technique. The mathematical model as well as numerical solution were validated using analytical solutions existing for specific cases of the model parameters.     

液流通过滑阀的流场结构的数值解析

液压控制系统中,流体通过滑阀的流动场的变化一直是实验和理论研究感兴趣的课题,由于这些流体流动的物理过程,其数学模型主要由一组具有复杂边界条件的非线性偏微分方     

Large eddy simulation of turbulent heat transport in the Strait of Gibraltar

We develop a numerical model for large eddy simulation of turbulent heat transport in the Strait of Gibraltar. The flow equations are the incompressible Navier–Stokes equations including Coriolis forces and density variation through the Boussinesq approximation. The turbulence effects are incorporated in the system by considering the Smagorinsky model. As a numerical solver we propose a finite element semi-Lagrangian method. The solution procedure consists of combining a non-oscillatory semi-Lagrangian scheme for time discretization with the finite element method for space discretization. Numerical results illustrate a buoyancy-driven circulations along the Strait of Gibraltar and the sea-surface temperature is flushed out and move to northeast coast. The Ocean discharge and the temperature difference are shown to control the plume structure.     

液体通过滑阀的阶跃响应的仿真研究

精确地了解滑阀的动态特性对液压控制系统的合理设计是很重要的。可是,滑阀的瞬变流体结构由于其非稳定性的复杂所以有关的信息较少。该文对流体通过滑阀的阶跃响应进行了数值解析计算。该研究所用的数值解析方法是先用等间隔的交错矩形网格。基于有限体积法将基础方程式离散化,然后用类似于SIMPLER法的迭代算法解离散化所得的差分方程组。压力差阶跃变化的情况下,做出了流动场随时间变化的流线图和流量及再附着点距离的时间变化图。数值计算结果说明了流体通过滑阀的阶跃响应可用具有不同的时间常数的指数函数来模拟。该文证实了理论模型和数值计算结果一致。     

A parallel, finite-volume algorithm for large-eddy simulation of turbulent flows

A parallel, finite-volume algorithm has been developed for large-eddy simulation (LES) of compressible turbulent flows. This algorithm includes piecewise linear least-square reconstruction, trilinear finite-element interpolation, Roe flux-difference splitting (FDS), and second-order MacCormack time marching. A systematic and consistent means of evaluating the surface and volume integrals of the control volume is described. Parallel implementation is done using the message-passing programming model. To validate the numerical method for turbulence simulation, LES of fully developed turbulent flow in a square duct is performed for a Reynolds number of 320 based on the average friction velocity and the hydraulic diameter of the duct. Direct numerical simulation (DNS) results are available for this test case, and the accuracy of this algorithm for turbulence simulations can be ascertained by comparing the LES solutions with the DNS results. For the first time, a finite volume method with Roe FDS was used for LES of turbulent flow in a square duct, and the effects of grid resolution, upwind numerical dissipation, and subgrid-scale dissipation on the accuracy of the LES are examined. Comparison with DNS results shows that the standard Roe FDS adversely affects the accuracy of the turbulence simulation. For accurate turbulence simulations, only 3–5% of the standard Roe FDS dissipation is needed.     

Dimension–Adaptive Tensor–Product Quadrature

We consider the numerical integration of multivariate functions defined over the unit hypercube. Here, we especially address the high–dimensional case, where in general the curse of dimension is encountered. Due to the concentration of measure phenomenon, such functions can often be well approximated by sums of lower–dimensional terms. The problem, however, is to find a good expansion given little knowledge of the integrand itself. The dimension–adaptive quadrature method which is developed and presented in this paper aims to find such an expansion automatically. It is based on the sparse grid method which has been shown to give good results for low- and moderate–dimensional problems. The dimension–adaptive quadrature method tries to find important dimensions and adaptively refines in this respect guided by suitable error estimators. This leads to an approach which is based on generalized sparse grid index sets. We propose efficient data structures for the storage and traversal of the index sets and discuss an efficient implementation of the algorithm. The performance of the method is illustrated by several numerical examples from computational physics and finance where dimension reduction is obtained from the Brownian bridge discretization of the underlying stochastic process.