Ghost-Cell Method with far-field coarsening and mesh adaptation for Cartesian grids

Cartesian grid methods for inviscid computational fluid dynamics offer great promise for the development of very rapid conceptual design tools. The present paper deals with a number of new features for Cartesian grid methods which appear to be particularly well suited for this application. A key ingredient is the implementation of non-penetration boundary conditions at solid walls which is based upon the curvature-corrected symmetry technique (CCST) developed by the present authors for body-fitted grids. The method introduces ghost cells near the boundaries whose values are developed from an assumed flow-field model in vicinity of the wall. This method was shown to be substantially more accurate than traditional surface boundary condition approaches. This improved boundary condition has been adapted to a Cartesian mesh formulation, which we termed the Ghost-Cell Method. In this approach, all cell centers exterior to the body are computed with fluxes at the four surrounding cell edges, without any cut cells which complicate other Cartesian mesh methods. Another typical drawback of non-adaptive Cartesian grid methods is that any Cartesian grid clustering near the body must be maintained to the far field boundary. To address this issue, we have introduced a far-field grid coarsening, based on the iblanking approach, which maintains the structured nature of the grid while computing only the active cell centers. In addition, to highlight the advantages of grid adaptation in connection with Cartesian mesh methods, we have introduced a rudimentary procedure which detects the shock position and automatically refines the mesh by locally reducing the grid dimension to one fourth of its original dimension. The merits of the Ghost-Cell Method are established by the computation of the compressible flow about circular cylinders. The results show the surface non-penetration condition to be satisfied in the limit of vanishing cell size and the method to be second-order accurate in space. The results of the far-field grid coarsening indicate that the numerical solutions are unaffected by the coarsening, while the number of the computed cells and the CPU time are reduced to less than 50% of the uncoarsened solution values. The results computed using the mesh adaptation at the shock indicate that the method is effective in reducing the shock transition region thickness, without modifying the flow solution away from the shock. Finally, some test cases with airfoils located at different positions have been considered and the results are proven to be practically independent of the position of the body with respect to the grid. Although this paper is limited to two-dimensional applications, the methodology is well-suited for general three-dimensional geometries, which will be the subject of future research.     

Multidimensional upwind scheme of diagonal Cartesian method for an advection-diffusion problem

The natural calculation region in fluid dynamics involves complex boundaries. When using the Cartesian grid to approximate complex boundaries, two difficulties develop: the boundary zigzag effect and disagreement of direction of grid line and velocity. The multidimensional upwind scheme of the diagonal Cartesian method (DCM), using both Cartesian grid lines and diagonal lines segments, is presented in this paper to simulate the complex boundaries of the multiple-layer quasi 3D model equations. The DCM improves the simulation accuracy for the boundaries and calculation time increases only slightly compared to the Cartesian method. In order to verify the new scheme, a test case is presented which rotates the cavity flow at 45° to compare the numerical calculation results at different Reynolds numbers. The test case shows that the scheme is accurate and efficient in improving the simulation results. Then the three-dimensional advection-diffusion processes in the tidal water of the Hongyanhe Power Plant are simulated using this model. Numerical results show that the scheme is not only efficient on an experiment basis, but also efficient and reliable when applied to a large scale natural water area.     

Numerical simulation of pyroclastic density currents using locally refined Cartesian grids

Pyroclastic density currents are ground hugging, hot, gas–particle flows representing the most hazardous events of explosive volcanism. Their impact on structures is a function of dynamic pressure, which expresses the lateral load that such currents exert over buildings. Several critical issues arise in the numerical simulation of such flows, which involve a rheologically complex fluid that evolves over a wide range of turbulence scales, and moves over a complex topography. In this paper we consider a numerical technique that aims to cope with the difficulties encountered in the domain discretization when an adequate resolution in the regions of interest is required. Without resorting to time-consuming body-fitted grid generation approaches, we use Cartesian grids locally refined near the ground surface and the volcanic vent in order to reconstruct the steep velocity and particle concentration gradients. The grid generation process is carried out by an efficient and automatic tool, regardless of the geometric complexity. We show how analog experiments can be matched with numerical simulations for capturing the essential physics of the multiphase flow, obtaining calculated values of dynamic pressure in reasonable agreement with the experimental measurements. These outcomes encourage future application of the method for the assessment of the impact of pyroclastic density currents at the natural scale.     

Flow simulations in arbitrarily complex cardiovascular anatomies – An unstructured Cartesian grid approach

Image guided computational fluid dynamics is attracting increasing attention as a tool for refining in vivo flow measurements or predicting the outcome of different surgical scenarios. Sharp interface Cartesian/Immersed-Boundary methods constitute an attractive option for handling complex in vivo geometries but their capability to carry out fine-mesh simulations in the branching, multi-vessel configurations typically encountered in cardiovascular anatomies or pulmonary airways has yet to be demonstrated. A major computational challenge stems from the fact that when such a complex geometry is immersed in a rectangular Cartesian box the excessively large number of grid nodes in the exterior of the flow domain imposes an unnecessary burden on both memory and computational overhead of the Cartesian solver without enhancing the numerical resolution in the region of interest. For many anatomies, this added burden could be large enough to render comprehensive mesh refinement studies impossible. To remedy this situation, we recast the original structured Cartesian formulation of Gilmanov and Sotiropoulos [Gilmanov A, Sotiropoulos F. A hybrid Cartesian/immersed boundary method for simulating flows with 3D, geometrically complex, moving bodies. J Comput Phys 2005;207(2):457–92] into an unstructured Cartesian grid layout. This simple yet powerful approach retains the simplicity and computational efficiency of a Cartesian grid solver, while drastically reducing its memory footprint. The method is applied to carry out systematic mesh refinement studies for several internal flow problems ranging in complexity from flow in a 90° pipe bend to flow in an actual, patient-specific anatomy reconstructed from magnetic resonance images. Finally, we tackle the challenging clinical scenario of a single-ventricle patient with severe arterio-venous malformations, seeking to provide a fluid dynamics prospective on a clinical problem and suggestions for procedure improvements. Results from these simulations demonstrate very complex cardiovascular flow dynamics and underscore the need for high-resolution simulations prior to drawing any clinical recommendations.     

Non-body-fitted Cartesian-mesh simulation of highly turbulent flows using multi-relaxation-time lattice Boltzmann method

This paper presents a lattice Boltzmann method (LBM) based study aimed at numerical simulation of highly turbulent and largely inclined flow around obstacles of curved geometry using non-body-fitted Cartesian meshes. The approach features (1) combining the interpolated bounce-back scheme with the LBM of multi-relaxation-time (MRT) type to enable the use of simple Cartesian mesh for the flow cases even with complex geometries; and (2) incorporating the Spalart–Allmaras (SA) turbulence model into LBM in order to represent the turbulent flow effect. The numerical experiments are performed corresponding to flows around an NACA0012 airfoil at Re=5×10⁵ and around a flat plate at Re=2×10⁴, respectively. The agreement between all simulation results obtained from this study and the data provided by other literature demonstrates the reliability of the enhanced LBM proposed in this paper for simulating, simply on Cartesian meshes, complex flows that may involve bodies of curved boundary, high Reynolds number, and large angle of attack.     

Numerical simulation of slider air bearings based on a mesh-free method for HDD applications

This paper focuses on the development of a computational method to be used as a tool for air bearing simulation and design in modern hard disk drive. A data density of 100 Gb/in.² has already been achieved in today’s production. The hard disk drive industry’s next goal is to increase the data density to 1 Tb/in.² . New features in air bearing designs include shaped rails, multiple etching depths and negative pressure pockets. Thus, mesh generation is a difficult task in the air bearing simulation. This, in turn, demands the development of an accurate and easy-to-use computational method to solve Reynolds equations based on various flow models. Least square finite difference scheme, one of mesh-less methods, is presented to solve the slider air bearing problems of hard disk drives. For each specified attitude, the air bearing pressure is obtained by solving the Reynolds equation using the mesh-free method. The discretized nonlinear systems of equations are solved by successive over-relaxation (SOR) implementation, and the results of the numerical solutions are compared with other numerical and experimental data.     

混合重叠网格通信优化算法

重叠网格技术广泛应用在复杂外型和运动边界问题的流场数值模拟中.本文在并行重叠网格隐式挖洞算法实现的基础上,提出了笛卡尔辅助网格和多块结构网格的混合重叠网格方法.通过笛卡尔辅助网格实现重叠网格洞边界和网格插值关系的快速建立.通过定义重叠区域网格权重、部件网格与背景网格绑定的方法,建立了混合网格的并行分配模式,有效减少重叠插值信息在各进程间的通信,实现计算负载和通信负载在各个进程的均匀分配.测试表明该方法可应用于数千万量级的重叠网格系统,可扩展至千核规模,高效的实现多个物体构成的复杂网格系统的重叠关系建立.     

Ghost-cell method for analysis of inviscid three-dimensional flows on Cartesian-grids

The present paper deals with the implementation of non-penetration boundary conditions at solid walls for three-dimensional inviscid flow computations on Cartesian grids. The crux of the method is the curvature-corrected symmetry technique (CCST) developed by the present authors for body-fitted grids. The method introduces ghost cells near the boundaries whose values are developed from an assumed flow-field model in vicinity of the wall consisting of a vortex flow, with locally symmetric distribution of entropy and total enthalpy. In three dimensions this procedure is implemented in the so-called “osculating plane”. This method was shown to be substantially more accurate than traditional surface boundary condition approaches. This improved boundary condition is adapted to a Cartesian mesh formulation, which we have termed the “ghost-cell method”. In this approach, all cell centers exterior to the body are computed with fluxes at the six surrounding cell faces, without any cut cell. A multiple-valued point technique is used to compute sharp edges. The merits of the ghost-cell method for three-dimensional inviscid flow computations are established by computing compressible and transonic flows about a sphere, an oblate and a prolate spheroid, a cylindrical wing with an end-plate, the ONERA M6 wing and detailed comparison to body-fitted grid computations and to published data. The computed results show the surface non-penetration condition to be satisfied in the limit of vanishing cell size and the method to be second-order accurate in space. The comparison with body-fitted results proves that the accuracy is comparable to the accuracy of CCST computations on body-fitted grids and remarkably superior to body-fitted computations based on traditional pressure extrapolation, non-penetration boundary conditions. In addition, we prove that the results are independent of the position of the body with respect to the grid. Finally, we show that the ONERA M6 wing results compare very well with published data.     

3D conforming power diagrams for radial LGR in CPG reservoir grids

Mesh generation becomes a crucial step in reservoir flow simulation of new generation. The mesh must faithfully represent the architecture of the reservoir and its heterogeneity. In (Flandrin et al. in IJNME 65(10):1639–1672, 2006) a three-dimensional hybrid mesh model was proposed to capture the radial characteristics of the flow around the wells. In this hybrid mesh, the reservoir is described by a non-uniform Cartesian structured mesh and the drainage areas around the wells are represented by structured radial circular meshes. Unstructured polyhedral meshes are used to connect these two kinds of structured grids. The construction of these transition meshes is based on 3D power diagrams (Aurenhammer in SIAM J Comput 16(1):78–96, 1987) to ensure finite volume properties such as mesh conformity, dual orthogonality and cell convexity. In this paper, we propose an extension of this hybrid model to the case where the reservoir is described by a corner point geometry (CPG) grid. At first, the CPG grid is mapped, in a reference space, into a non-uniform Cartesian grid by minimizing the mapping deformation. Then, a hybrid mesh is generated in this reference space using the previous method. Finally, this mesh is mapped back into the real space. Some quality criterions are introduced to measure and improve the quality of the polyhedral transition mesh.     

带主动倾斜补偿功能的混合型光学头三维力矩器

一、引言从CD发展到HD DVD、BD,光存储的数据容量和读写速度有了迅速的增长。大容量光存储需要减小盘面上的光斑尺寸,要求采用NA更高的物镜和波长更短的激光。然而,高NA物镜和短波长激光的使用会造成光盘倾斜容差的降低、盘片厚度公差的严格化、焦深的减小和球差的增加。这些变化可以通过以下各式表达:     

Helmholtz共振腔气动噪声数值仿真

为探究出一套完整、准确的气动噪声仿真方法,用FLUENT和Actran仿真Helmholtz共振腔旁接管道系统模型.针对流场仿真,采用六面体网格建模,分析选择合适的网格密度,明确网格及边界条件的影响,以获得准确的声源信息;运用Lighthill声类比方法对声场进行仿真,采用数值计算、传声损失仿真和气动噪声仿真计算等3种方法提取管道内部场点声压级频谱曲线,分析曲线峰值频率特征,包括共振频率分析和声模态分析等.采用CFD软件与声学仿真软件相结合的方法,可以有效进行流场和声场的仿真.     

An immersed boundary method on Cartesian adaptive grids for the simulation of compressible flows around arbitrary geometries

In this article, we present an immersed boundary method for the simulation of compressible flows of complex geometries encountered in aerodynamics. The immersed boundary methods allow the mesh not to conform to obstacles, whose influence is taken into account by modifying the governing equations locally (either by a source term within the equation or by imposing the flow variables or fluxes locally, similarly to a boundary condition). A main feature of the approach which we propose is that it relies on structured Cartesian grids in combination with a dedicated HPC Cartesian solver, taking advantage of their low memory and CPU time requirements but also the automation of the mesh generation and adaptation. Turbulent flow simulations are performed by solving the Reynolds-averaged Navier–Stokes equations or by a Large-Eddy simulation approach, in combination with a wall function at high Reynolds number, to mitigate the cell count resulting from the isotropic nature of Cartesian cells. The objective of this paper is to demonstrate that this automatic workflow is fast and robust and enables to get quantitative aerodynamics results on geometrically complex configurations. Results obtained are in good agreement with classical body-fitted approaches but with a significant reduction of the time of the whole process, that is a day for RANS simulations, including the mesh generation.

     

Friction effect on ball positioning of an automatic balancer in optical disk drives

This study was aimed at evaluating the perfect balancing position of an automatic ball balancer installed in optical disk drives taking into consideration the effects of the rolling friction, speed ratio, and scaling parameter on ball positioning. A mathematical model that is employed to derive the dynamic equations of the ABB system was constructed. Stability of the steady-state solutions was then analyzed. A numerical simulation and an experimental study were conducted to verify the mathematical model. The simulation and experimental results were in good agreement.     

A fast numerical method for flow analysis and blade design in centrifugal pump impellers

A numerical methodology is developed to simulate the turbulent flow in a 2-dimensional centrifugal pump impeller and to compute the characteristic performance curves of the entire pump. The flow domain is discretized with a polar, Cartesian mesh and the Reynolds-averaged Navier-Stokes (RANS) equations are solved with the control volume approach and the k-ε turbulence model. Advanced numerical techniques for adaptive grid refinement and for treatment of grid cells that do not fit the irregular boundaries are implemented in order to achieve a fully automated grid construction for any impeller design, as well as to produce results of adequate precision and accuracy. After estimating the additional hydraulic losses in the casing and the inlet and outlet sections of the pump, the performance of the pump can be predicted using the numerical results from the impeller section only. The regulation of various energy loss coefficients involved in the model is carried out for a commercial pump, for which there are available measurements. The predicted overall efficiency curve of the pump was found to agree very well with the corresponding experimental data. Finally, a numerical optimization algorithm based on the unconstrained gradient approach is developed and combined with the evaluation software in order to find the impeller geometry that maximizes the pump efficiency, using as free design variables the blade angles at the leading and the trailing edge. The results verified that the optimization process can converge very fast and to reasonable optimal values.     

A posteriori error estimation by postprocessor independent of method of flowfield calculation

We consider a postprocessor that is able to analyze the flow-field generated by an external (unknown) code so as to determine the error of useful functionals. The residuals engendered by the action of a high-order finite-difference stencil on a numerically computed flow-field are used for adjoint based a posteriori error estimation. The method requires information on the physical model (PDE system), flowfield parameters and corresponding grid and may be constructed without availability of detailed information on the numerical method used for the flow computation.     

A numerical study of developing slurry flow in the entrance region of a horizontal pipe

In this paper, a simplified 3-D algebraic slip mixture (ASM) model was introduced to obtain the numerical solution in sand-water slurry flow. In order for the study to obtain the precise numerical solution in fully developed turbulent flow, the RNG k-ε turbulent model was used with the algebraic slip mixture model. An unstructured (block-structured), non-uniform grid was chosen to discretize the entire computation domain, and a control volume finite difference method (CVFDM) was applied to solve the governing equations. The mean pressure gradients from the numerical solution in the fully developed turbulent flow were compared with the authors’ experimental data and that in the open literature to validate the simulation results. The solutions were found to be in good agreement with the experimental data. The numerical investigations have focused mainly on illustrating and comparing the developing processes of volume fraction and density distributions, mean velocity profiles, and mean skin friction coefficient distributions in the entrance region. It was found that the difference of friction factors between single- and double-species slurries increases along flow direction in most part of the entrance region.     

Analytical and numerical description for isothermal gas flows in microchannels

Analytical solutions for the pressure and the velocity profiles in a microchannel are derived from the quasi gasdynamic equations (QGD). An expansion method according to a small geometric parameter ɛ is undertaken to obtain the isothermal flow parameters. The deduced expression of the mass flow rate is similar to the analytical expression obtained from the Navier-Stokes equations with a second order slip boundary condition and gives results in agreement with the measurements. The analytical expression of the pressure predicts accurately the measured pressure distribution. The effects of the rarefaction and of the compressibility on pressure distributions are discussed. The numerical calculations based on the full system of the QGD equations were carried out for different sizes of the microchannels and for different gases. The numerical results confirm the validity of the analytical approach.     

A pressure-correction method and its applications on an unstructured Chimera grid

In this paper, an unstructured Chimera mesh method is used to compute incompressible flow around a rotating body. To implement the pressure correction algorithm on unstructured overlapping sub-grids, a novel interpolation scheme for pressure correction is proposed. This indirect interpolation scheme can ensure a tight coupling of pressure between sub-domains. A moving-mesh finite volume approach is used to treat the rotating sub-domain and the governing equations are formulated in an inertial reference frame. Since the mesh that surrounds the rotating body undergoes only solid body rotation and the background mesh remains stationary, no mesh deformation is encountered in the computation. As a benefit from the utilization of an inertial frame, tensorial transformation for velocity is not needed. Three numerical simulations are successfully performed. They include flow over a fixed circular cylinder, flow over a rotating circular cylinder and flow over a rotating elliptic cylinder. These numerical examples demonstrate the capability of the current scheme in handling moving boundaries. The numerical results are in good agreement with experimental and computational data in literature.     

A Parallel Overset Grid High-Order Flow Solver for Large Eddy Simulation

This work describes the development and validation of a parallel high-order compact finite difference Navier–Stokes solver for application to large-eddy simulation (LES) and direct numerical simulation. The implicit solver can employ up to sixth-order spatial formulations and tenth-order filtering. The parallelization of the solver is founded on the overset grid technique. LES were then performed for turbulent channel flow with Reynolds numbers ranging from Re _τ=180 to 590, and flow past a circular cylinder with a transitional wake at Re _D =3900. The channel flow solutions were obtained using both an implicit LES (ILES) approach and a dynamic sub-grid scale model. The ILES method obtained virtually identical solutions at half the computational cost. The original vector and new parallel solvers produce indistinguishable mean flow solutions for the circular cylinder. Repeating the cylinder simulation on a much finer mesh resulted in significantly better agreement with experimental data in the near wake than the coarse grid solution and other previous numerical studies.     

基于笛卡尔切割单元法的复杂河道地理信息系统环评可视化

复杂河道中污染物扩散计算及其在地理信息系统(GIS)上的可视化,对于地表水环境影响评价(EIA)具有非常重要的意义,但在网格生成、污染物计算模型及计算结果可视化方面存在着诸多困难。针对点源岸边排放河流污染物计算及基于GIS可视化中的难点问题,提出了基于切割单元法的地面水环境影响评价可视化方法。将切割单元法应用于网格剖分,通过切割单元交点追踪算法及河道轮廓线内背景网格筛取算法,生成了复杂河道笛卡尔网格。提出了基于污染物二维稳态衰减模式的网格自适应加密与稀疏算法,在非结构化笛卡尔网格基础上采用了基于河流几何信息判断的点源岸边排放河流污染预测算法与区域填充算法,实现了环境影响评价计算结果的可视化显示。通过一个河流污染环境影响评价可视化的实例,验证了所提方法的可行性与有效性。