Overlapping Grid System Research Articles

Discrete Vortex Prediction of Flows around a Cylinder Near a Wall Using Overlapping Grid System

Modelling of unidirectional and oscillatory flows around a cylinder near a wall using an overlapping grid system is carried out. The circular grid system of the cylinder was overlapped with the rectangular grid system of the wall. The use of such an overlapping grid system is intended to reduce the CPU time compared to the cloud scheme in which vortex-to-vortex interaction is used, i.e., especially in calculating the shedding vortex velocity, since calculating the vortices velocity takes the longest CPU time. This method is not only time efficient, but also gives a better distribution of surface vorticity as the scattered vortices around the body are now concentrated on a grid point. Therefore, grid-to-grid interaction is used instead of vortex-to-vortex interaction. Velocity calculation was also carried out using this overlapping grid in which the new incremental shift position was summed up to obtain the total new vortices position. The engineering applications of this topic are to simulate the loading of submarine pipeline placed close to the seabed or to simulate the flow as a result of the scouring process below the cylinder since there is space for the fluid to flow beneath it. The in-line and transverse force coefficients are found by integrating the pressure around the cylinder surface. The flow patterns are then obtained and presented. The comparison of the results with experimental evidence is presented and the range of good results is discussed.

Discrete Vortex Method Of Flow Around A Cylinder In A Channel Using Simple Grid System

Modelling of unidirectional and oscillatory flows around a cylinder in a channel using a simple overlapping grid system are carried out. The importance of this cylinder-wall configuration is the effect of blockage which suppress the development of the vortex shedding The polar grid system of the cylinder is then overlapped with the rectangular grid system of the wall. The length of rectangular grid element is about the same as the length of the polar grid system in the cylinder surface. The use of such overlapping grid system is for reducing the CPU time, i.e. in calculating the vortex velocity since the CPU time in calculating the vortices velocity takes the longest time. This method is not only time efficient, but also gives a better distribution of surface vorticity as the scattered vortices around the body are now concentrated on grid point. In this study there is no vortex-to-vortex interaction, but instead it uses node-to-node interactions. Velocity calculation also uses this overlapping grid in which the new incremental shift position then summed up to get the total new vortices position. In this overlapping system the grid can be either off or on depend on process involved to get rid of the nodes not being used. The engineering applications of this topic is to simulate the loading pipeline placed in the channel such as in the heat exchanger or simulation of U-tube experiment or other system. The in-line and transverse force coefficients are found by integrating the pressure around the cylinder surface. The flow patterns are then can be obtained and presented. The comparison of the results with experimental evidence is presented and also the range of good results is discussed.

Fluid flow around NACA 0012 airfoil at low-Reynolds numbers with hybrid lattice Boltzmann method

We simulate the two-dimensional fluid flow around National Advisory Committee for Aeronautics (NACA) 0012 airfoil using a hybrid lattice Boltzmann method (HLBM), which combines the standard lattice Boltzmann method with an unstructured finite-volume formulation. The aim of the study is to assess the numerical performances and the robustness of the computational method. To this purpose, after providing a convergence study to estimate the overall accuracy of the method, we analyze the numerical solution for different values of the angle of attack at a Reynolds number equal to 103. Subsequently, flow fields at Reynolds numbers up to 104 are computed for a zero angle of attack configuration. A grid refinement scheme is applied to the uniformly spaced component of the overlapping grid system to further enhance the numerical efficiency of the model. The results demonstrate the capability of the HLBM to achieve high accuracy near solid curved walls, thus providing a viable alternative in the realm of off-lattice Boltzmann methods based on body-fitted mesh.

Discrete Vortex Prediction of Flow around Two Cylinders in Side by Side using Simple Grid System

Modelling of flows around two cylinders in side by side arrangement using a simple overlapping grid system is carried out. The use of such grid system is intended to give a considerable reduction in terms of the CPU time, especially during the calculation of the vortex velocity. It has been shown that this method is not only time efficient, but also gives a better distribution of surface vorticity as the scattered vortices around the cylinder are now concentrated on grid point located at uniform distance from the cylinder. The engineering applications of this topic is to simulate the loading on structural elements due to the presence of anodes. The in-line and transverse force coefficients and the flow patterns obtained are presented in order to provide more detail description of the flow phenomena and interaction involved. The comparison of the results with both experimental and numerical evidence is also presented and the range within which the algorithm produces good results is identified.

Hybrid lattice Boltzmann method on overlapping grids.

In this work, a hybrid lattice Boltzmann method (HLBM) is proposed, where the standard lattice Boltzmann implementation based on the Bhatnagar-Gross-Krook (LBGK) approximation is combined together with an unstructured finite-volume lattice Boltzmann model. The method is constructed on an overlapping grid system, which allows the coexistence of a uniform lattice nodes spacing and a coordinate-free lattice structure. The natural adaptivity of the hybrid grid system makes the method particularly suitable to handle problems involving complex geometries. Moreover, the provided scheme ensures a high-accuracy solution near walls, given the capability of the unstructured submodel of achieving the desired level of refinement in a very flexible way. For these reasons, the HLBM represents a prospective tool for solving multiscale problems. The proposed method is here applied to the benchmark problem of a two-dimensional flow past a circular cylinder for a wide range of Reynolds numbers and its numerical performances are measured and compared with the standard LBGK ones.

An Exact and Efficient Privacy-Preserving Spatiotemporal Matching in Mobile Social Networks

With the rapid development of mobile smartphone and its built-in location-aware devices, people are possible to establish trust relationships and further interaction with each other based their matched interests, hobbies, experiences, or spatiotemporal profiles. However, the possibility of sensitive information leakage and heavy computation overhead constrain the widespread use of the matching schemes in mobile social networks. Many privacy-preserving matching schemes were proposed recently years, but how to achieve privacy-preserving spatiotemporal matching exactly and efficiently remains an open question. In this paper, the authors propose a novel spatiotemporal matching scheme. The overlapping grid system is introduced into the scheme to improve the accuracy of spatiotemporal matching, and many repetitive records in a user's spatiotemporal profile are counted as one item so as to cut down the computation overhead. Their scheme decreases the spatiotemporal matching error, and promotes the efficiency of private matchmaking simultaneously. Thorough security analysis and evaluation results indicate that our scheme is effective and efficient.

壁がある地面近傍でホバリングするヘリコプタロータの数値解析

In rescue operations and emergency medical services, helicopters are frequently required to operate near the ground with obstacles such as buildings and sidewalls of highway. In this paper, numerical analysis of helicopter rotor hovering in close proximity to the ground with an obstacle is done by solving unsteady 3D compressible Euler equations with an overlapped grid system. The obstacle is simulated by a wall vertically set up on the ground. The parameters for numerical analysis are the rotor height and distance from the rotor-hub-center to the wall. The effects of combinations of these parameters on the flowfields around the rotor, inflow distributions on the rotor disc and behaviors of blade flapping motion are discussed. It is also clarified the cause that the helicopter rotor hovering in close proximity to the ground with a wall does not have the enough ground effect depending on the combinations of these parameters.

Patch Assembly: An Automated Overlapping Grid Assembly Strategy

This paper presents a strategy called patch assembly for assembling overlapping grid systems. This strategy has been designed to deal efficiently with specific grid assembly cases. These are cases where the chimera technique is used to add a new feature, described in a patch grid, to a geometry defined in a background grid. The patch assembly algorithm automatically performs the blanking of the background grid using simple and robust algorithms. In particular, the algorithm is not based on any geometric mask, which can be difficult to build. The blanking performed ensures a minimum overlap between grids. This grid assembly strategy is applied to a simple two-dimensional case and to a big three-dimensional wing-body configuration for modeling control surfaces. On both configurations, results are compared to results obtained on grid setups manually set with masks. A favorable influence of the minimum overlap produced has been observed on these configurations.

Aerodynamic/Acoustic Analysis for Main Rotor and Tail Rotor of Helicopter

A simulation method for full helicopter configuration is constructed by combining an unsteady Euler code and an aero-acoustic code based on the Ffowcs-Williams and Hawkings formulation. The flow field and helicopter noise are calculated using a moving overlapped grid system, and the mutual effect of main rotor and tail rotor are studied for the helicopter in hover or forward flight. In the hovering flight calculation, the tip vortex of the tail rotor is dragged by the induced flow of the main rotor, and the detailed phenomena of the flow pattern are captured well. In the forward-flight calculation, noises from the main rotor and tail rotor are predicted to show tail rotor noise for both self noise and the interaction noise with the main-rotor wake. Comparison of noise magnitude shows the relative importance of tail rotor noise according to flight conditions.

주기 회전하는 원형 실린더 주위 층류 유동장의 수치 시뮬레이션

The effects of rotary oscillation on the unsteady laminar flow past a circular cylinder. are numerically investigated in the present study. The numerical solutions for the 20 Wavier-Stokes equation are obtained using a finite volume method Tn the framework of an overlapping grid system. The vortex formation behind a circular cylinder and the hydrodynamics of wake flows for different rotary oscillation conditions are analyzed from the results of numerical simulation. The lock-on region is defined as the region that the natural shedding frequency due to the Karmann Vortex shedding and the forcing frequency due to the forced oscillating a cylinder are nearly same, and the quasi-periodic states are observed around that region. At the intersection between lock-on and non-lock-on region the shedding frequency is bifurcated. After the bifurcation, one frequency fellows the forcing frequency(<TEX>$S_f$</TEX>) and the other returns to the natural shedding frequency(<TEX>$St_0$</TEX>). in the quasi-periodic states, the variation of magnitudes and relevant phase changes of <TEX>$C_L$</TEX> with forcing phase are examined.

Finite-difference simulation of green water impact on fixed and moving bodies

A numerical method was developed to predict the water impact pressure caused by green water phenomena. The density function method was employed in the framework of a locally refined overlapping grid system. The simple problem of a rectangular body placed in regular waves was considered and the simulation results were compared with tank experiments. Good agreement with experiment was shown for wave–body interactions and for the pressure values at three different positions on the body. The case of a rectangular body with a vertical wall on the deck was also considered and the comparison showed satisfactory agreement. It was demonstrated that this method could be extended to a moving body problem, in which the body was free to undergo heave, pitch, and surge motions.

Evaluation of added resistance in regular incident waves by computational fluid dynamics motion simulation using an overlapping grid system

A computational fluid dynamics simulation method called WISDAM-X was developed to evaluate the added resistance of ships in waves. The Reynolds-averaged Navier–Stokes (RANS) equation was solved by the finite-volume method and a MAC-type solution algorithm. An overlapping grid system was employed to implement rigorous wave generation, the interactions of ships with incident waves, and the resultant ship motions. The motion of the ship is simultaneously solved by combining the solution of the motion of the ship with the solution of the flow about the ship. The free surface is captured by treatment by the density-function method. The accuracy of WISDAM-X is examined by a comparison with experimental data from a container carrier hull form, and shows a fairly good agreement with respect to ship motion and added resistance. Simulations were also conducted for a bow-form series of a medium-speed tanker to examine the effectiveness of the WISDAM-X method as a design tool for a hull form with a smaller resistance in waves. It was confirmed that the WISDAM-X method can evaluate the added resistance with sufficient relative accuracy and can be used as a design tool for ships.

IDO method with higher hermite interpolation and its accuracy check by the use of advection‐diffusion equation

AbstractThe IDO method, known as a numerical method suitable for partial differential equations containing an advection term, is improved in terms of its accuracy. In the method proposed in this paper, the order of Hermite interpolation is increased with a parameter h in order to deal with the higher order differential coefficients as independent variables. (In the conventional IDO method, h = 3 for calculation of the advection term and h = 5 for calculation of the diffusion term.) When this method is applied to a one‐dimensional advection‐diffusion equation, it is found that the numerical error is reduced to about 1/5 of that in the conventional IDO method if h = 7 is used. By using two mutually overlapping grid systems, the scheme becomes stable. Further stability is achieved by applying the time‐splitting method. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(8): 11–18, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10124

Prediction of wind noise radiated from passenger cars and its evaluation based on auralization

Abstract This paper describes the prediction of radiated wind noise from automobiles and its reduction. The Lighthill acoustic analogy was employed to estimate the wind noise at far field. In order to compute accurate pressure fluctuations, which play a role as the noise sources in the analogy, an overlapped grid system is used to calculate flow fields in detail with a finite-difference method. This approach was applied to predict the wind noise radiated from a door mirror and a front pillar. Measured data are compared with the computed results of pressure fluctuations on the side-window surface. The predicted pressure fluctuations agree well with the experimental results. Then, shapes of the front pillar and the door mirror were modified based on the computed results so as to reduce the wind noise. The effects of the modification were proved by additional experiments.

An Algorithm for Assembling Overlapping Grid Systems

A general purpose algorithm for assembling overlapping grid systems for solving partial differential equations (PDEs) is described. The method combines and improves on the techniques implemented in the codes Beggar, CMPGRD, DCF3D, and PEGSUS. The present algorithm, which has been implemented for the two-dimensional case in the code Xcog, starts by calculating a global definition of the boundary of the computational domain based on the location of the physical boundaries in all component grids. The global boundary description isused to identify all grid points outside of the computational domain. The remaining points are classified according to the priority of the component grids in the overlapping grid. If the overlap between the components is sufficiently large, all remaining points can either interpolate from an overlapping grid or be used to discretize the PDE. The algorithm can therefore construct an overlapping grid for implicit (coupled) interpolation in one pass and needs only to iterate to ensure explicit (decoupled) interpolation. If the algorithm fails due to insufficient overlap between the components, the main parts of the grid will still be valid. This enables the code to report inconsistent grid points to the user, to facilitate an improvement of the input. Discrepancies between the boundary representations where the grids overlap are handled by a mismatch tolerance, which is estimated automatically. The interpolation data are corrected for the boundary mismatch, and it is shown how the interpolation error in a thin boundary layer is substantially reduced by this correction.

Hole-Cutting for Three-Dimensional Overlapping Grids

A hole-cutting technique for assembling overlapping grid systems for solving partial differential equations is presented. In the present method, the closed surfaces on the boundary of the three-dimensional computational domain are represented by hybrid surface grids. The hybrid grids are composed of nonoverlapping structured surface grids joined by an unstructured layer of triangles. Each hybrid grid is constructed from a subset of the physical boundary points on the faces of the component grids. The holes in the component grids are made by using a two-step mark-and-fill method. We first locate all grid cells that intersect the hybrid surface grids. We then apply the ray method to determine whether the grid points in these intersected grid cells are inside or outside the region bounded by the hybrid surface grids. As a result, the boundary of the hole region will be marked and it is a simple matter to then remove all points from the hole by starting from the outside points and traversing along all three grid directions until an inside point is found. To locate the intersecting grid cells, we employ the ray method augmented by an octree-based search technique together with Newton's method to invert the mappings corresponding to each component grid. We demonstrate the hole-cutting method by running the code Chalmesh to generate overlapping grids for a sphere in a box, around the stern of a ship, and around a three-bladed ship propeller.

Implicit finite difference methods on composite grids

Interpolation techniques are developed for solving partial differential equations using implicit finite-difference methods on multi-component overlapping grid systems.