Search results

The averaged Navier‐Stokes and the k‐e turbulence model equations are used to simulate turbulent flows in some internal flow cases. The discrete equations are solved by different variations of Multigrid methods. These include both steady state as well as time dependent solvers. Locally refined grids can be added dynamically in all cases. The Multigrid schemes result in fast convergence rates, whereas local grid refinements allow improved accuracy with rational increase in problem size. The applications of the solver to a 3‐D (cold) furnace model and to the simulation of the flow in a wind tunnel past an object prove the efficiency of the Multigrid scheme with local grid refinement.

Size fit and economic efficiency are two crucial aspects that need to be considered in designing a sizing system. However, there could exist a trade-off between those aspects in order to establish a practical sizing system. The purpose of this paper is to develop a sequential hybrid method of grid and optimization to generate a practical sizing system using anthropometric data.

The proposed sequential hybrid method consisted of two sequential steps, which employs grid method and optimization method. In the initial step, the grid method creates primary grids that accommodate a designated percentage (e.g. 90%) of users with best size fit. In the subsequent step, the optimization method generated additional grids to provide acceptable fit, with minimum fit penalty scores for users unaccommodated by the primary grids. Our method was applied to the development of a sizing system for men's military jackets. The proposed method performances were evaluated in terms of accommodation percentage, size fit and number of sizing categories.

Our proposed method resulted in 26 primary grids during the initial step, which cover 90% of users. Next, we generated six additional grids during the subsequent step that provide minimum fit penalty scores for the rest (10%) users.

The main contributions of this paper are as follows: consider accommodation percentage, size fit and number of sizing categories in the design of sizing system; combine the grid and optimization methods and evaluate a sizing system for men's military jackets. The proposed method is applicable to develop optimal sizing systems for multiple-size products.

An adaptive grid solution method is described for computing the time accurate solution of an unsteady flow problem. The solution method consists of three parts: a grid point redistribution method; an unsteady Euler equation solver; and a temporal coupling routine that links the dynamic grid to the flow solver. The grid movement technique is a direct curve by curve method containing grid controls that generate a smooth grid that resolves the severe solution gradients and the sharp transitions in the solution gradients. By design, the temporal coupling procedure provides a grid that does not lag the solution in time. The adaptive solution method is tested by computing the unsteady inviscid solutions for a one‐dimensional shock tube and a two‐dimensional shock vortex interaction. Quantitative comparisons are made between the adaptive solutions, theoretical solutions and numerical solutions computed on stationary grids. Test results demonstrate the good temporal tracking of the solution by the adaptive grid, and the ability of the adaptive method to capture an unsteady solution of comparable accuracy to that computed on a stationary grid containing significantly more grid points than used in the adaptive grid.

The purpose of this paper is to develop a new finite difference method for solving the seismic wave propagation in fluid-solid media, which can be described by the acoustic and viscoelastic wave equations for the fluid and solid parts, respectively.

In this paper, the authors introduced a coordinate transformation method for seismic wave simulation method. In the new method, the irregular fluid–solid interface is transformed into a horizontal interface. Then, a multi-block coordinate transformation method is proposed to mesh every layer to curved grids and transforms every interface to horizontal interface. Meanwhile, a variable grid size is used in different regions according to the shape and the velocity within each region. Finally, a Lebedev-standard staggered coupled grid scheme for curved grids is applied in the multi-block coordinate transformation method to reduce the computational cost.

The instability in the auxiliary coordinate system caused by the standard staggered grid scheme is resolved using a curved grid viscoelastic wave field separation strategy. Several numerical examples are solved using this new method. It has been shown that the new method is stable, efficient and highly accurate in solving the seismic wave equation defined on domain with irregular fluid–solid interface.

First, the irregular fluid–solid interface is transformed into a horizontal interface by using the coordinate transformation method. The conversion between pressures and stresses is easy to implement and adaptive to different irregular fluid–solid interface models, because the normal stress and shear stress vanish when the normal angle is 90° in the interface. Moreover, in the new method, the strong false artificial boundary reflection and instability caused by ladder-shaped grid discretion are resolved as well.

Detailed results of numerical calculations of transient, 2D incompressible flow around and in the wake of a square prism at Re = 100, 200 and 500 are presented. An implicit finite‐difference operator‐splitting method, a version of the known SIMPLEC‐like method on a staggered grid, is described. Appropriate theoretical results are presented. The method has second‐order accuracy in space, conserving mass, momentum and kinetic energy. A new modification of the multigrid method is employed to solve the elliptic pressure problem. Calculations are performed on a sequence of spatial grids with up to 401 × 321 grid points, at sequentially halved time steps to ensure grid‐independent results. Three types of flow are shown to exist at Re = 500: a steady‐state unstable flow and two which are transient, fully periodic and asymmetric about the centre line but mirror symmetric to each other. Discrete frequency spectra of drag and lift coefficients are presented.

The purpose of this paper is twofold: to describe and evaluate the life grid as a methodology for historical research; and to provide an example application investigating the dynamics of family meals over a lifetime by pairing life course theory with the life grid method of obtaining oral histories.

To explore how the meanings and processes of meals change, the authors conducted interviews with 15 respondents aged 80 years old and over, on the topic of family meals.

The paper discusses the merits of using the life grid method to analyze lifetime family consumption behavior. The findings of this example study provide insight as to how the roles, responsibilities, and loyalties of our participants had changed through births, deaths, marriages, wars, economic periods, illnesses, and the process of aging, leading to changes in dining.

The benefit of the life grid method described in this paper is its ability to minimize recall bias. In addition, the overt process of cross‐referencing events throughout the course of the interviews via the life grid method proved to be a helpful aid in identifying patterns and symmetries during the interpretation stage.

We study the sparse grid combination technique as an efficient method for the solution of fluid dynamics problems. The combination technique needs only O(h^–1_n(log(h^–1_n))^d–1) grid points for d‐dimensional problems, instead of O(h^–d_n) grid points used by the full grid method. Here, h_n = 2^–n denotes the mesh width of the grids. Furthermore, provided that the solution is sufficiently smooth, the accuracy (with respect to the L₂‐ and the L_∞‐norm) of the sparse grid combination solution is O(h^α_n(log(h^–1_n))^d–1), which is only slightly worse than O(h^α_n) obtained by the full grid solution. Here, α includes the order of the underlying discretization scheme, as well as the influence of singularities. Thus, the combination technique is very economic on both storage requirements and computing time, but achieves almost the same accuracy as the usual full grid solution. Another advantage of the combination technique is that only simple data structures are necessary. Where other sparse grid methods need hierarchical data structures and thus specially designed solvers, the combination method handles merely d‐dimensional arrays. Thus, the implementation of the combination technique can be based on any “black box solver”. However, for reasons of efficiency, an appropriate multigrid solver should be used. Often, fluid dynamics problems have to be solved on rather complex domains. A common approach is to divide the domain into blocks, in order to facilitate the handling of the problem. We show that the combination technique works on such blockstructured grids as well. When dealing with complicated domains, it is often desirable to grade a grid around a singularity. Graded grids are also supported by the combination technique. Finally, we present the first results of numerical experiments for the application of the combination method to CFD problems. There, we consider two‐dimensional laminar flow problems with moderate Reynolds numbers, and discuss the advantages of the combination method.

The purpose of this paper is to investigate and improve a new method of unstructured rotational dynamic overset grids, which can be used to simulate the unsteady flows around rotational parts of aircraft.

The computational domain is decomposed into two sub-domains, namely, the rotational sub-domain which contains the rotational boundaries, and the stationary sub-domain which contains the remainder flow field including the stationary boundaries. The artificial boundaries and restriction boundaries are used as the restriction condition to generate the entire computational grid, and then the overset grids are established according to the radius parameters of artificial boundaries set previously. The deformation of rotational boundary is treated by using the linear spring analogy method which is suitable for the dynamic unstructured grid. The unsteady Navier-Stokes/Euler equations are solved separately in the rotational sub-domain and stationary sub-domain, and data coupling is accomplished through the overlapping area. The least squares method is used to interpolate the flow variables for the artificial boundary points with a higher calculating precision. Implicit lower-upper symmetric-Gauss-Seidel (LU-SGS) time stepping scheme is implemented to accelerate the inner iteration during the unsteady simulation.

The airfoil steady flow, airfoil pitching unsteady flow, three-dimensional (3-D) rotor flow field, rotor-fuselage interaction unsteady flow field and the flutter exciting system unsteady flow field are numerically simulated, and the results have good agreements with the experimental data. It is shown that the present method is valid and efficient for the prediction of complicated unsteady problems which contain rotational dynamic boundaries.

The results are entirely based on computational fluid dynamics (CFD), and the 3D simulations are based on the Euler equations in which the viscous effect is ignored. The current work shows further applicable potential to simulate unsteady flow around rotational parts of aircraft.

The current study can be used to simulate the two-dimensional airfoil pitching, 3-D rotor flow field, rotor-fuselage interaction and the flutter exciting system unsteady flow. The work will help the aircraft designer to get the unsteady flow character around rotational parts of aircraft.

A new type of rotational dynamic overset grids is presented and validated, and the current work has a significant contribution to the development of unstructured rotational dynamic overset grids.

The use of the prominent FDTD method for the time domain solution of electromagnetic wave propagation past devices with small geometrical details can require very fine grids and can lead to very important computational time and storage. The purpose is to develop a numerical method able to handle possibly non‐conforming locally refined grids, based on portions of Cartesian grids in order to use existing pre‐ and post‐processing tools.

A Discontinuous Galerkin method is built based on bricks and its stability, accuracy and efficiency are proved.

It is found to be possible to conserve exactly the electromagnetic energy and weakly preserves the divergence of the fields (on conforming grids). For non‐conforming grids, the local sets of basis functions are enriched at subgrid interfaces in order to get rid of possible spurious wave reflections.

Although the dispersion analysis is incomplete, the numerical results are really encouraging it is shown the proposed numerical method makes it possible to handle devices with extremely small details. Further investigations are possible with different, higher‐order discontinuous finite elements.

This paper can be of great value for people wanting to migrate from FDTD methods to more up to date time‐domain methods, while conserving existing pre‐ and post‐processing tools.

The paper aims to expand the scope of application of the lattice Boltzmann method (LBM), especially in the field of aircraft engineering. The traditional LBM is usually applied to incompressible flows at a low Reynolds number, which is not sufficient to satisfy the needs of aircraft engineering. Devoted to tackling the defect, the paper proposes a developed LBM combining the subgrid model and the multiple relaxation time (MRT) approach. A multilayer adaptive Cartesian grid method to improve the computing efficiency of the traditional LBM is also employed.

The subgrid model and the multilayer adaptive Cartesian grid are introduced into MRT-LBM for simulations of incompressible flows at a high Reynolds number. Validated by several typical flow simulations, the numerical methods in this paper can efficiently study the flows under high Reynolds numbers.

Some numerical simulations for the lid-driven flow of cavity, flow around iced GLC305, LB606b and ONERA-M6 are completed. The paper presents the investigation results, indicating that the methods are accurate and effective for the separated flow after icing.

LBM is developed with the addition of the subgrid model and the MRT method. A numerical strategy is proposed using a multilayer adaptive Cartesian grid method and its treatment of boundary conditions. The paper refers to innovative algorithm developments and applications to the aircraft engineering, especially for iced wing simulations with flow separations.