Fourth order accurate compact scheme with group velocity control (GVC)

For solving complex flow field with multi-scale structure higher order accurate schemes are preferred. Among high order schemes the compact schemes have higher resolving efficiency. When the compact and upwind compact schemes are used to solve aerodynamic problems there are numerical oscillations near the shocks. The reason of oscillation production is because of non-uniform group velocity of wave packets in numerical solutions. For improvement of resolution of the shock a parameter function is introduced in compact scheme to control the group velocity. The newly developed method is simple. It has higher accuracy and less stencil of grid points.

Hydrothermal Instability Of Thermocapillary Convection In Large-Prandtl-Number Liquid Bridges Under Microgravity

Linear stability analysis was performed to study the mechanism of transition of thermocapillary convection in liquid bridges with liquid volume ratios ranging from 0.4 to 1.2, aspect ratio of 0.75 and Prandtl number of 100. 2-D governing equations were solved to obtain the steady axi-symmetric basic flow and temperature distributions. 3-D perturbation equations were discretized at the collocation grid points using the Chebyshev-collocation method. Eigenvalues and eigenfunctions were obtained by using the Q-R. method. The predicted critical Marangoni numbers and critical frequencies were compared with data from space experiments. The disturbance of the temperature distribution on the free surface causes the onset of oscillatory convection. It is shown that the origin of instability is related to the hydrothermal origin for convections in large-Prandtl-number liquid bridges. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Statistical Interpolation Method of Turbulent Phase Screen

A relative displacement between the grid points of optical fields and those of phase screens may occur in the simulation of light propagation through the turbulent atmosphere. A statistical interpolator is proposed to solve this problem in this paper. It is evaluated by the phase structure function and numerical experiments of light propagation through atmospheric turbulence with/without adaptive optics (AO) and it is also compared with the well-known linear interpolator under the same condition. Results of the phase structure function show that the statistical interpolator is more accurate in comparison with the linear one, especially in the high frequency region. More importantly, the long-exposure results of light propagation through the turbulent atmosphere with/without AO also show that the statistical interpolator is more accurate and reliable than the linear one. (C) 2009 Optical Society of America.

Compact difference approximation with consistent boundary condition

For simulating multi-scale complex flow fields it should be noted that all the physical quantities we are interested in must be simulated well. With limitation of the computer resources it is preferred to use high order accurate difference schemes. Because of their high accuracy and small stencil of grid points computational fluid dynamics (CFD) workers pay more attention to compact schemes recently. For simulating the complex flow fields the treatment of boundary conditions at the far field boundary points and near far field boundary points is very important. According to authors' experience and published results some aspects of boundary condition treatment for far field boundary are presented, and the emphasis is on treatment of boundary conditions for the upwind compact schemes. The consistent treatment of boundary conditions at the near boundary points is also discussed. At the end of the paper are given some numerical examples. The computed results with presented method are satisfactory.

A block SPP algorithm for multidimensional tridiagonal equations with optimal message vector length

A parallel strategy for solving multidimensional tridiagonal equations is investigated in this paper. We present in detail an improved version of single parallel partition (SPP) algorithm in conjunction with message vectorization, which aggregates several communication messages into one to reduce the communication cost. We show the resulting block SPP can achieve good speedup for a wide range of message vector length (MVL), especially when the number of grid points in the divided direction is large. Instead of only using the largest possible MVL, we adopt numerical tests and modeling analysis to determine an optimal MVL so that significant improvement in speedup can be obtained.

A self-consistent field theory study on the morphologies of linear ABCBA and H-shaped (AB)(2)C(BA)(2) block copolymers

By using a combinatorial screening method based on the self-consistent field theory, we investigate the equilibrium morphologies of linear ABCBA and H-shaped (AB)(2)C(BA)(2) block copolymers in two dimensions. The triangle phase diagrams of both block copolymers are constructed by systematically varying the volume fractions of blocks A, B, and C. In this study, the interaction energies between species A, B, and C are set to be equal. Four different equilibrium morphologies are identified, i.e., the lamellar phase (LAM), the hexagonal lattice phase (HEX), the core-shell hexagonal lattice phase (CSH), and the two interpenetrating tetragonal lattice phase (TET2). For the linear ABCBA block copolymer, the reflection symmetry is observed in the phase diagram except for some special grid points, and most of grid points are occupied by LAM morphology. However, for the H-shaped (AB)(2)C(BA)(2) block copolymer, most of the grid points in the triangle phase diagram are occupied by CSH morphology, which is ascribed to the different chain architectures of the two block copolymers. These results may help in the design of block copolymers with different microstructures.

电离层垂直TEC映射函数的实验观测与统计特性

When used in the determining the total electron content (TEC), which may be the most important ionospheric parameter, the worldwide GPS observation brings a revolutionary change in the ionospheric science. There are three steps in the data processing to retrieve GPS TEC: (1) to estimate slant TEC from the measurements of GPS signals; (2) to map the slant TEC into vertical; and (3) to interpolate the vertical TEC into grid points. In this scientific dissertation we focus our attention on the second step, the mapping theory and method to convert slant TEC into vertical. This is conventionally done by multiplying on the slant TEC a mapping function which is usually determined by certain models of electron density profile. Study of the vertical TEC mapping function is of significance in GPS TEC measurement. This paper first reviews briefly the three steps in GPS TEC mapping process. Then we compare the vertical TEC mapping function which were respectively calculated from the electron density profiles of the ionospheric model and retrieved from the observation of worldwide GPS TEC. We also perform the statistical analysis on the observational mapping functions. The main works and results are as follows: 1. We calculated the vertical TEC mapping functions for both SLM and Chapman models, and discussed the modulation of the ionosphere height to the mapping functions. We use two simple models, single layer model (SLM) and Chapman models, of the ionospheric electron density profiles to calculate the vertical TEC mapping function. In the case of the SLM, we discuss the control of the ionospheric altitude, i.e., the layer height hipp, to the mapping function. We find that the mapping function decreases rapidly as hipp increases. For the Chapman model we study also the control mapping function by both ionospheric altitude indicated by the peak electron density height hmF2, and the scale height, H, which present the thickness of the ionosphere. It is also found that the mapping function decreases rapidly as hmF2 increases. and it also decreases as H increases. 2. Then we estimate the mapping functions from the GPS observations and compare them with those calculated from the electron density models. We first, proposed a new method to estimate the mapping functions from GPS TEC data. This method is then used to retrieve the observational mapping function from both the slant TEC (TECS) provided by International GPS Service (IGS）and vertical TEC provide by JPL Global Ionospheric Maps (GIMs). Then we compare the observational mapping function with those calculated from the electron density models, SLM and Chapman. We find that the values of the observational mapping functions are much smaller than that from the model mapping functions, when the zenith angle is large enough. We attribute this to the effect of the plasmasphere which is above about 1000 km. 3. We statistically analyze the observational mapping functions and reveal their climatological changes. Observational mapping functions during 1999-2007 are used in our statistics. The main results are as follows. (1) The observational mapping functions decrease obviously with the decrement of the solar activity which is represented by the F10.7 index; (2) In annual variations of the observational mapping functions, the semiannual component is found at low-latitudes, and the remarkable seasonal variations at mid- and high-latitudes. (3) The diurnal variation of the observational mapping functions is that they are large in daytime and small at night, they become extremely small in the early morning before sunrise. (4) The observational mapping functions change with latitudes that they are smaller at lower latitudes and larger at higher. All of the above variations of the observational mapping functions are explained by the existence of the plasmasphere, which changes more slowly with time and more rapidly with latitude than the ionosphere does . In summary, our study on the vertical TEC mapping function imply that the ionosphere height has a modulative effect on the mapping function. We first propose the concept of the 'observational mapping functions' , and provide a new method to calculate them. This is important in improving the TEC mapping. It may also possible to retrieving the plasmaspheric information from GPS observations.

Computation of Viscous Incompressible Flow using Pressure Correction Method on Unstructured Chimera Grid

In this paper, a pressure correction algorithm for computing incompressible flows is modified and implemented on unstructured Chimera grid. Schwarz method is used to couple the solutions of different sub-domains. A new interpolation to ensure consistency between primary variables and auxiliary variables is proposed. Other important issues such as global mass conservation and order of accuracy in the interpolations are also discussed. Two numerical simulations are successfully performed. They include one steady case, the lid-driven cavity and one unsteady case, the flow around a circular cylinder. The results demonstrate a very good performance of the proposed scheme on unstructured Chimera grids. It prevents the decoupling of pressure field in the overlapping region and requires only little modification to the existing unstructured Navier–Stokes (NS) solver. The numerical experiments show the reliability and potential of this method in applying to practical problems.

The cellular structure of a two-dimensional H2/O2/Ar detonation wave

In this paper, the cellular structure of a two-dimensional detonation wave in a low pressure H2/O2/Ar mixture calculated with a detailed chemical reaction model, high order scheme and high resolution grids is investigated. The regular cellular structure is produced about 1 ms after introducing perturbations in the reaction zone of a steady one-dimensional detonation wave. It is found from the present resolution study that the discrepancies concerning the structure type arising from the coarser grid employed can be resolved using a sufficiently fine grid size of 0.05 mm and below and shows a double-Mach-like strong-type configuration. During the structure evolution process, the structure configuration does not change much in the periods before and after the triple point collision. Through the triple point collision, three regular collision processes are observed and are followed by a quick change to the double-Mach-like configuration. The simulated structure tracks show that there are three different tracks associated with different triple points or the kink on the transverse wave. Comparisons with previous work and experiments indicate the presence of a strong structure for an ordinary detonation.

A Multimoment Finite-Volume Shallow-Water Model On The Yin-Yang Overset Spherical Grid

A numerical model for shallow-water equations has been built and tested on the Yin-Yang overset spherical grid. A high-order multimoment finite-volume method is used for the spatial discretization in which two kinds of so-called moments of the physical field [i.e., the volume integrated average ( VIA) and the point value (PV)] are treated as the model variables and updated separately in time. In the present model, the PV is computed by the semi-implicit semi-Lagrangian formulation, whereas the VIA is predicted in time via a flux-based finite-volume method and is numerically conserved on each component grid. The concept of including an extra moment (i.e., the volume-integrated value) to enforce the numerical conservativeness provides a general methodology and applies to the existing semi-implicit semi-Lagrangian formulations. Based on both VIA and PV, the high-order interpolation reconstruction can only be done over a single grid cell, which then minimizes the overlapping zone between the Yin and Yang components and effectively reduces the numerical errors introduced in the interpolation required to communicate the data between the two components. The present model completely gets around the singularity and grid convergence in the polar regions of the conventional longitude-latitude grid. Being an issue demanding further investigation, the high-order interpolation across the overlapping region of the Yin-Yang grid in the current model does not rigorously guarantee the numerical conservativeness. Nevertheless, these numerical tests show that the global conservation error in the present model is negligibly small. The model has competitive accuracy and efficiency.

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. (C) 2007 Elsevier Ltd. All rights reserved.

Sediment incipience in turbulence generated in a square tank by a vertically oscillating grid

The failure of hydraulic structures in many estuaries and coastal regions around the world has been attributed to sediment transport and local scour. The sediment incipience in homogenous turbulence generated by oscillating grid is studied in this paper. The turbulent flow is measured by particle tracer velocimetry (PTV) technique. The integral length scale and time scale of turbulence are obtained. The turbulent flow near the wall is measured by local optical magnification. The sediment incipience is described by static theory. The relationship of probability of sediment incipience and the turbulent kinetic energy were obtained experimentally and theoretically. The distribution of the turbulent kinetic energy near the wall is found to obey the power law and the turbulent energy is further identified as the dynamic mechanism of sediment incipience.

Numerical investigation of dynamic stall of an oscillating aerofoil

The flow structure around an NACA 0012 aerofoil oscillating in pitch around the quarter-chord is numerically investigated by solving the two-dimensional compressible N-S equations using a special matrix-splitting scheme. This scheme is of second-order accuracy in time and space and is computationally more efficient than the conventional flux-splitting scheme. A 'rigid' C-grid with 149 x 51 points is used for the computation of unsteady flow. The freestream Mach number varies from 0.2 to 0.6 and the Reynolds number from 5000 to 20,000. The reduced frequency equals 0.25-0.5. The basic flow structure of dynamic stall is described and the Reynolds number effect on dynamic stall is briefly discussed. The influence of the compressibility on dynamic stall is analysed in detail. Numerical results show that there is a significant influence of the compressibility on the formation and convection of the dynamic stall vortex. There is a certain influence of the Reynolds number on the flow structure. The average convection velocity of the dynamic stall vortex is approximately 0.348 times the freestream velocity.

Numerical Analyses of Transonic Fluid/Structure interaction in Aircraft Engineering

Through the coupling between aerodynamic and structural governing equations, a fully implicit multiblock aeroelastic solver was developed for transonic fluid/stricture interaction. The Navier-Stokes fluid equations are solved based on LU-SGS (lower-upper symmetric Gauss-Seidel) Time-marching subiteration scheme and HLLEW (Harten-Lax-van Leer-Einfeldt-Wada) spacing discretization scheme and the same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Transfinite interpolation (TFI) is used for the grid deformation of blocks neighboring the flexible surfaces. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between fluid and structure. The developed code was fort validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. In the subsonic and transonic range, the calculated flutter speeds and frequencies agree well with experimental data, however, in the supersonic range, the present calculation overpredicts the experimental flutter points similar to other computations. Then the flutter character of a complete aircraft configuration is analyzed through the calculation of the change of structural stiffness. Finally, the phenomenon of aileron buzz is simulated for the weakened model of a supersonic transport wing/body model at Mach numbers of 0.98 and l.05. The calculated unsteady flow shows, on the upper surface, the shock wave becomes stronger as the aileron deflects downward, and the flow behaves just contrary on the lower surface of the wing. Corresponding to general theoretical analysis, the flow instability referred to as aileron buzz is induced by a stronger shock alternately moving on the upper and lower surfaces of wing. For the rigid structural model, the flow is stable at all calculated Mach numbers as observed in experiment

Euler Solution Using Adaptive Cartesian Grid With A Gridless Boundary Treatment

A quadtree-based adaptive Cartesian grid generator and flow solver were developed. The grid adaptation based on pressure or density gradient was performed and a gridless method based on the least-square fashion was used to treat the wall surface boundary condition, which is generally difficult to be handled for the common Cartesian grid. First, to validate the technique of grid adaptation, the benchmarks over a forward-facing step and double Mach reflection were computed. Second, the flows over the NACA 0012 airfoil and a two-element airfoil were calculated to validate the developed gridless method. The computational results indicate the developed method is reasonable for complex flows.