Numerical simulation of steady compressible flows using a zonal formulation. Part II: viscous flows

Viscous flow simulations are usually based on the Navier–Stokes equations representing the balance of mass, momentum, and energy. For many high Reynolds number flows, the viscous effects are only limited to small regions in the neighborhood of solid surfaces and in the wakes. We present here a zonal formulation with a reduced system of equations in the outer inviscid flow region. As in part I of this work, the velocity components are calculated from a generalized form of the Cauchy–Riemann equations with non-vanishing vorticity only in the inner region, where the governing equations including the viscous terms are solved. The viscous effects are transferred to the Cauchy–Riemann equations through a forcing function (vorticity), and the process is repeated until convergence. Preliminary results are presented and compared to standard Navier–Stokes calculations for two and three dimensional flow problems.     

Numerical simulation of viscous flow over non-smooth surfaces

The incompressible viscous flow over several non-smooth surfaces is simulated numerically by using the lattice Boltzmann method. A numerical strategy for dealing with a curved boundary with second-order accuracy for velocity field is presented. The drag evaluation is performed by the momentum-exchange method. The streamline contours are obtained over surfaces with different shapes, including circular concave, circular convex, triangular concave, triangular convex, regular sinusoidal wavy and irregular sinusoidal wavy, are obtained. The flow patterns are discussed in detail. The velocity profiles over different kinds of non-smooth surfaces are investigated. The numerical results show that the lattice Boltzmann method is reliable, accurate, easy to implement, and can provide valuable help for some engineering practices.     

Large-eddy simulation of multi-component compressible turbulent flows using high resolution methods

The ability of a finite volume Godunov and a semi-Lagrangian large-eddy simulation (LES) method to predict shock induced turbulent mixing has been examined through simulations of the half-height experiment [Holder and Barton. In: Proceedings of the international workshop on the physics of compressible turbulent mixing, 2004]. Very good agreement is gained in qualitative comparisons with experimental results for combined Richtmyer-Meshkov and Kelvin-Helmholtz instabilities in compressible turbulent multi-component flows. It is shown that both numerical methods can capture the size, location and temporal growth of the main flow features. In comparing the methods, there is variability in the amount of resolved turbulent kinetic energy. The semi-Lagrangian method has constant dissipation at low Mach number, thus allowing the initially small perturbations to develop into Kelvin-Helmholtz instabilities. These are suppressed at the low Mach stage in the Godunov method. However, there is an excellent agreement in the final amount of fluid mixing when comparing both numerical methods at different grid resolutions.     

Numerical analysis of a 2-D viscous sintering problem with non-smooth boundaries

By viscous sintering it is meant the process of bringing a granular compact to a temperature at which the viscosity of the material becomes low enough for surface tension to cause the particles to deform and coalesce, whereby the material transport can be modelled as a viscous incompressible newtonian volume flow. Here a two-dimensional model is considered. A Boundary Element Method is applied to solve the governing Stokes creeping flow equations for an arbitrarily initial shaped fluid region. In this paper we show that the viscous sintering problem is well-conditioned from an evolutionary point of view. However as boundary value problem at each time step, the problem is ill-conditioned when the contact surfaces of the particles are small, i.e. in the early stages of the coalescence. This is because the curvature of the boundary at those places can be very large. This ill-conditioning is illustrated by an example: the coalescence of two equal circles. This example demonstrates the main evolutionary features of the sintering phenomenon very well. A numerical consequence of this ill-conditioning is that special care has to be taken for distributing and redistributing the nodal points at these boundary parts. Therefore an algorithm for this node redistribution is outlined. Several numerical examples sustain the analysis.     

高精度自适应hp-FEM在电法测井数值模拟中的应用*

介绍了电法测井数值模拟的建模方法并提出一种新型的自适应高阶有限元方法(hp-FEM)用于求解各向异性地层中的电场问题。电场数值模型在相同的误差精度下,从计算时间和计算自由度的角度对h-FEM、p-FEM和hp-FEM进行了计算比较。数值结果表明,在各向同性和各向异性模式下,该自适应hp-FEM的性能(指数速率收敛)明显优于h-FEM和p-FEM。探讨了算法的收敛性,提出的hp-FEM可以改进现有的正演模拟方法,提高分析的正确性和工作效率,对于减小研究周期有重要的应用价值。     

Numerical analysis of homogeneous condensation in rarefaction wave in a shock tube by the space-time CESE method

A detailed numerical investigation has been carried out for the homogeneous condensation of water vapor in a non-stationary rarefaction wave generated in a shock tube. The space-time CESE method has been adopted to simulate the mutual interaction of condensation with the rarefaction wave for an extremely long time. It is found that the homogeneous condensation in the rarefaction wave has a significant influence on the flow due to the latent heat release and the continuous change of cooling rate. Three stages can be defined in this process: the initial stage which contains the onset of the condensation and the formation of the condensation shock waves in both downstream and upstream directions, the oscillating stage which is characterized as the repeat of quench and onset of condensation in the expansion fan approximately in a logarithm time manner, and the asymptotic stage which the oscillating waves are damping out with time and no apparent condensation shock wave is formed.     

Numerical simulations of viscous rotating flows using a new pressure-based method

This paper describes the development and application of a parabolic finite-volume procedure for the computation of viscous rotating flows having complex geometries. A parabolic numerical scheme has been developed to include the influence of the Coriolis force on pressure corrections. Two-equation turbulence models were employed to account for the effect of turbulence on the flows. Numerical tests for 2-D flows have been conducted, and the results show that computation with the new pressure-based method gives reasonably good agreement with the experiments.     

高压动态校准的水激波管

提出了预压水激波管动态校准方法。通过施加预压给水激波管产生的脉冲信号,在水激波管所产生的频率丰富的脉冲信号基础上叠加不同的静态预压,利用准δ脉冲校准原理,对高压测试系统进行动态校准。对3种高压传感器的测试数据分别建立了数学模型,进行了频谱分析,得出了3种高压传感器的频率响应特性。     

Numerical simulation of radially converging shock waves in a bubble cavity

This paper presents a numerical technique investigating the final stage of focusing a radially converging nonspherical shock wave in the neighborhood of center of the axially symmetric cavitation bubble subjected to strong compression. Hydrodynamic model used includes liquid compressibility, heat conductivity of vapor and liquid, as well as evaporation and condensation on the interphase surface; the realistic wide-range equations of state are used. The calculation is performed on moving grids with explicit accentuation of the bubble surface. This technique is based on the TVD modification of the Godunov second order accuracy scheme in space and time. Its efficiency is due to an allowance for the special features of the problem in the final stage of focusing of nonspherical shock wave in the central part of the bubble. After the value of deformation of the shock exceeds the threshold (i.e., when the shock wave becomes largely nonspherical) in the central field of the bubble the curvilinear radially diverging grid is changed by the rectilinear oblique-angled grid close to Cartesian. At the same moment, the spherical immovable system of the reference frame is changed to a cylindrical system. The recalculation of the cell parameters from grid to grid is made by the method of conservative interpolation. The efficiency of the proposed approach is shown by the test problem’s calculation results and an illustrative example.     

Numerical simulation of shock diffraction on unstructured meshes

Shock diffraction over geometric obstacles is performed on two-dimensional unstructured triangular meshes using the AUSM+ flux-vector splitting scheme. Numerical simulations of shock diffraction using structured grids are reviewed in the literature, as are experimental results corresponding to the flow conditions studied. Present unstructured grid results for popular and challenging two-dimensional shock diffraction problems are presented and compared to experimental data and photographs. Benchmark and example test cases were chosen to cover a wide variety of Mach numbers for weak and strong shock waves, and for square and circular geometries. Both single and multiple obstacles are considered, as are obstacles located in the free field and confined in a channel.     

Numerical simulation of high Rayleigh number convection

A direct numerical simulation of thermal convection between horizontal plane boundaries has been performed, at a Rayleigh number Ra=9800Ra _c , where Ra _c is the critical Rayleigh number for the onset of convection. The flow is found to be fully turbulent, and analysis of the probability distributions for temperature fluctuations indicates that this is within the hard turbulence regime, as defined by the Chicago group. Good agreement is shown to exist between their experiments and the present simulation.     

一维理想磁控等离子体激波管流动仿真

推导了磁场作用下等离子体流动的控制方程,采用加入人工粘性项的MacCormack二阶格式对方程进行了离散.计算了在不同磁场作用下,一维理想磁控等离子体在激波管内的流动情况.计算结果表明,在施加磁场作用后,激波管内的波系结构发生了明显的改变,磁场强度在激波的影响下发生了重新分布.     

Numerical simulation of the failure of composite materials by using the grid-characteristic method

This is an overview of the existing criteria of the failure of the composite materials and of the results of the application of some of them to simulate a low-speed hit on the composition material for the three-dimensional statement of the problem. Simulation is made by means of the grid-characteristic method. Reasons are given for the selection of specific criteria and they are compared with each other.     

Parallel-multigrid computation of unsteady incompressible viscous flows using a matrix-free implicit method and high-resolution characteristics-based scheme

A three-dimensional parallel unstructured non-nested multigrid solver for solutions of unsteady incompressible viscous flow is developed and validated. The finite-volume Navier–Stokes solver is based on the artificial compressibility approach with a high-resolution method of characteristics-based scheme for handling convection terms. The unsteady flow is calculated with a matrix-free implicit dual time stepping scheme. The parallelization of the multigrid solver is achieved by multigrid domain decomposition approach (MG-DD), using single program multiple data (SPMD) and multiple instruction multiple data (MIMD) programming paradigm. There are two parallelization strategies proposed in this work, first strategy is a one-level parallelization strategy using geometric domain decomposition technique alone, second strategy is a two-level parallelization strategy that consists of a hybrid of both geometric domain decomposition and data decomposition techniques. Message-passing interface (MPI) and OpenMP standard are used to communicate data between processors and decompose loop iterations arrays, respectively. The parallel-multigrid code is used to simulate both steady and unsteady incompressible viscous flows over a circular cylinder and a lid-driven cavity flow. A maximum speedup of 22.5 could be achieved on 32 processors, for instance, the lid-driven cavity flow of Re = 1000. The results obtained agree well with numerical solutions obtained by other researchers as well as experimental measurements. A detailed study of the time step size and number of pseudo-sub-iterations per time step required for simulating unsteady flow are presented in this paper.     

Numerical simulation of the MHD equations by a kinetic-type method

We introduce a flux-splitting formula for the approximation of the ideal MHD equations in conservative form. The Faraday equation is considered as the average of an abstract kinetic equation, giving a flux-splitting formula. For the other part of the equations, we generalize formally the classical half-Maxwellian flux-splitting of the Euler equations. Numerical results on MHD shock tube problems are displayed.     

Inertia based filtering of high resolution images using a GPU cluster

The scheme of inertia based anisotropic diffusion is a very powerful noise reducing and structure preserving image processing operator. This paper presents an implementation of this time consuming filter process on a cluster of Nvidia Tesla high performance computing processors, which can be applied to very large amounts of data in only a few minutes. Applying the inertia based diffusion filter to high resolution image stacks of neuron cells provides fully automatic geometric reconstructions of these images on a scale of <1μm. Such a high throughput and automatic image processing tool has great impact on various research areas, in particular the fast growing field of computational neuroscience, where one encounters increasing amount of microscopy data that needs to be processed.     

Multizone decomposition for simulation of time-dependent problems using the multiquadric scheme

This paper discusses the application of the multizone decomposition technique with multiquadric scheme for the numerical solutions of a time-dependent problem. The construction of the multizone algorithm is based on a domain decomposition technique to subdivide the global region into a number of finite subdomains. The reduction of ill-conditioning and the improvement of the computational efficiency can be achieved with a smaller resulting matrix on each subdomain. The proposed scheme is applied to a hypothetical linear two-dimensional hydrodynamic model as well as a real-life nonlinear two-dimensional hydrodynamic model in the Tolo Harbour of Hong Kong to simulate the water flow circulation patterns. To illustrate the computational efficiency and accuracy of the technique, the numerical results are compared with those solutions obtained from the same problem using a single domain multiquadric scheme. The computational efficiency of the multizone technique is improved substantially with faster convergence without significant degradation in accuracy.     

基于LS-DYNA的爆炸流场荷载的数值模拟研究

随着微型计算机计算能力的提高以及数值方法和商业软件的推动,基于有限元方法的数值模拟在科学和工程研究中得到广泛应用,一些复杂的物理问题可以容易地进行数值模拟研究。介绍了在微型机上基于LS-DYNA软件分别使用普通ALE方法和ALE映射方法模拟限制空间内爆炸波流场荷载的方法,并对结果进行了比较分析。研究表明,爆炸波传播及荷载可以在微型机上进行有效模拟;ALE网格映射方法对于普通ALE方法是一种改进,可以降低结果对网格的敏感性。     

Numerical simulation of AC electrothermal micropump using a fully coupled model

The classic model by Ramos et al. for numerical simulation of alternating current electrothermal (ACET) flow is a decoupled model based on an electrothermal force derived using a linear perturbation method, which is not appropriate for the applications, where Joule heating is large and the effect of temperature rise on material properties cannot be neglected. An electrically–thermally–hydrodynamically coupled (fully coupled) ACET flow model considering variable electrical and thermophysical properties of the fluids with temperature was developed. The model solves AC electrical equations and is based on a more general electrostatic force expression. Comparisons with the classic decoupled model were conducted through the numerical simulations of an ACET micropump with asymmetric electrode pairs. It was found that when temperature rise is small the fully coupled model has the same results with the classic model, and the difference between the two models becomes larger and larger with the increasing temperature. The classic decoupled model underestimates the maximum temperature rise and pumping velocity, since it cannot consider the increase in electrical conductivity and the decrease in viscosity with temperature. The critical frequencies where the lowest velocity occurs or pumping direction reverses are shifted to higher frequencies with the increasing voltage according to the fully coupled model, while are kept unchanged according to the classic model.