NND schemes and numerical simulation of axial symmetric free jet flows

Through a study on one-dimensional Navier-Stokes equations, it was found that the spurious oscillations occuring near shock waves with finite difference equations are related to the dispersion term in the corresponding modified differential equations. If the sign of dispersion coefficient is properly adjusted so that the sign changes across shock waves, the undesirable oscillations can be totally suppressed. Based on this finding, the non-oscillatory, containing no free parameters and dissipative shheme (NND scheme) is developed. This scheme is one of “TVD”. The axisymmetric free jet flows are simulated numerically using this scheme. The results obtained by the present scheme are compared with the experimental picture. It is shown that the agreement is very good, and that this scheme has advantages of high resolution for capturing shocks and contact discontinuities. Project supported by National Science Foundation of China     

Vectorized Directional Sweep Based Parallelization Method for Factored Alternating Direction Implicit (ADI) Schemes

A new parallelization method is proposed for factored alternating direction implicit (ADI) schemes based on the vectorized global domain directional sweep. This approach, when combined with multi-partitioning domain decomposition, significantly reduces the frequency of necessary communication calls and minimizes processor idling during the sweeping processes. The present parallelization approach is applied to a number of vectorized two-dimensional compressible Navier-Stokes solvers. The codes vary in complexity from laminar to algebraic turbulence closure model and finally the strongly coupled Navier-Stokes and K-e equations. Implementation is conducted using PVM (Parallel Virtual Machine) message passing tool on the Cray T3D massively parallel processing (MPP) machine. The implemented parallel codes are assessed in terms of accuracy and parallel performance.     

Implicit FEM‐FCT algorithms and discrete Newton methods for transient convection problems

A new generalization of the flux‐corrected transport (FCT) methodology to implicit finite element discretizations is proposed. The underlying high‐order scheme is supposed to be unconditionally stable and produce time‐accurate solutions to evolutionary convection problems. Its nonoscillatory low‐order counterpart is constructed by means of mass lumping followed by elimination of negative off‐diagonal entries from the discrete transport operator. The raw antidiffusive fluxes, which represent the difference between the high‐ and low‐order schemes, are updated and limited within an outer fixed‐point iteration. The upper bound for the magnitude of each antidiffusive flux is evaluated using a single sweep of the multidimensional FCT limiter at the first outer iteration. This semi‐implicit limiting strategy makes it possible to enforce the positivity constraint in a very robust and efficient manner. Moreover, the computation of an intermediate low‐order solution can be avoided. The nonlinear algebraic systems are solved either by a standard defect correction scheme or by means of a discrete Newton approach, whereby the approximate Jacobian matrix is assembled edge by edge. Numerical examples are presented for two‐dimensional benchmark problems discretized by the standard Galerkin finite element method combined with the Crank–Nicolson time stepping. Copyright © 2007 John Wiley & Sons, Ltd.     

A regularised one-dimensional drop formation and coalescence model using a total variation diminishing (TVD) scheme on a single Eulerian grid

The breakup of an axisymmetric viscous jet is considered in the lubrication approximation. The discretised equations are solved on a fixed equidistant one-dimensional Eulerian grid. The governing equations are implemented in a conservative second order accurate total variation diminishing (TVD) scheme, preventing the numerical diffusivity. Singularities that occur at pinchoff and coalescence are regularised by a small modification on the surface tension. The modification is of the order of the spatial step Δx. This regularisation ensures that the solution of the presented numerical model converges to the exact solution of the breakup of a jet in the lubrication approximation. The results of the presented numerical model agree quantitatively with the analytical solution of the Rayleigh–Plateau instability, and with experimental results on the final stage of the Rayleigh–Plateau instability.     

Implicit LES of free and wall‐bounded turbulent flows based on the discontinuous Galerkin/symmetric interior penalty method

This paper presents the second validation step of a compressible discontinuous Galerkin solver with symmetric interior penalty (DGM/SIP) for the direct numerical simulation (DNS) and the large eddy simulation (LES) of complex flows. The method has already been successfully validated for DNS of an academic flow and has been applied to flows around complex geometries (e.g. airfoils and turbomachinery blades). During these studies, the advantages of the dissipation properties of the method have been highlighted, showing a natural tendency to dissipate only the under‐resolved scales (i.e the smallest scales present on the mesh), leaving the larger scales unaffected. This phenomenon is further enhanced as the polynomial order is increased. Indeed, the order increases the dissipation at the largest wave numbers, while its range of impact is reduced. These properties are spectrally compatible with a subgrid‐scale model, and hence DGM may be well suited to be used for an implicit LES (ILES) approach. A validation of this DGM/ILES approach is here investigated on canonical flows, allowing to study the impact of the discretisation on the turbulence for under‐resolved computations. The first test case is the LES of decaying homogeneous isotropic turbulence (HIT) at very high Reynolds number. This benchmark allows to assess the spectral behaviour of the method for implicit LES. The results are in agreement with theory and are even slightly more accurate than other numerical results from literature, obtained using a pseudo‐spectral (PS) method with a state‐of‐the‐art subgrid‐scale model. The second benchmark is the LES of the channel flow. Three Reynolds numbers are considered: Re_τ=395, 590 and 950. The results are compared with DNS of Moser et al. and Hoyas et al., also using PS methods. Both averaged velocity and fluctuations are globally in good agreement with the reference, showing the ability of the method to predict equilibrium wall‐bounded flow turbulence. To show that the method is able to perform accurate DNS, a DNS of HIT at Re_λ=64 and a DNS of the channel flow at Re_τ=180 are also performed. The effects of the grid refinement are investigated on the channel flow at Re_τ=395, highlighting the improvement of the results when refining the mesh in the spanwise direction. Finally, the modification of the ILES parameters, that is the Riemann solver and of the SIP coefficient, is studied on both cases, showing a significant influence on the choice of the Riemann solver. Copyright © 2015 John Wiley & Sons, Ltd.     

An arbitrary Lagrangian Eulerian (ALE) formulation for free surface flows using the characteristic‐based split (CBS) scheme

An arbitrary Lagrangian Eulerian (ALE) method for non‐breaking free surface flow problems is presented. The characteristic‐based split (CBS) scheme has been employed to solve the ALE equations. A simple mesh smoothing procedure based on coordinate averaging (Laplacian smoothing) is employed in the calculations. The mesh velocity is calculated at each time step and incorporated as part of the scheme. Results presented show an excellent agreement with the available experimental data. Copyright © 2005 John Wiley & Sons, Ltd.     

A divergence-free semi-implicit finite volume scheme for ideal,viscous, and resistive magnetohydrodynamics

In this paper, we present a novel pressure-based semi-implicit finite volume solver for the equations of compressible ideal, viscous, and resistive magnetohydrodynamics (MHD). The new method is conservative for mass, momentum, and total energy, and in multiple space dimensions, it is constructed in such a way as to respect the divergence-free condition of the magnetic field exactly, also in the presence of resistive effects. This is possible via the use of multidimensional Riemann solvers on an appropriately staggered grid for the time evolution of the magnetic field and a double curl formulation of the resistive terms. The new semi-implicit method for the MHD equations proposed here discretizes the nonlinear convective terms as well as the time evolution of the magnetic field explicitly, whereas all terms related to the pressure in the momentum equation and the total energy equation are discretized implicitly, making again use of a properly staggered grid for pressure and velocity. Inserting the discrete momentum equation into the discrete energy equation then yields a mildly nonlinear symmetric and positive definite algebraic system for the pressure as the only unknown, which can be efficiently solved with the (nested) Newton method of Casulli et al. The pressure system becomes linear when the specific internal energy is a linear function of the pressure. The time step of the scheme is restricted by a CFL condition based only on the fluid velocity and the Alfvén wave speed and is not based on the speed of the magnetosonic waves. Being a semi-implicit pressure-based scheme, our new method is therefore particularly well suited for low Mach number flows and for the incompressible limit of the MHD equations, for which it is well known that explicit density-based Godunov-type finite volume solvers become increasingly inefficient and inaccurate because of the more and more stringent CFL condition and the wrong scaling of the numerical viscosity in the incompressible limit. We show a relevant MHD test problem in the low Mach number regime where the new semi-implicit algorithm is a factor of 50 faster than a traditional explicit finite volume method, which is a very significant gain in terms of computational efficiency. However, our numerical results confirm that our new method performs well also for classical MHD test cases with strong shocks. In this sense, our new scheme is a true all Mach number flow solver.     

Fluid interface detection technique based on neighborhood particles centroid deviation (NPCD) for particle methods

Particle‐based CFD methods are powerful approaches to investigate free surface, multiphase flows, and fluid structure interaction problems because of their ability of tracking moving fluid interface even with huge deformations or fragmentation and merging. However, many fluid interface particle detection techniques are simple to implement but with low accuracy or provide relatively good detection results at complicated implementation cost or higher computational time. In case of incompressible flow simulation methods solving the Poisson equation of pressure, such as the moving particle semi‐implicit method, boundary particles detection techniques' accuracy affects precision and stability of pressure computation and interaction between fluid phases. In the present work, a new fluid interface particle detection technique is proposed to improve the accuracy of the boundary particles detection and keep the implementation easy. Denominated as the neighborhood particles centroid deviation technique, it is a two‐criteria technique based on the particle number density and the neighborhood particles weighted geometric center deviation. Compared with other techniques, the proposed neighborhood particles centroid deviation technique shows the best results by eliminating false interface particles inside the fluid domain and keeping the interface particles layer thin and regular. As a result, relatively stable pressure time histories and more consistent pressure and velocity fields are achieved. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.     

PETN、RDX和HMX炸药爆轰参数的数值模拟

用吉布斯自由能最小原理,通过解化学平衡方程组,求解PETN、RDX和HMX炸药爆轰产物系统的平衡组分,计算结果与用BKW和LJD方法计算的结果相近。用自编的程序从碳的石墨相、金刚石相、类石墨液相和类金刚石液相4种相态中确定出炸药爆轰产物中游离碳更可能存在的相态,并用此相态计算碳的吉布斯自由能。以WCA状态方程作为爆轰气相产物的物态方程,对PETN、RDX和HMX炸药爆轰参数作了预言,爆轰CJ点的爆速、爆压和爆温的计算结果与实验值吻合得很好。     

混合不确定度量化方法及其在计算流体动力学迎风格式中的应用

针对流体力学数值求解间断问题时,初始状态含有偶然和认知混合型的不确定性,将认知不确定度作为外层,偶然不确定度作为内层,分别使用非嵌入多项式混沌方法(non-intrusive polynomial chaos,NIPC)和概率盒(P-box)理论处理偶然不确定度和认知不确定度,发展了流体力学数值求解过程中,初始状态含有混合不确定度传播量化的一种方法。以迎风格式和黎曼解法器求解Sod问题为例,评估了左状态密度(偶然不确定度)和理想气体多方指数(认知不确定度)对模型输出结果的影响,有效验证了该方法的可行性。     

Simple efficient algorithm (SEA) for shallow flows with shock wave on dry and irregular beds

An explicit Godunov‐type solution algorithm called SEA (simple efficient algorithm) has been introduced for the shallow water equations. The algorithm is based on finite volume conservative discretisation method. It can deal with wet/dry and irregular beds. Second‐order accuracy, in both time and space, is achieved using prediction and correction steps. A very simple and efficient flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purposes. In order to make sure about the balance between the flux gradient and the bed slope, treatment of the source term has been done using a new procedure inspired mainly by the physical rather than mathematical consideration. SEA has been applied to one‐dimensional problems, although it can equally be applied to multi‐dimensional problems. In order to assess the capability of proposed algorithm in dealing with practical applications, several test cases have been examined. Copyright © 2007 John Wiley & Sons, Ltd.     

Identification of stiffness, dissipation and input parameters of randomly excited non-linear systems: Capability of restricted potential models (RPM)

A dynamic identification technique in the time domain for time invariant systems under random external forces is presented. This technique is based on the use of the class of restricted potential models (RPM), which are characterized by a non-linear stiffness and a special form of damping, that is a product of the input power spectral density (PSD) matrix and the velocity gradient of a non-linear function of the total mechanical energy. By applying stochastic differential calculus and by specific analytical manipulations, some algebraic equations, depending on the response statistics and on the mechanic parameters that characterize RPM, are obtained. These equations can be used for the dynamic identification of the above mechanic parameters once the response statistics of the system to be identified are evaluated. The proposed technique allows one to identify single-degree-of-freedom or multi-degrees-of-freedom systems in the case of unmeasurable input. Further, the probabilistic characteristics of the external forces can be completely estimated in terms of PSD matrix.     

Lorentz group SOo(5, 1) for perfect elastoplasticity with large deformation and a consistency numerical scheme

How to effectively deal with non-linearity and accurately fulfill the consistency condition is essential for modeling and computing in plasticity. Utilizing the concepts of two phases and homogeneous coordinates, we obtain a linear representation of a constitutive model of perfect elastoplasticity with large deformation, and, furthermore, a linear irreducible representation, which contains a five-order spin tensor. The underlying vector space is found to be the projective realization of a composite space resulting from a surgery on Minkowski spacetime ⁵⁺¹. The irreducible representation in the vector space admits of the projective proper orthochronous Lorentz group PSO_o(5, 1) in the on (or elastoplastic) phase and the special Euclidean group SE(5) in the off (or elastic) phase. The input path dictates symmetry switching between the two groups. Based on such symmetry a numerical scheme is devised which preserves the consistency condition for every time step. The consistency scheme is shown to be stabler, more accurate, and more efficient than the current numerical schemes developed directly based upon the model itself, because the new scheme preserves the internal symmetry SO_o(5, 1) of the model in the on phase so as to locate the stress point automatically on the yield surface at each time step without iterations at all.     

PANSYSTEMS PHILOSOPHY,PANSYSTEMS MATHEMATICS(PPPM)AND APPLICATIONS TO APTMS:AFFAIROLOGY,PHYSICS,TECHNOLOGY,MEDICIEN AND STRATEGICS(Ⅱ)

A new type of philosophy and mathematics from the pansystems view is introduced here, including the 7 philosophy theories (7PT) and related mathematizing researches. Many second/third philosophies are developed within pansystems framework and related applications to APTMS.     

PANSYSTEMS PHILOSOPHY,PANSYSTEMS MATHEMATICS(PPPM) AND APPLICATIONS TO APTMS:AFFAIROLOGY,PHYSICS,TECHNOLOGY,MEDICINE AND STRATEGICS(Ⅰ)

A new type of philosophy and mathematics from the pansystems view isintroduced here,including the7 philosophic theories(7PT)and related mathematicresearches.Many second/third philosophies are developed within pansystems framework and related applications to APTMS.     

Finite element analysis of transient fluid flow with free surface using VOF (volume-of-fluid) method and adaptive grid

The VOF method is adopted for the finite element analysis of transient fluid flow with a free surface. In particular, an adaptation technique for generating an adaptive grid is incorporated to capture a higher resolution of the free surface configuration. An adaptive grid is created through the refinement and mergence of elements. In this domain the elements in the surface region are made finer than those in the remaining regions for more efficient computation. Also, three techniques based on the VOF method are newly developed to increase the accuracy of the analysis, namely the filling pattern, advection treatment and free surface smoothing techniques. Using the proposed numerical techniques, radial flow with a point source and the collapse of a dam are analysed. The numerical results agree well with the theoretical solutions as well as with the experimental results. Through comparisons with the numerical results of several cases using different grids, the efficiency of the proposed technique is verified. © 1998 by John Wiley & Sons, Ltd.     

Psychophysiology,Cortical Arousal and Dynamical Complexity (DCX)

Recent studies in brain dynamics have utilized a dependent variable calculated from the electroencephalogram (EEG) known as dimensional complexity (DC _x ), where variables such as scalp locus, cognitive task difficulty, or cortical arousal, are manipulated to test quantitative hypotheses regarding brain-state changes. The technique has been criticised on technical and theoretical grounds, yet its application to experimental time series in many domains has succeeded in yielding information about cortical activity which either complements or surpasses spectral band analysis, and other linear-stochastic techniques. The aim of this paper is to provide a pedagogical review of the contribution of dimensional complexity studies in understanding the psychophysiology of cortical arousal by outlining strategies for the successful estimation of DC _x as an empirical measure.     

Flow evolution of a turbulent submerged two-dimensional rectangular free jet of air. Average Particle Image Velocimetry (PIV) visualizations and measurements

The paper presents average flow visualizations and measurements, obtained with the Particle Image Velocimetry (PIV) technique, of a submerged rectangular free jet of air in the range of Reynolds numbers from Re = 35,300 to Re = 2200, where the Reynolds number is defined according to the hydraulic diameter of a rectangular slot of height H. According to the literature, just after the exit of the jet there is a zone of flow, called zone of flow establishment, containing the region of mixing fluid, at the border with the stagnant fluid, and the potential core, where velocity on the centerline maintains a value almost equal to the exit one. After this zone is present the zone of established flow or fully developed region. The goal of the paper is to show, with average PIV visualizations and measurements, that, before the zone of flow establishment is present a region of flow, never mentioned by the literature and called undisturbed region of flow, with a length, L_U, which decreases with the increase of the Reynolds number. The main characteristics of the undisturbed region is the fact that the velocity profile maintains almost equal to the exit one, and can also be identified by a constant height of the average PIV visualizations, with length, L_CH, or by a constant turbulence on the centerline, with length L_CT. The average PIV velocity and turbulence measurements are compared to those performed with the Hot Film Anemometry (HFA) technique. The average PIV visualizations show that the region of constant height has a length L_CH which increases from L_CH = H at Re = 35,300 to L_CH = 4–5H at Re = 2200. The PIV measurements on the centerline of the jet show that turbulence remains constant at the level of the exit for a length, L_CT, which increases from L_CT = H at Re = 35,300 to L_CT = 4–5H at Re = 2200. The PIV measurements show that velocity remains constant at the exit level for a length, L_U, which increases from L_U = H at Re = 35,300 to L_U = 6H at Re = 2200 and is called undisturbed region of flow. In turbulent flow the length L_U is almost equal to the lengths of the regions of constant height, L_CH, and constant turbulence, L_CT. In laminar flow, Re = 2200, the length of the undisturbed region of flow, L_U, is greater than the lengths of the regions of constant height and turbulence, L_CT = L_CH = 4–5H. The average PIV and HFA velocity measurements confirm that the length of potential core, L_P, increases from L_P = 4–5H at Re = 35,300 to L_P = 7–8H at Re = 2200, and are compared to the previous experimental and theoretical results of the literature in the zone of mixing fluid and in the fully developed region with a good agreement.