Explicit characteristic‐based finite volume element method for level set equation

Accurate modeling of interfacial flows requires a realistic representation of interface topology. To reduce the computational effort from the complexity of the interface topological changes, the level set method is widely used for solving two‐phase flow problems. This paper presents an explicit characteristic‐based finite volume element method for solving the two‐dimensional level set equation. The method is applicable for the case of non‐divergence‐free velocity field. Accuracy and performance of the proposed method are evaluated via test cases with prescribed velocity fields on structured grids. By given a velocity field, the motion of interface in the normal direction and the mean curvature, examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time. Copyright © 2010 John Wiley & Sons, Ltd.     

An adaptive numerical scheme for solving incompressible 2‐phase and free‐surface flows

In this paper, we present a numerical scheme for solving 2‐phase or free‐surface flows. Here, the interface/free surface is modeled using the level‐set formulation, and the underlying mesh is adapted at each iteration of the flow solver. This adaptation allows us to obtain a precise approximation for the interface/free‐surface location. In addition, it enables us to solve the time‐discretized fluid equation only in the fluid domain in the case of free‐surface problems. Fluids here are considered incompressible. Therefore, their motion is described by the incompressible Navier‐Stokes equation, which is temporally discretized using the method of characteristics and is solved at each time iteration by a first‐order Lagrange‐Galerkin method. The level‐set function representing the interface/free surface satisfies an advection equation that is also solved using the method of characteristics. The algorithm is completed by some intermediate steps like the construction of a convenient initial level‐set function (redistancing) as well as the construction of a convenient flow for the level‐set advection equation. Numerical results are presented for both bifluid and free‐surface problems.     

An unstructured finite element model for incompressible two-phase flow based on a monolithic conservative level set method

We present a robust numerical method for solving incompressible, immiscible two-phase flows. The method extends both a monolithic phase conservative level set method with embedded redistancing and a semi-implicit high-order projection scheme for variable-density flows. The level set method can be initialized conveniently via a simple phase indicator field instead of a signed distance function (SDF). To process the indicator field into a SDF, we propose a new partial differential equation-based redistancing method. We also improve the monolithic level set scheme to provide more accuracy and robustness in full two-phase flow simulations. Specifically, we perform an extra step to ensure convergence to the signed distance level set function and simplify other aspects of the original scheme. Lastly, we introduce consistent artificial viscosity to stabilize the momentum equations in the context of the projection scheme. This stabilization is algebraic, has no tunable parameters and is suitable for unstructured meshes and arbitrary refinement levels. The overall methodology includes few numerical tuning parameters; however, for the wide range of problems that we solve, we identify only one parameter that strongly affects performance of the computational model and provide a value that provides accurate results across all the benchmarks presented. This methodology results in a robust, accurate, and efficient two-phase flow model, which is mass- and volume-conserving on unstructured meshes and has low user input requirements, making it attractive for real-world applications.     

Space potential particles to enhance the stability of projection-based particle methods

Particle methods have been seldom verified by a Karman vortex simulation, which is commonly performed as a typical benchmark in computational fluid dynamics. This is mainly due to a difficulty in suppression of occurrence of unphysical voids manifested usually in a strong vortex on account of definition of free surface by the Lagrangian tracking framework with inconsistency in volume conservation. This paper presents a simple and effective scheme as a free-surface boundary condition of projection-based particle methods, namely the MPS (moving particle semi-implicit) and Incompressible SPH (ISPH) methods to handle the free surface with consistency in volume conservation. The new scheme is introduced into the Poisson pressure equation (PPE) with consideration of a potential in void space as space potential particle (SPP), to reproduce physical motions of particles around free surface through a particle–void interaction. The enhancing effect of the newly proposed SPP scheme is shown by simulating a few numerical tests, including a whirling water flow, a two-phase surfacing flow, and a set of Karman vortex simulations.     

基于WENO-THINC/WLIC模型的水气二相流数值模拟

水气二相流与诸多领域的实际工程问题密切相关.对二相流运动进行高精度的数值模拟是计算流体力学研究的难点和热点.针对开敞水域的自由表面流运动问题,将水和空气均视为不可压缩流体,采用五阶加权基本无震荡(weighted essentially non-oscillatory,WENO)格式求解描述流体运动的纳维斯托克斯(Na...     

RKDG有限元方法计算流体与刚体耦合

用Level set方法配合Runge-Kutta discontinuous Galerkin (RKDG)有限元方法求解流体与刚体耦合问题。用RKDG有限元方法求解欧拉方程,通过求解Level set方程对界面进行追踪,并用推广的Ghost fluid方法对流刚界面进行处理。数值实验表明,该方法具有较高的分辨率。由于该方法不需要对移动网格进行处理,因此可以处理任意形状的拓扑问题,并且很容易推广到三维。     

Development of level set method with good area preservation to predict interface in two‐phase flows

A two‐step conservative level set method is proposed in this study to simulate the gas/water two‐phase flow. For the sake of accuracy, the spatial derivative terms in the equations of motion for an incompressible fluid flow are approximated by the coupled compact scheme. For accurately predicting the modified level set function, the dispersion‐relation‐preserving advection scheme is developed to preserve the theoretical dispersion relation for the first‐order derivative terms shown in the pure advection equation cast in conservative form. For the purpose of retaining its long‐time accurate Casimir functionals and Hamiltonian in the transport equation for the level set function, the time derivative term is discretized by the sixth‐order accurate symplectic Runge–Kutta scheme. To resolve contact discontinuity oscillations near interface, nonlinear compression flux term and artificial damping term are properly added to the second‐step equation of the modified level set method. For the verification of the proposed dispersion‐relation‐preserving scheme applied in non‐staggered grids for solving the incompressible flow equations, three benchmark problems have been chosen in this study. The conservative level set method with area‐preserving property proposed for capturing the interface in incompressible fluid flows is also verified by solving the dam‐break, Rayleigh–Taylor instability, bubble rising in water, and droplet falling in water problems. Good agreements with the referenced solutions are demonstrated in all the investigated problems. Copyright © 2010 John Wiley & Sons, Ltd.     

Interface transport scheme of a two‐phase flow by the method of characteristics

In this paper, we study an interface transport scheme of a two‐phase flow of an incompressible viscous immiscible fluid. The problem is discretized by the characteristics method in time and finite elements method in space. The interface is captured by the level set function. Appropriate boundary conditions for the problem of mold filling are investigated, a new natural boundary condition under pressure effect for the transport equation is proposed, and an algorithm for computing the solution is presented. Finally, numerical experiments show and validate the effectiveness of the proposed scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

A Simplified Model and Similarity Solutions for Interfacial Evolution of Two-Phase Flow in Porous Media

For two-phase flows of immiscible displacement processes in porous media, we proposed a simplified model to capture the interfacial fronts, which is given by explicit expressions and satisfies the continuity conditions of pressure and normal velocity across the interface. A new similarity solution for the interfacial evolution in the rectangular coordinate system was derived by postulating a first-order approximation of the velocity distribution in the region that the two-phase fluids co-exist. The interfacial evolution equation can be explicitly expressed as a linear function, where the slope of the interfacial equation is simply related to the mobility ratio of two-phase fluids in porous media. The application of the proposed solutions to predictions of interfacial evolutions in carbon dioxide injected into saline aquifers was illustrated under different mobility ratios and operational parameters. For the purpose of comparison, the numerical solutions obtained by level set method and the similarity solutions based on the Dupuit assumptions were presented. The results show that the proposed solution can give a better approximation of interfacial evolution than the currently available similarity solutions, especially in the situation that the mobility ratio is large. The proposed approximate solutions can provide physical insight into the interfacial phenomenon and be readily used for rapidly screening carbon dioxide storage capacity in subsurface formations and monitoring the migration of carbon dioxide plume.

     

A conservative local interface sharpening scheme for the constrained interpolation profile method

A conservative local interface sharpening scheme has been developed for the constrained interpolation profile method with the conservative semi‐Lagrangian scheme, because the conservative semi‐Lagrangian scheme does not feature a mechanism to control the interface thickness, thus causing an increase of numerical error with the advance of the time step. The proposed sharpening scheme is based on the conservative level set method proposed by Olsson and Kreiss. However, because their method can cause excessive deformation of the free‐surface in certain circumstances, we propose an improvement of the method by developing a local sharpening technique. Several advection tests are presented to assess the correctness of the advection and the improved interface sharpening scheme. This is followed by the validations of dam‐breaking flow and the rising bubble flows. The mass of the fluid is exactly conserved and the computed terminal velocity of the rising bubble agrees well with the experiments compared with other numerical methods such as the volume of fluid method (VOF), the front tracking method, and the level set method. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical prediction of droplet dynamics in turbulent flow,using the level set method

In the present article, the droplet dynamics in turbulent flow is numerically predicted. The modelling is based on an interfacial marker-level set (IMLS) method, coupled with the Reynolds-averaged Navier–Stokes (RANS) equations to predict the dynamics of turbulent two-phase flow. The governing equations for time-dependent, two-dimensional and incompressible two-phase flow are described in both phases and solved separately using a control volume approach on structured cell-centred collocated grids. The topological changes of the interface are predicted by applying the level set approach. The kinematic and dynamic conditions on the interface separating the two phases are satisfied. The numerical method proposed is validated against a well-known computational fluid dynamics problem. Further, the deformation and breakup of a single droplet either suddenly moved in air or exposed to turbulent stream are numerically investigated. In general, the developed numerical method demonstrates remarkable capability in predicting the characteristics of complex turbulent two-phase flows.     

Numerical simulation of unsteady multidimensional free surface motions by level set method

This paper presents a numerical method that couples the incompressible Navier–Stokes equations with the level set method in a curvilinear co‐ordinate system for study of free surface flows. The finite volume method is used to discretize the governing equations on a non‐staggered grid with a four‐step fractional step method. The free surface flow problem is converted into a two‐phase flow system on a fixed grid in which the free surface is implicitly captured by the zero level set. We compare different numerical schemes for advection of the level set function in a generalized curvilinear format, including the third order quadratic upwind interpolation for convective kinematics (QUICK) scheme, and the second and third order essentially non‐oscillatory (ENO) schemes. The level set equations of evolution and reinitialization are validated with benchmark cases, e.g. a stationary circle, a rotating slotted disk and stretching of a circular fluid element. The coupled system is then applied to a travelling solitary wave, and two‐ and three‐dimensional dam breaking problems. Some interesting free surface phenomena are revealed by the computational results, such as, the large free surface vortices, air entrapment and splashing of the water surge front. The computational results are in excellent agreement with theoretical predictions and experimental data, where they are available. Copyright © 2003 John Wiley & Sons, Ltd.     

A combination of parabolized Navier–Stokes equations and level-set method for stratified two-phase internal flow

A novel methodology is proposed for the numerical computation of pressure-driven gravity-stratified flows along channels comprising two immiscible phases. The parabolized Navier–Stokes equations are combined with the level set approach, resulting into a downstream-marching problem in which the solution is computed at each cross-section based on upstream information only. A main difficulty in the implementation of the approach for internal flows is the conservation of the mass flow rates, which is addressed by extending to two-phase flows the method proposed by Patankar and Spalding (1972) and Raythby and Schneider (1979), and by adding an explicit forcing term in the equation for the advection of the level function. The combination of high-order finite differences and sparse storage and algebra used here allows a fully-coupled integration of the parabolized equations, as opposed to the more classical segregated approaches. This enables a very efficient calculation of the complete downstream-developing flow field.     

非规则区域中拉普拉斯方程的有限分析5点格式

建立了非规则区域的有限分析5点格式,增加了有限分析法对不规则边界的适应性。应用所提出的方法对水利工程中常见的有压和无压流动进行了计算,与实验和前人的计算结果相比较,本文的方法都能得到较为满意的结果。本文的计算格式也可以应用到其他非规则区域的计算中。     

AN APPLICATION OF THE CBS SCHEME IN THE FLUID-MEMBRANE INTERACTION

提出了一种不可压缩流体与弹性薄膜耦合问题的特征线分裂有限元解法. 首先, 给出了流场和结构的控制方程. 然后, 对流场、结构以及流固耦合的具体求解过程进行了描述. 其中, 流场求解采用改进特征线分裂方法和双时间步方法相结合的隐式求解方式, 并利用艾特肯加速法对每个时间步的迭代收敛过程进行了加速处理;结构部分的空间离散和时间积分分别采用伽辽金有限元方法和广义方法, 并通过牛顿迭代法对所得非线性代数方程组进行了求解;流场网格的更新采用弹簧近似法;流场、结构两求解模块之间采用松耦合方式.最后, 采用该方法对具有弹性底面的方腔顶盖驱动流问题进行了求解, 验证了算法的准确性和稳定性.此外, 计算结果表明艾特肯加速法可以显著地提高双时间步方法迭代求解过程的收敛速度.     

双相各向异性介质弹性波场有限差分正演模拟

从双相各向异性介质模型出发,以Boit理论为基础,推导了斜方晶系各向异性介质-阶弹性波动方程,引入固、流体密度比和孔隙几何参数,将Biot方程系数简化为测量简单、物理意义明确的物理量,采用交错网格技术建立了各向异性孔隙介质波动方程的高精度差分格式,并首次对这类差分格式的频散特性和稳定性作了详细分析讨论,解决了计算稳定性和边界反射问题,与解析解的对比以及理论模型的数值模拟都表明,该方法不仅大大降低了计算量,提高了正演速度,并且具有良好的稳定性和精确性。     

Highlights of two-phase critical flow: On the links between maximum flow rates,sonic velocities,propagation and transfer phenomena in single and two-phase flows

To improve the understanding of two-phase critical flow phenomena, both single- and two-phase flows are studied in parallel. This can be done only if compatible mathematical models are used for both flows. In particular, since the evolution of the fluid or of the mixture is, in fact, a consequence of the transfers at the wall and at the interface, it is more rational to postulate transfer laws than to assume fluid, or mixture, evolutions.It is shown that the mathematical form of the above transfer laws is of primary importance, and it is proposed to allow for the presence, in the transfer terms, of partial derivatives of dependent variables.The critical flow condition is discussed within the above framework. A necessary critical flow criterion is obtained by equating to zero the determinant of the set of equations describing the steady-state flow. This criterion must be complemented by the study of the compatibility conditions of the set.It is verified that a flow is critical when disturbances, initiated downstream of some “critical” section, cannot propagate upstream of this section. A decrease of the outlet pressure has therefore no effect on the flow parameters upstream of the critical section, and the flow rate is maximum.Examples are given to demonstrate the potentialities of the method. It is shown that appropriate assumptions on the transfer laws enable existing models to be discussed.     

Numerical simulation of free‐surface flow using the level‐set method with global mass correction

A new numerical method that couples the incompressible Navier–Stokes equations with the global mass correction level‐set method for simulating fluid problems with free surfaces and interfaces is presented in this paper. The finite volume method is used to discretize Navier–Stokes equations with the two‐step projection method on a staggered Cartesian grid. The free‐surface flow problem is solved on a fixed grid in which the free surface is captured by the zero level set. Mass conservation is improved significantly by applying a global mass correction scheme, in a novel combination with third‐order essentially non‐oscillatory schemes and a five stage Runge–Kutta method, to accomplish advection and re‐distancing of the level‐set function. The coupled solver is applied to simulate interface change and flow field in four benchmark test cases: (1) shear flow; (2) dam break; (3) travelling and reflection of solitary wave and (4) solitary wave over a submerged object. The computational results are in excellent agreement with theoretical predictions, experimental data and previous numerical simulations using a RANS‐VOF method. The simulations reveal some interesting free‐surface phenomena such as the free‐surface vortices, air entrapment and wave deformation over a submerged object. Copyright © 2009 John Wiley & Sons, Ltd.     

基于气液相界面捕捉的统一气体动理学格式

气液相界面运动的研究无论是在科学还是工程领域都是非常重要的. 其中, 非平衡流动的计算尤其受到关注. 基于此, 我们构造了捕捉气液相界面的统一气体动理学格式. 由于统一气体动理学格式将自由输运和粒子碰撞耦合起来更新宏观物理量和微观分布函数, 故而可以求解非平衡流动. 具体思路是, 通过将范德瓦尔斯状态方程所表达的非理想气体效应引入统一气体动理学格式之中来捕捉气液相界面, 两相的分离与共存通过范德瓦尔斯状态方程描述. 由于流体在椭圆区域是不稳定的, 因此气液相界面可以通过蒸发和凝结过程自动捕捉. 如此, 一个锋锐的相界面便可以通过数值耗散和相变而得到. 利用该方法得到麦克斯韦等面积律(Maxwell construction)对应的数值解, 并与其相应的理论解相比较, 二者符合良好. 而后, 通过对范德瓦尔斯状态方程所描述的液滴表面张力进行数值计算, 验证了Laplace定理. 此外, 通过模拟两个液滴的碰撞融合过程, 进一步证明了该格式的有效性. 但是, 由于范德瓦尔斯状态方程的特性, 其所构造的格式仅适用于液/气两相密度比小于5的情况.      

DCD格式在破碎发射药床两相流内弹道计算中的应用

利用DCD(dispersion controlled dissipative scheme)格式,提出了一种研究发射装药发射安全性问题的两相流内弹道计算方法。将内弹道气固两相流动力学方程组中与压力有关的项进行变形,实现了用同一种格式对气相和固相统一处理,而无须分别对待,采用DCD格式无须数值粘性和人工滤波,提高了计算精度。实例计算了某榴弹内弹道两相流动力学,计算结果与实验结果吻合较好。把破碎发射药床视为混合装药结构,用DCD格式计算了发射药床不同破碎程度对发射安全性的影响。计算结果表现出了通常计算方法难以反映的破碎发射药床内弹道压力极为剧烈的变化过程和极高的危险膛压。 更多还原