Implementation of the moving particle semi-implicit method on GPU

The Moving Particle Semi-implicit (MPS) method performs well in simulating violent free surface flow and hence becomes popular in the area of fluid flow simulation. However, the implementations of searching neighbouring particles and solving the large sparse matrix equations (Poisson-type equation) are very time-consuming. In order to utilize the tremendous power of parallel computation of Graphics Processing Units (GPU), this study has developed a GPU-based MPS model employing the Compute Unified Device Ar...     

Finite-difference method for the Navier-Stokes equations in a variable domain with curved boundaries

A semi-implicit finite-difference scheme is proposed for solving the nonlinear viscous compressible Navier-Stokes equations. Coordinate transformations are constructed that yield a uniform mesh in the computational plane even though the physical domain under consideration is time-varying and curvilinear. The finite-difference scheme was tested using model examples.     

基于MPS方法的汽泡冷凝与融合特性研究

移动粒子半隐式（Moving Particle Semi-implicit,MPS）数值方法在追踪汽液相界面上较传统网格方法有很大优势,本研究基于MPS方法对过冷水中单个蒸汽泡的冷凝行为进行了数值模拟研究。计算结果与Kamei的实验结果符合较好并表明,汽泡冷凝寿命与汽泡初始尺寸呈近似线性关系,低过冷度下大汽泡的变形会加...     

Multidomain mixed variational analysis of transport flow through elastoviscoplastic porous media

Multidomain mixed nonlinear transport and flow phenomena through elastoviscoplastic porous media is variationally analyzed. Mixed variational formulations of the poro-mechanical system are established via composition duality methods, determining solvability results on the basis of duality principles. The conformation of the coupled physical system corresponds to constrained transport processes driven by a compressible Darcian flow, in a quasistatic elastoviscoplastic deformable subsurface porous media, modeled variationally by primal evolution mixed transport and consolidation, and dual evolution mixed flow and quasistatic deformation. For parallel computing, non-overlapping multidomain decomposition methods based on variational macro-hybridization, are presented and discussed, providing a natural multi-physics approach for the coupled transport flow and deformation system. For computational realizations, internal variational macro-hybrid mixed semi-discrete approximations are given, as well as primal and dual fully discrete semi-implicit time marching schemes. Furthermore, the corresponding coupled transport-flow-deformation system is concluded and analyzed, proposing natural resolution coupling techniques.     

Coupled MPS-modal superposition method for 2D nonlinear fluid-structure interaction problems with free surface

In this paper, a coupled MPS-modal superposition method is developed for 2D nonlinear fluid-structure interaction problems. In this method, the rigid-body and relatively small elastic deformation are coupled together, which considers the mutual effect between them. The elastic deformation of the structure is represented by a mode superposition formulation, which is more efficient compared with FEM, regardless of the size of the structure. For 2D cases, if the first three modes are chosen to represent the flexible deformation of the structure, it only results in a 6×6 matrix equation to be solved. For the fluid motion, the modified Moving Particle Semi-implicit (MPS) method, which significantly reduces the fluctuation of pressure calculation of the original MPS method, is used.Two nonlinear problems, i.e. breaking-water-dam impacting a floating beam and flexible wedge slamming into the water are simulated to demonstrate the performance of the developed method. The numerical simulations show that this coupling model is capable of providing stable results that are generally in good agreement with the available experimental data. For the highly nonlinear case with very large rigid motions, the mutual effect between elastic deformation and rigid motions could accumulate to a relatively remarkable level shown by the curves of trajectories or acceleration history of the body mass centre. This also indicates the importance of mutual effect to analyse highly nonlinear FSI problems with large rigid-body motions and relatively small flexible deformation.     

一种改进的MPS粒子作用模型

从分析角度出发,为移动粒子半隐式法(MPS)提供了一组新的粒子作用模型,该模型在粒子局部坐标系下进行泰勒展开,同步获取各算子的粒子近似式,确保了离散精度的一致性.方法对于随机分布的粒子和边界附近的粒子同样适用.文中利用三个算例对该方法进行了检验,计算结果与分析解符合较好.最后,运用该方法成功模拟了自由面流动的二维溃坝问题.     

粒子法中自由表面粒子识别

针对移动粒子半隐式法MPS（Moving Particle Semi-implicit Method）基于粒子数密度来判断自由表面会出现将内部粒子误判为自由表面粒子的问题,提出了一种结合几何法和体积法的自由表面粒子判定方法。通过对溃坝问题进行数值模拟,结果表明,全新的自由表面粒子判定方法对流体平稳运动以及剧烈运动两种工况,都能准确地判断出自由表面粒子,解决了基于粒子数密度判断方法因粒子分布稀疏产生误判的问题。[JP2]这种全新的自由表面粒子判定方法对今后采用MPS方法计算两相流问题时,两种介质在界面处的传热传质计算有重要意义。     

Error analysis and iterative methods in pseudospectral semi-implicit simulations: an application to compressible convection

Compressible convection is an interesting field for numerical experiments. Rapidly varying small-scale flow structures appear as the Rayleigh number Ra increases, demanding larger spatial resolution under more and more severe Courant stability conditions. Coupling a pseudospectral approximation in space to a semi-implicit scheme in time allows one to increase the size of Δ ts, though at each time step a system of algebraic equations, whose size increases with the spatial resolution, must be solved by means of direct or iterative methods. The former allows one to minimize the consumption of CPU time but leads to unacceptable demand of memory. The efficiency and cost of the latter, on the other hand, depend heavily on the choice of the preconditioning operator and on the allowed error tolerance. In this paper we check the capabilities of iterative-like methods and we achieve the main goal of drastically reducing the memory storage with respect to direct methods, without increasing the CPU time. © 1997 John Wiley & Sons, Ltd.     

A multigrid semi-implicit finite difference method for the two-dimensional shallow water equations

A multigrid semi-implicit finite difference method is presented to solve the two-dimensional shallow water equations which describe the behaviour of basin water under the influence of the Coriolis force, atmospheric pressure gradients and tides. The semi-implicit finite difference method discretizes implicitly both the gradient of the water elevation in the momentum equations and the velocity divergence in the continuity equations and explicitly the convective terms using an Eulerian–Lagrangian approach. At each time step we apply the multigrid computation to solve the resulting linear, symmetric, pentadiagonal system of discrete equations. The multigrid algorithm, defined on staggered grids, provides accelerated convergence histories. We numerically simulate the water circulation in a closed rectangular basin, centrally crossed by a deeper channel. Moreover, simulation of the circulation in San Pablo Bay shows the high flexibility and applicability of this method to concrete problems. Visualizations of the computed variables, water depth and velocity, are shown by figures. Displays of convergence histories show promising multigrid acceleration. © 1997 John Wiley & Sons, Ltd.     

上游静止方柱尾流对下游方柱体尾激振动效应影响

基于半隐式特征线分裂算子有限元法,对低雷诺数下串列布置上游静止方柱--下游双自由度运动方柱体结构的尾激振动问题进行了研究.首先与现有文献结果进行对比验证该方法的正确性.然后着重分析了雷诺数($Re$)与折减速度$(U_{\rm r})$两个关键参数对下游方柱尾激振动响应的影响,同时将计算结果与单方柱工况进行了对比. 数值计算结果表明,雷诺数和折减速度对下游方柱的振幅、振动频率和运动轨迹等动力响应特性的影响较大.随着雷诺数的增大,双柱系统的互扰效应从以涡激效应为主逐渐转变为尾激效应发挥主导作用,从而导致下游方柱的振动响应增强.单方柱工况结构运动轨迹均呈"8"字形. 然而,下游方柱的运动轨迹会随着雷诺数的增加而变得复杂.雷诺数较小时($Re\!=\!40$, 80),下游方柱的运动轨迹基本为"8"字形. 雷诺数较大时($Re\!=\!120$, 160,200), 下游方柱的运动轨迹会出现双"8"字形. 同时,下游方柱的尾流场特性主要呈现2S, 2S*, 2P, 2T, P+S和稳态6种模式.最后, 通过对流场特性进行分析,揭示了串列双方柱系统尾激振动效应的作用机理.