共查询到20条相似文献,搜索用时 109 毫秒
1.
通过构造新的平衡分布函数和结合分区自适应网格加密方法,对不带扩散项的平衡辐射流体力学方程,构造二阶的分子动理学BGK-AMR格式.一方面在关心的计算区域中局部加密计算网格,提高计算精度的同时大大节省了计算网格数量和计算时间;另一方面,不同于已有的参数强耦合平衡分布函数,新构造的平衡分布函数中各参数不相互依赖,简化了辐射流体力学分子动理学格式的计算.一维和二维的数值算例显示了格式的性能. 相似文献
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提出一种基于WENO重构的高阶(至少三阶)移动网格动理学格式.利用流体力学方程的积分形式得到移动网格上离散格式,再利用自适应移动网格方法移动网格,进而得到网格速度,利用WENO重构得到高阶插值多项式,最后使用时间方向上精确的动理学数值方法构造数值通量,得到移动网格单元上新的物理量.数值实验表明这种格式同时具有高精度、高分辨率的特点. 相似文献
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在Voronoi网格上利用一种基于回路积分法的有限体积法构造扩散方程的的差分格式.在这种特殊的网格上离散扩散方程比通常在四边形网格上离散的格式要简单,不会引进角点未知量,提高了对网格边上的流的离散精度,及差分格式整体精度.这种Voronoi网格上的扩散计算也可以与单元中心流体力学计算耦合.数值算例表明这种格式比四边形网格上的格式精度高,且能更好的应对网格扭曲情形. 相似文献
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三维笛卡儿坐标系中Lagrange流体力学的显式相容有限元方法(英文) 总被引:1,自引:0,他引:1
将Caramana等人提出的相容算法思想和有限元方法相结合,提出三维笛卡儿坐标系中Lagrange流体力学的显式相容有限元方法.采用三线性六面体单元和交错网格进行空间离散,利用质量集中进行显式求解,无需求解线性代数方程组.时间离散可采用两步显式Runge-Kutta格式.用边人工粘性消除激波振荡,用子网格扰动压力抑制网格的非物理变形.给出若干标准算例.数值算例表明,该方法具有较高的计算精度和计算效率,同时具有很好的对称性和总能量守恒性,总能量计算误差为计算机浮点计算截断误差. 相似文献
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利用流体力学方程的积分形式给出非结构移动网格上离散格式,利用自适应移动网格方法移动网格,进而得到网格速度.对振动Naca0012翼型问题,分三种类型确定网格速度,再结合Riemann问题的解法器构造数值通量,得到移动网格单元上新的物理量.数值实验表明这种格式同时具有高效、高分辨率的特点. 相似文献
11.
Margarete O. Domingues Sônia M. Gomes Olivier Roussel Kai Schneider 《Journal of computational physics》2008,227(8):3758-3780
We present a fully adaptive numerical scheme for evolutionary PDEs in Cartesian geometry based on a second-order finite volume discretization. A multiresolution strategy allows local grid refinement while controlling the approximation error in space. For time discretization we use an explicit Runge–Kutta scheme of second-order with a scale-dependent time step. On the finest scale the size of the time step is imposed by the stability condition of the explicit scheme. On larger scales, the time step can be increased without violating the stability requirement of the explicit scheme. The implementation uses a dynamic tree data structure. Numerical validations for test problems in one space dimension demonstrate the efficiency and accuracy of the local time-stepping scheme with respect to both multiresolution scheme with global time stepping and finite volume scheme on a regular grid. Fully adaptive three-dimensional computations for reaction–diffusion equations illustrate the additional speed-up of the local time stepping for a thermo-diffusive flame instability. 相似文献
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We present a full three-dimensional, featured-data algorithm for time-domain fluorescence diffuse optical tomography that inverts the Laplace-transformed time-domain coupled diffusion equations and employs a pair of appropriate transform-factors to effectively separate the fluorescent yield and lifetime parameters. By use of a time-correlation single-photon counting system and the normalized Born formulation, we ex-perimentally validate that the proposed scheme can achieve simultaneous reconstruction of the fluorescent yield and lifetime distributions with a reasonable accuracy. 相似文献
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On the Fully Implicit Solution of a Phase-Field Model for Binary Alloy Solidification in Three Dimensions 下载免费PDF全文
Christopher E. Goodyer Peter K. Jimack rew M. Mullis Hongbiao Dong & Yu Xie 《advances in applied mathematics and mechanics.》2012,4(6):665-684
A fully implicit numerical method, based upon a combination of
adaptively refined hierarchical meshes and geometric multigrid, is
presented for the simulation of binary alloy solidification in
three space dimensions. The computational techniques are presented for a
particular mathematical model, based upon the phase-field approach,
however, their applicability is of greater generality than for the
specific phase-field model used here. In particular, an implicit
second order time discretization is combined with the use of second order
spatial differences to yield a large nonlinear system of algebraic
equations as each time step. It is demonstrated that these equations
may be solved reliably and efficiently through the use of a nonlinear
multigrid scheme for locally refined grids. In effect, this paper
presents an extension of earlier research in two space
dimensions (J. Comput. Phys., 225 (2007), pp. 1271-1287) to fully
three-dimensional problems. This extension is validated against earlier
two-dimensional results and against some of the limited results
available in three dimensions, obtained using an explicit scheme.
The efficiency of the implicit approach and the multigrid solver are
then demonstrated and some sample computational results for the
simulation of the growth of dendrite structures are presented. 相似文献
14.
Shravan K. Veerapaneni Denis Gueyffier Denis Zorin George Biros 《Journal of computational physics》2009,228(7):2334-2353
We present a new method for the evolution of inextensible vesicles immersed in a Stokesian fluid. We use a boundary integral formulation for the fluid that results in a set of nonlinear integro-differential equations for the vesicle dynamics. The motion of the vesicles is determined by balancing the non-local hydrodynamic forces with the elastic forces due to bending and tension. Numerical simulations of such vesicle motions are quite challenging. On one hand, explicit time-stepping schemes suffer from a severe stability constraint due to the stiffness related to high-order spatial derivatives and a milder constraint due to a transport-like stability condition. On the other hand, an implicit scheme can be expensive because it requires the solution of a set of nonlinear equations at each time step. We present two semi-implicit schemes that circumvent the severe stability constraints on the time step and whose computational cost per time step is comparable to that of an explicit scheme. We discretize the equations by using a spectral method in space, and a multistep third-order accurate scheme in time. We use the fast multipole method (FMM) to efficiently compute vesicle–vesicle interaction forces in a suspension with a large number of vesicles. We report results from numerical experiments that demonstrate the convergence and algorithmic complexity properties of our scheme. 相似文献
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对流扩散方程的指数型摄动差分法 总被引:7,自引:0,他引:7
改进了作者所提出的对流扩散方程四阶指数型摄动差分格式,并阐明其在高Reynolds数适应性和节省计算量方面的显著优点。指数型摄动差分法经改进后具有较为简便的形式,克服了其他紧致高阶格式不能使用于高Reynolds数问题的致命弱点。文中针对计算流体力学的基本困难,作一至三维流动模型方程和自然对流传热问题的精细计算,且以双精制算法检验格式的四阶精度,表明摄动差分法能在较粗的网格下给出相当准确的结果,十分显著地节省计算机时,并对"激波"和"边界层"等高Reynolds数效应有极高的分辨能力。 相似文献
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For the three-dimensional incompressible Navier–Stokes equations, we present a formulation featuring velocity, vorticity and helical density as independent variables. We find the helical density can be observed as a Lagrange multiplier corresponding to the divergence-free constraint on the vorticity variable, similar to the pressure in the case of the incompressibility condition for velocity. As one possible practical application of this new formulation, we consider a time-splitting numerical scheme based on an alternating procedure between vorticity–helical density and velocity–Bernoulli pressure systems of equations. Results of numerical experiments include a comparison with some well-known schemes based on pressure–velocity formulation and illustrate the competitiveness on the new scheme as well as the soundness of the new formulation. 相似文献
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一种三维环流模型及其应用 总被引:1,自引:0,他引:1
本文建立了一种广泛适用于大陆架浅海的三维环流模型。模型的支配方程是具有自由面的三维非线性瞬态Navier-Stokes方程。支配方程经σ坐标变换后与边界条件一起在空间交错网格系统上用差分法求解。为提高计算效率,基于问题的物理性质引入过程分裂概念没计了计算框架:将三维流动过程分成长重力波的传播(外模式)和速度的垂向剪变(内模式)两大组成部分,对每个部分分别选用最适宜各自物理特性和数值行为的数值方法求解。最后做为本模型的应用实例,计算了渤海三维潮流,获得了很好的结果。 相似文献
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K.S.C. Peerenboom J. van Dijk J.H.M. ten Thije Boonkkamp L. Liu W.J. Goedheer J.J.A.M. van der Mullen 《Journal of computational physics》2011,230(9):3525-3537
The Stefan–Maxwell equations for multi-component diffusion result in a system of coupled continuity equations for all species in the mixture. We use a generalization of the exponential scheme to discretize this system of continuity equations with the finite volume method. The system of continuity equations in this work is obtained from a non-singular formulation of the Stefan–Maxwell equations, where the mass constraint is not applied explicitly. Instead, all mass fractions are treated as independent unknowns and the constraint is a result of the continuity equations, the boundary conditions, the diffusion algorithm and the discretization scheme. We prove that with the generalized exponential scheme, the mass constraint can be satisfied exactly, although it is not explicitly applied. A test model from the literature is used to verify the correct behavior of the scheme. 相似文献
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The method of regularized Stokeslets is a numerical approach to approximating solutions of fluid–structure interaction problems in the Stokes regime. Regularized Stokeslets are fundamental solutions to the Stokes equations with a regularized point-force term that are used to represent forces generated by a rigid or elastic object interacting with the fluid. Due to the linearity of the Stokes equations, the velocity at any point in the fluid can be computed by summing the contributions of regularized Stokeslets, and the time evolution of positions can be computed using standard methods for ordinary differential equations. Rigid or elastic objects in the flow are usually treated as immersed boundaries represented by a collection of regularized Stokeslets coupled together by virtual springs which determine the forces exerted by the boundary in the fluid. For problems with boundaries modeled by springs with large spring constants, the resulting ordinary differential equations become stiff, and hence the time step for explicit time integration methods is severely constrained. Unfortunately, the use of standard implicit time integration methods for the method of regularized Stokeslets requires the solution of dense nonlinear systems of equations for many relevant problems. Here, an alternate strategy using an explicit multirate time integration scheme based on spectral deferred corrections is incorporated that in many cases can significantly decrease the computational cost of the method. The multirate methods are higher-order methods that treat different portions of the ODE explicitly with different time steps depending on the stiffness of each component. Numerical examples on two nontrivial three-dimensional problems demonstrate the increased efficiency of the multi-explicit approach with no significant increase in numerical error. 相似文献