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大时间步长叠波格式最初思想为LeVeque提出的大时间步长Godunov格式,通过叠加间断分解发出的强波来构造数值格式.原方法只给出了间断强波的穿越叠加方法,文章对其进行了完善,并推广到多维.针对膨胀波提出了一种网格单元分解法可以自动满足熵条件,避免出现非物理解.给出了格式的具体计算公式,并用单个守恒律方程、一维/多维Euler方程组进行了数值计算.计算结果表明,新格式除了可以采用大时间步长的优点外,在一定范围内随CFL数增加其耗散反而更低,因而对激波接触间断膨胀波的分辨率更高. 相似文献
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本文给出了一个模拟叶栅内准三维定常和非定常粘性流动的数值方法。对于定常流动,采用TVD Lax-Wendroff格式和代数湍流模型求解雷诺平均Navier-Stokes方程,使用当地时间步长和多网格技术使计算加速收敛到定常状态;对于非定常流动,使用双时间步长和全隐式离散,采用与求解定常流动相似的多网格方法求解隐式离散方程。文中给出了VKI透平叶栅内的定常流结果和1.5级透平叶栅内的非定常数值结果。 相似文献
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本文采用自适应移动网格与Level Set函数相耦合的方法来实现气-液两相流的数值模拟与计算.作为自适应网格方法的一种,移动网格方法主要是为了解决发展方程的计算问题而设计的方法.文中给出了移动网格的生成方程,并针对方程的非线性,给出了一种半隐式的离散方法用于进行求解.本文将移动网格方法与Level Set方法相耦合,将控制流体运动的Navier-Stokes方程以及追踪相界面的Level Set方程转换到曲线坐标下,应用一套曲线坐标方程组来同时描述气、液两相流的运动规律,成功实现了对气-液两相流问题的数值模拟.通过对顶盖驱动流的计算以及对液滴沉降现象的模拟计算,验证了本文方法的可靠性.本文对常重力与微重力下两气泡融合的发展规律进行了数值模拟,通过分析对比,得到了重力对两气泡融合变形的影响规律. 相似文献
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We present an immersed interface method for solving the incompressible steady Stokes equations involving fixed/moving interfaces and rigid boundaries (irregular domains). The fixed/moving interfaces and rigid boundaries are represented by a number of Lagrangian control points. In order to enforce the prescribed velocity at the rigid boundaries, singular forces are applied on the fluid at these boundaries. The strength of singular forces at the rigid boundary is determined by solving a small system of equations. For the deformable interfaces, the forces that the interface exerts on the fluid are calculated from the configuration (position) of the deformed interface. The jumps in the pressure and the jumps in the derivatives of both pressure and velocity are related to the forces at the fixed/moving interfaces and rigid boundaries. These forces are interpolated using cubic splines and applied to the fluid through the jump conditions. The positions of the deformable interfaces are updated implicitly using a quasi-Newton method (BFGS) within each time step. In the proposed method, the Stokes equations are discretized via the finite difference method on a staggered Cartesian grid with the incorporation of jump contributions and solved by the conjugate gradient Uzawa-type method. Numerical results demonstrate the accuracy and ability of the proposed method to simulate incompressible Stokes flows with fixed/moving interfaces on irregular domains. 相似文献
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Novel energy dissipative method on the adaptive spatial discretization for the Allen–Cahn equation
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《中国物理 B》2021,30(7):70201-070201
We propose a novel energy dissipative method for the Allen–Cahn equation on nonuniform grids. For spatial discretization, the classical central difference method is utilized, while the average vector field method is applied for time discretization. Compared with the average vector field method on the uniform mesh, the proposed method can involve fewer grid points and achieve better numerical performance over long time simulation. This is due to the moving mesh method, which can concentrate the grid points more densely where the solution changes drastically. Numerical experiments are provided to illustrate the advantages of the proposed concrete adaptive energy dissipative scheme under large time and space steps over a long time. 相似文献
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A kind of three-dimensional(3-D) sound ray tracing algorithm in heterogeneous media is studied. This algorithm includes two steps: the first step computes the wavefront traveltimes forward; the second step traces the sound rays backward. In the first step, the computation of wavefront traveltimes at discrete grid points from the sound source, was found on Eikonal equation solutions and carried out by GMM (Group marching method) wavefront marching method based on level set. In the second step, sound ray tracing was proceeded gradually from the receiver to each cell towards the sound source, with wavefront traveltimes computed in the first step. Time values on arbitrary positions in each cuboid cell can be expressed by linear interpolation of wavefront traveltimes at the same cell's grid points. Thus, an algorithm of 3-D sound ray tracing in heterogeneous media is put forward. The simulation results indicate that this method can improve both the accuracy and the efficiency of 3-D sound ray tracing greatly. 相似文献
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With many superior features, Runge–Kutta discontinuous Galerkin method (RKDG), which adopts Discontinuous Galerkin method (DG) for space discretization and Runge–Kutta method (RK) for time integration, has been an attractive alternative to the finite difference based high-order Computational Aeroacoustics (CAA) approaches. However, when it comes to complex physical problems, especially the ones involving irregular geometries, the time step size of an explicit RK scheme is limited by the smallest grid size in the computational domain, demanding a high computational cost for obtaining time accurate numerical solutions in CAA. For computational efficiency, high-order RK method with nonuniform time step sizes on nonuniform meshes is developed in this paper. In order to ensure correct communication of solutions on the interfaces of grids with different time step sizes, the values at intermediate-stages of the Runge–Kutta time integration on the elements neighboring such interfaces are coupled with minimal dissipation and dispersion errors. Based upon the general form of an explicit p-stage RK scheme, a linear coupling procedure is proposed, with details on the coefficient matrices and execution steps at common time-levels and intermediate time-levels. Applications of the coupling procedures to Runge–Kutta schemes frequently used in simulation of fluid flow and acoustics are given, including the third-order TVD scheme, and low-storage low dissipation and low dispersion (LDDRK) schemes. In addition, an analysis on the stability of coupling procedures on a nonuniform grid is carried out. For validation, numerical experiments on one-dimensional and two-dimensional problems are presented to illustrate the stability and accuracy of proposed nonuniform time-step RKDG scheme, as well as the computational benefits it brings. Application to a one-dimensional nonlinear problem is also investigated. 相似文献
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Mikhail Z. Tokar 《Journal of computational physics》2010,229(7):2625-2633
In diverse media the characteristics of mass and heat transfer may undergo spontaneous and abrupt changes in time and space. This can lead to the formation of regions with strongly reduced transport, so called transport barriers (TB). The presence of interfaces between regions with qualitatively and quantitatively different transport characteristics impose severe requirements to methods and numerical schemes used by solving of transport equations. In particular the assumptions made in standard methods about the solution behavior by representing its derivatives fail in points where the transport changes abruptly. The situation is complicated further by the fact that neither the formation time nor the positions of interfaces are known a priori. A numerical approach, operating reliably under such conditions, is proposed. It is based on the introduction of a new dependent variable related to the variation after one time step of the original one integrated over the volume. In the vicinity of any grid knot the resulting differential equation is approximated by a second order ordinary differential equation with constant coefficients. Exact analytical solutions of these equations are conjugated between knots by demanding the continuity of the total solution and its first derivative. As an example the heat transfer in media with heat conductivity decreasing abruptly when the temperature e-folding length exceeds a critical value is considered. The formation of TB both at a heating power above the critical level and caused with radiation energy losses non-linearly dependent on the temperature is modeled. 相似文献
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两介质段瞬变流的修正特征线法 总被引:1,自引:0,他引:1
本文针对变波速可压缩两介质段非定常流的数值模拟,提出了修正特征线法。为使计算网格保持矩形,将一个大于1的修正因子α引入动量方程,从而在一定的范围内对特征线斜率进行调整,并据此确定时间和空间步长。其中因不满足稳定性条件而造成的误差由修正因子对动量方程进行修正。这种方法适用于一般瞬变流和振荡流。为解决介质界面连续移动的问题,本文提出了可自动调节空间步长的浮动网格,这使计算单元介质得以保持单一。通过在压力项中加入人工粘性改善了计算的稳定性。文章最后给出了计算实例。 相似文献
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The present paper presents a hybrid meshfree-and-Cartesian grid method for simulating moving body incompressible viscous flow problems in 3D space. The method combines the merits of cost-efficient and accurate conventional finite difference approximations on Cartesian grids with the geometric freedom of generalized finite difference (GFD) approximations on meshfree grids. Error minimization in GFD is carried out by singular value decomposition (SVD). The Arbitrary Lagrangian–Eulerian (ALE) form of the Navier–Stokes equations on convecting nodes is integrated by a fractional-step projection method. The present hybrid grid method employs a relatively simple mode of nodal administration. Nevertheless, it has the geometrical flexibility of unstructured mesh-based finite-volume and finite element methods. Boundary conditions are precisely implemented on boundary nodes without interpolation. The present scheme is validated by a moving patch consistency test as well as against published results for 3D moving body problems. Finally, the method is applied on low-Reynolds number flapping wing applications, where large boundary motions are involved. The present study demonstrates the potential of the present hybrid meshfree-and-Cartesian grid scheme for solving complex moving body problems in 3D. 相似文献
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Ding Li Zhiliang Lu & Tongqing Guo 《advances in applied mathematics and mechanics.》2014,6(1):120-134
Aiming at a complex multi-block structured grid, an efficient dynamic mesh
generation method is presented in this paper, which is based on radial basis functions
(RBFs) and transfinite interpolation (TFI). When the object is moving, the multi-block
structured grid would be changed. The fast mesh deformation is critical for numerical
simulation. In this work, the dynamic mesh deformation is completed in two steps. At
first, we select all block vertexes with known deformation as center points, and apply
RBFs interpolation to get the grid deformation on block edges. Then, an arc-lengthbased TFI is employed to efficiently calculate the grid deformation on block faces and
inside each block. The present approach can be well applied to both two-dimensional
(2D) and three-dimensional (3D) problems. Numerical results show that the dynamic
meshes for all test cases can be generated in an accurate and efficient manner. 相似文献