To develop an efficient numerical scheme for two-dimensional convection diffusion equation using Crank-Nicholson and ADI, time-dependent nonlinear system is discussed. These schemes are of second order accurate in apa...To develop an efficient numerical scheme for two-dimensional convection diffusion equation using Crank-Nicholson and ADI, time-dependent nonlinear system is discussed. These schemes are of second order accurate in apace and time solved at each time level. The procedure was combined with Iterative methods to solve non-linear systems. Efficiency and accuracy are studied in term of L2, L∞ norms confirmed by numerical results by choosing two test examples. Numerical results show that proposed alternating direction implicit scheme was very efficient and reliable for solving two dimensional nonlinear convection diffusion equation. The proposed methods can be implemented for solving non-linear problems arising in engineering and physics.展开更多
An efficient high-order immersed interface method （IIM） is proposed to solve two-dimensional （2D） heat problems with fixed interfaces on Cartesian grids, which has the fourth-order accuracy in the maximum norm in ...An efficient high-order immersed interface method （IIM） is proposed to solve two-dimensional （2D） heat problems with fixed interfaces on Cartesian grids, which has the fourth-order accuracy in the maximum norm in both time and space directions. The space variable is discretized by a high-order compact （HOC） difference scheme with correction terms added at the irregular points. The time derivative is integrated by a Crank-Nicolson and alternative direction implicit （ADI） scheme. In this case, the time accuracy is just second-order. The Richardson extrapolation method is used to improve the time accuracy to fourth-order. The numerical results confirm the convergence order and the efficiency of the method.展开更多
应用内外解匹配的方法和驻相法推导了柱坐标系下地震引起的水面波动方程的解,即推导了地震海啸波生成与传播的理论方程,并对越洋地震海啸理论方程进行了求解。基于Boussinesq方程出发,建立了二维越洋海啸波传播数学模型,并对越洋海啸进...应用内外解匹配的方法和驻相法推导了柱坐标系下地震引起的水面波动方程的解,即推导了地震海啸波生成与传播的理论方程,并对越洋地震海啸理论方程进行了求解。基于Boussinesq方程出发,建立了二维越洋海啸波传播数学模型,并对越洋海啸进行了数值计算,计算方法采用有限差分方法,差分格式采用交替方向隐格式(Alternating Direction Implicit即ADI方法)。利用越洋海啸计算模式对发生在大洋中的地震海啸进行了模拟,将数值模拟结果与地震海啸波理论方程的计算结果进行了比较,两种计算结果吻合较好。展开更多
研究了直驱风电场次同步振荡分析的降阶模型,提出了基于交替方向隐式(alternating direction implicit,ADI)的平衡截断方法。首先,根据直驱式永磁同步风电机组的数学表征搭建风电场的数学模型,采用ADI方法迭代求解李亚普诺夫方程,得到...研究了直驱风电场次同步振荡分析的降阶模型,提出了基于交替方向隐式(alternating direction implicit,ADI)的平衡截断方法。首先,根据直驱式永磁同步风电机组的数学表征搭建风电场的数学模型,采用ADI方法迭代求解李亚普诺夫方程,得到可控的格莱姆矩阵与可观的格莱姆矩阵;然后,采用平衡截断的方法得到降阶模型;通过对比全阶模型与降阶模型的时域仿真波形、Bode图、计算耗时以及次同步振荡模式,验证了方法的有效性。仿真结果表明,降阶模型与全阶模型具有很好的一致性,同时计算速度提高,降阶阶数大大降低。展开更多
In this paper, a two-dimensional nonlinear coupled Gray Scott system is simulated with a finite difference scheme and a finite volume technique. Pre and post-processing lead to a new solution called GSmFoam by underst...In this paper, a two-dimensional nonlinear coupled Gray Scott system is simulated with a finite difference scheme and a finite volume technique. Pre and post-processing lead to a new solution called GSmFoam by understandin<span>g geometry settings and mesh information. The concentration profile chan</span>ges over time, as does the intensity of the contour patterns. The OpenFoam solver gives you the confidence to compare the pattern result with efficient numerical algorithms on the Gray Scott model.展开更多
文摘To develop an efficient numerical scheme for two-dimensional convection diffusion equation using Crank-Nicholson and ADI, time-dependent nonlinear system is discussed. These schemes are of second order accurate in apace and time solved at each time level. The procedure was combined with Iterative methods to solve non-linear systems. Efficiency and accuracy are studied in term of L2, L∞ norms confirmed by numerical results by choosing two test examples. Numerical results show that proposed alternating direction implicit scheme was very efficient and reliable for solving two dimensional nonlinear convection diffusion equation. The proposed methods can be implemented for solving non-linear problems arising in engineering and physics.
基金supported by the National Natural Science Foundation of China(No.51174236)the National Basic Research Program of China(973 Program)(No.2011CB606306)the Opening Project of State Key Laboratory of Porous Metal Materials(No.PMM-SKL-4-2012)
文摘An efficient high-order immersed interface method （IIM） is proposed to solve two-dimensional （2D） heat problems with fixed interfaces on Cartesian grids, which has the fourth-order accuracy in the maximum norm in both time and space directions. The space variable is discretized by a high-order compact （HOC） difference scheme with correction terms added at the irregular points. The time derivative is integrated by a Crank-Nicolson and alternative direction implicit （ADI） scheme. In this case, the time accuracy is just second-order. The Richardson extrapolation method is used to improve the time accuracy to fourth-order. The numerical results confirm the convergence order and the efficiency of the method.
文摘应用内外解匹配的方法和驻相法推导了柱坐标系下地震引起的水面波动方程的解,即推导了地震海啸波生成与传播的理论方程,并对越洋地震海啸理论方程进行了求解。基于Boussinesq方程出发,建立了二维越洋海啸波传播数学模型,并对越洋海啸进行了数值计算,计算方法采用有限差分方法,差分格式采用交替方向隐格式(Alternating Direction Implicit即ADI方法)。利用越洋海啸计算模式对发生在大洋中的地震海啸进行了模拟,将数值模拟结果与地震海啸波理论方程的计算结果进行了比较,两种计算结果吻合较好。
文摘研究了直驱风电场次同步振荡分析的降阶模型,提出了基于交替方向隐式(alternating direction implicit,ADI)的平衡截断方法。首先,根据直驱式永磁同步风电机组的数学表征搭建风电场的数学模型,采用ADI方法迭代求解李亚普诺夫方程,得到可控的格莱姆矩阵与可观的格莱姆矩阵;然后,采用平衡截断的方法得到降阶模型;通过对比全阶模型与降阶模型的时域仿真波形、Bode图、计算耗时以及次同步振荡模式,验证了方法的有效性。仿真结果表明,降阶模型与全阶模型具有很好的一致性,同时计算速度提高,降阶阶数大大降低。
文摘In this paper, a two-dimensional nonlinear coupled Gray Scott system is simulated with a finite difference scheme and a finite volume technique. Pre and post-processing lead to a new solution called GSmFoam by understandin<span>g geometry settings and mesh information. The concentration profile chan</span>ges over time, as does the intensity of the contour patterns. The OpenFoam solver gives you the confidence to compare the pattern result with efficient numerical algorithms on the Gray Scott model.
