本文研究了求解三维不可压缩矢量势磁流体力学方程组的一阶投影时间离散算法。该方程组是将原磁流体力学方程组中的磁场B写成旋度形式,即引入B = curlA。通过构造矢量势磁流体力学方程组的数值算法,使得磁场的数值解在全离散层面满足无...本文研究了求解三维不可压缩矢量势磁流体力学方程组的一阶投影时间离散算法。该方程组是将原磁流体力学方程组中的磁场B写成旋度形式,即引入B = curlA。通过构造矢量势磁流体力学方程组的数值算法,使得磁场的数值解在全离散层面满足无散度条件。本文主要通过构造一阶投影格式,使得速度场的数值解也满足无散度条件,且所构造的投影格式对于任意时间步长都是无条件稳定的。在合理的正则性假设下,我们得到了速度和磁矢量势的一阶时间收敛阶。最后,通过数值算例验证了收敛性结果。In this paper, we consider a first-order projection finite element scheme for the three-dimensional incompressible magnetohydrodynamic system. This system of equations is to write the magnetic field B in the original magnetohydrodynamic equations in the curl form, which introduces B = curlA. By constructing the numerical algorithm of the system, the numerical solution of the magnetic field satisfies the divergence-free condition in fully discrete level. In this paper, by constructing the first-order projection scheme so that the numerical solution of the velocity field satisfies the divergence-free condition, and the constructed projection scheme is unconditionally stable for any time step. Under a reasonable regularity assumption, we derive the first-order temporal convergence order of the velocity and magnetic vector potential. Finally, the convergence results are verified by numerical examples.展开更多
利用黎曼精确解和行波法相结合,在一维浅水方程中实现大时间步长(Large Time Step,LTS)格式,并采用多波近似解决稀疏波断裂的问题,采用随机选取法(Random Choice Method,RCM)解决非线性方程使用LTS格式出现的震荡问题.一系列数值试验发...利用黎曼精确解和行波法相结合,在一维浅水方程中实现大时间步长(Large Time Step,LTS)格式,并采用多波近似解决稀疏波断裂的问题,采用随机选取法(Random Choice Method,RCM)解决非线性方程使用LTS格式出现的震荡问题.一系列数值试验发现,通过多波近似和随机选取法对大时间步长格式的改进,提高了计算效率,减小了震荡,取得了很好的计算效果.展开更多
文摘本文研究了求解三维不可压缩矢量势磁流体力学方程组的一阶投影时间离散算法。该方程组是将原磁流体力学方程组中的磁场B写成旋度形式,即引入B = curlA。通过构造矢量势磁流体力学方程组的数值算法,使得磁场的数值解在全离散层面满足无散度条件。本文主要通过构造一阶投影格式,使得速度场的数值解也满足无散度条件,且所构造的投影格式对于任意时间步长都是无条件稳定的。在合理的正则性假设下,我们得到了速度和磁矢量势的一阶时间收敛阶。最后,通过数值算例验证了收敛性结果。In this paper, we consider a first-order projection finite element scheme for the three-dimensional incompressible magnetohydrodynamic system. This system of equations is to write the magnetic field B in the original magnetohydrodynamic equations in the curl form, which introduces B = curlA. By constructing the numerical algorithm of the system, the numerical solution of the magnetic field satisfies the divergence-free condition in fully discrete level. In this paper, by constructing the first-order projection scheme so that the numerical solution of the velocity field satisfies the divergence-free condition, and the constructed projection scheme is unconditionally stable for any time step. Under a reasonable regularity assumption, we derive the first-order temporal convergence order of the velocity and magnetic vector potential. Finally, the convergence results are verified by numerical examples.
文摘利用黎曼精确解和行波法相结合,在一维浅水方程中实现大时间步长(Large Time Step,LTS)格式,并采用多波近似解决稀疏波断裂的问题,采用随机选取法(Random Choice Method,RCM)解决非线性方程使用LTS格式出现的震荡问题.一系列数值试验发现,通过多波近似和随机选取法对大时间步长格式的改进,提高了计算效率,减小了震荡,取得了很好的计算效果.
