轴对称二维流体方程的多重网格求解
Multigrid solver for axisymmetrical 2D fluid equations
摘要：
本文发展了一种求解二维定常轴对称流体方程的有效算法。该算法采用多重网格方法以及偏微分方程组的标准隐式离散格式。多重网格方法相对于网格点数量的线性允许我们使用$256\times 256$网格，在那里我们可以在几分钟内获得解决方案。通过使用多级网格（$256\times 256$网格上的初始解是从$128\times 128$网格外推的稳态解，这允许使用“长”积分时间步长），部分地避免了由于系统的非线性引起的时间限制。流体求解器可用作直流放电混合代码的基础。
英文摘要：
We have developed an efficient algorithm for steady axisymmetrical 2D fluid equations. The algorithm employs multigrid method as well as standard implicit discretization schemes for systems of partial differential equations. Linearity of the multigrid method with respect to the number of grid points allowed us to use $256\times 256$ grid, where we could achieve solutions in several minutes. Time limitations due to nonlinearity of the system are partially avoided by using multi level grids(the initial solution on $256\times 256$ grid was extrapolated steady solution from $128\times 128$ grid which allowed using "long" integration time steps). The fluid solver may be used as the basis for hybrid codes for DC discharges.
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