The piecewise-linear predictor-corrector code - A Lagrangian-remap method for astrophysical flows
The piecewise-linear predictor-corrector code - A Lagrangian-remap method for astrophysical flows
复制标题
分段线性预测校正器代码 - 天体物理流的拉格朗日重映射方法
DOI：
10.1086/191833
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发表时间：
1993
影响因子：
8.7
通讯作者：
J. Hawley
中科院分区：
文献类型：
--
作者：
E. A. Lufkin;J. Hawley
我们描述了一种用于求解非线性流体方程的时显式有限差分算法。该方法在使用算子分裂和人工粘度方面与现有的欧拉方案类似，不同之处在于我们使用预测校正器求解拉格朗日运动方程，然后重新映射到固定的欧拉网格。重新映射被制定为消除与坐标奇点相关的误差，并具有任意顺序重新映射的一般规定。我们对标准问题进行一系列全面的测试。自收敛测试表明，该代码在平滑的二维流（包括压力、重力和曲线几何）中具有二阶收敛率。虽然在理想化问题上不如高阶黎曼求解方案那么准确，但预测校正拉格朗日重映射代码具有很大的灵活性，可应用于各种天体物理问题。
We describe a time-explicit finite-difference algorithm for solving the nonlinear fluid equations. The method is similar to existing Eulerian schemes in its use of operator-splitting and artificial viscosity, except that we solve the Lagrangian equations of motion with a predictor-corrector and then remap onto a fixed Eulerian grid. The remap is formulated to eliminate errors associated with coordinate singularities, with a general prescription for remaps of arbitrary order. We perform a comprehensive series of tests on standard problems. Self-convergence tests show that the code has a second-order rate of convergence in smooth, two-dimensional flow, with pressure forces, gravity, and curvilinear geometry included. While not as accurate on idealized problems as high-order Riemann-solving schemes, the predictor-corrector Lagrangian-remap code has great flexibility for application to a variety of astrophysical problems.