无振荡、无自由参数格式在数值模拟盔型磁场中太阳风流动的应用

提出了一种离散二维三分量理想磁流体力学守恒型方程组（MHD）的算法（NNDMHD），它有效地控制了磁场散度不为零误差对动量方程组的影响，把气体动力学中计算跨音速流动问题的有效算法——无振荡、无自由参数（NND）格式推广应用到MHD方程组中。利用该算法首先对常见一维和二维算例进行数值试验，得到比较好的结果，消除了间断处的非物理振荡。然后对太阳风在子午面轴对称盔形磁场位形中流动进行数值试验，在这个算例中，物理量沿径向变化大，NNDMHD格式仍然能够有效地控制磁场散度离散不为零误差导致的非物理流动。这个算例的计算结果表明：在网格划分比通常情况和稀4倍时，该算法仍保持很好的计算稳定性。

APPLICATION OF NON-OSCILLATORY,NON-FREE PARAMETER DIFFERENCE SCHEME ON SIMULATION OF SOLAR WIND FLOW IN A HELMET MAGNETIC STRUCTURE

An algorithm called NNDMHD for the two-dimensional, three-component, eight-variable and time-dependent magnetohydrodynamic (MHD) conservative equations is proposed. It reduces Lorentz force error caused by numerical magnetic field divergence's non-zero error in a method of dividing magnetic field into two parts, a potential one invariant of time and a non-potential one varying with time. Then, NNDMHD could be developed from the Non-oscillatory, Non-free parameter Difference scheme (NND), which is very effective in numerical simulation of gas-dynamical transonic flow.At first, numerical tests on NNDMHD are carried out on a typical one-dimensional Riemann case and a two-dimensional Orszag-Tang example. The good numerical results agree with those of references and exhibit no non-physical oscillation near discontinuities. Then, example of solar wind flow in a helmet magnetic field structure being axisymmetric in meridian plane is taken for NNDMHD numerical test. In this example, although physical variables vary in a large scale (-10-4) in radial direction, NNDMHD can still reduce Lorentz force error caused by numerical magnetic field divergence's non-zero error. The numerical result in this example shows that: although the grid mesh is coarser four times than that of usual one, NNDMHD can still keep stable in computation for final steady state result.