In this paper, the WLS-ENO (Weighted-Least-Squares based Essentially Non-Oscillatory) reconstruction is modified to maintain the conservation of the cell average values. Furthermore, the divergence-free constraint is combined with the conservative WLS-ENO reconstruction, which can make the magnetic field locally divergence-free. The main merit of the proposed reconstruction scheme is that it can keep both the divergence-free constraint and ENO property for the magnetic field without using any limiter. We apply the scheme to the simulations of ideal MHD equations within the framework of a positivity-preserving finite volume method. The convergence, the magnetic field divergence error and the capability for low plasma-beta of the scheme are tested by some MHD benchmark problems.

在本文中，修改了 WLS-ENO（基于加权最小二乘法的基本非振荡）重建以保持单元平均值的守恒。此外，无发散约束与保守的 WLS-ENO 重建相结合，可以使磁场局部无发散。所提出的重建方案的主要优点是它可以在不使用任何限制器的情况下保持磁场的无发散约束和 ENO 特性。我们将该方案应用于在保正性有限体积方法框架内的理想 MHD 方程的模拟。通过一些MHD基准问题测试了该方案的收敛性、磁场发散误差和低等离子体β的能力。