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目前常用的限制器大都是基于一维构造,无法在多维情况下保证物理量的单调特性进而导致非物理振荡.为弥补传统方法的这一构造缺陷,多维限制器(MLP)通过多维修正使单元通量值介于周围相邻单元通量的最大值和最小值之间,在保证求解精度的情况下有效避免了多维振荡.基于一维激波管、无黏涡及激波边界层干扰等算例,对高精度MLP的特性进行了研究分析.结果显示:3阶MLP在连续和间断区域均可有效地避免多维振荡;与高阶WENO(Weighted Essentially Non-Oscillatory)方法相比,3阶MLP不仅算法简单、易于实现,还可显著提高求解的精度、保单调性及收敛性.因此可用于工程及科学研究的复杂流动,具有较好的应用前景.
The most commonly used limiters are based on one-dimensional structures and can not guarantee the monotonic properties of physical quantities in multidimensional situations, which in turn leads to non-physical oscillation.In order to make up for this structural defect of the traditional methods, Multidimensional Limiter (MLP) Which is between the maximum value and the minimum value of fluxes of neighboring units and effectively avoids the multi-dimensional oscillation under the condition of ensuring the accuracy of solution.On the basis of 1-D shock tube, no viscous vortex and shock boundary layer disturbance The results show that the 3-order MLP can effectively avoid the multi-dimensional oscillation in continuous and discontinuous regions. Compared with the WENO (Weighted Essentially Non-Oscillatory) method, the 3-order MLP Not only the algorithm is simple and easy to implement, but also can significantly improve the accuracy of the solution, the warranty of tonality and the convergence, so it can be used for complex flow in engineering and scientific research, and has a good application prospect.