论文标题
改进的自适应改进的映射WENO方法
A modified adaptive improved mapped WENO method
论文作者
论文摘要
我们通过使用几个自适应控制功能和信号函数的平滑近似来提出一个新的映射WENO方案系列。提出的方案介绍了适应性，并接受了映射函数中参数的广泛允许范围。因此，他们有能力达到最佳的收敛率，即使接近临界点。特别是，这些具有微调参数的新方案之一说明了解决不连续性问题时的重要优势。它产生具有高分辨率的数值解决方案而不会产生虚假振荡，尤其是在长期输出时间。
We propose a new family of mapped WENO schemes by using several adaptive control functions and a smoothing approximation of the signum function. The proposed schemes introduce the adaptivity and admit an extensive permitted range of the parameters in the mapping functions. Consequently, they have the capacity to achieve optimal convergence rates, even near critical points. Particularly, one of these new schemes with fine-tuned parameters illustrates a significant advantage when solving problems with discontinuities. It produces numerical solutions with high resolution without generating spurious oscillations, especially for long output times.
