New mapped unequal-sized trigonometric WENO scheme for hyperbolic conservation laws
New mapped unequal-sized trigonometric WENO scheme for hyperbolic conservation laws
复制标题
双曲守恒定律的新映射不等大小三角WENO方案
DOI：
10.1016/j.compfluid.2022.105585
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发表时间：
2022
影响因子：
2.8
通讯作者：
Jun Zhu
中科院分区：
文献类型：
--
作者：
Yan Zhang;Jun Zhu
本文设计了一种新的有限差分映射不等大小三角加权基本非振荡格式（mus - 2o），用于求解双曲型守恒律、高振荡问题和一些包含低密度、低压或低能的极端问题。为了减小三角多项式空间中线性权值与非线性权值之间的差异，提出了一种新的映射函数和相应的新的映射非线性权值。在模拟一些高振荡问题时，它可以得到较小的数值误差，甚至在光滑区域的临界点附近也能得到极小的五阶最优收敛。该方案利用三个不等大小的模板来设计三个不等次三角多项式，其最优线性权值可以设为任意正数，条件是它们的和为1。这是我们第一次在整个大模板上重建一个高阶三角多项式，而许多经典的高阶WENO空间重建只重建边界点或离散正交点处的值。用大量的基准算例，包括高振荡问题和一些极端问题，证明了这种新的有限差分mu - twenty格式的良好表示。
This paper designs a new finite difference mapped unequal-sized trigonometric weighted essentially non-oscillatory (MUS-TWENO) scheme for solving hyperbolic conservation laws, highly oscillation problems, and some extreme problems containing low density, low pressure, or low energy. A new mapping function and associated new mapped nonlinear weights are proposed to reduce the difference between the linear weights and nonlinear weights in trigonometric polynomial space. It could get smaller numerical errors and obtain optimal fifth-order convergence with a tiny ɛ even near critical points in smooth regions when simulating some highly oscillatory problems. This new MUS-TWENO scheme uses three unequal-sized stencils to design three unequal degree trigonometric polynomials and the sophisticated optimal linear weights can be set as any positive numbers on condition that their summation is one. It is the first time that we can reconstruct a high degree trigonometric polynomial over the whole big stencil, while many classical high-order WENO spatial reconstructions only reconstruct the values at the boundary points or discrete quadrature points. Extensive benchmark examples including highly oscillatory problems and some extreme problems are used to testify the good representations of this new finite difference MUS-TWENO scheme.