A New Type of Finite Volume WENO Schemes for Hyperbolic Conservation Laws
A New Type of Finite Volume WENO Schemes for Hyperbolic Conservation Laws
复制标题
一种新型的双曲守恒定律有限体积WENO方案
DOI：
10.1007/s10915-017-0486-8
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发表时间：
2017
影响因子：
2.5
通讯作者：
Qiu Jianxian
中科院分区：
文献类型：
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作者：
Zhu Jun;Qiu Jianxian
Zhu和Qiu（J Comput Phys 318：110-121，2016）设计了一种新的双曲型守恒律有限差分加权基本无振荡（韦诺）格式，在这篇续文中，我们将这种方法推广到多维有限体积格式。与经典的有限体积韦诺格式相比，新的WENO格式有两个主要的优点：上级（舒，在：Quarteroni（艾德）的非线性双曲方程的高级数值逼近，数学讲义，CIME子系列，Springer，柏林，1998），第一个是相关联的线性权重可以是任何正数，仅要求它们的总和等于1，第二是它们的简单性和易于在工程应用中扩展到多维。新的韦诺重建是一个四次多项式与两个线性多项式的凸组合，定义在不等大小的空间stenches在传统的韦诺方式。这些新的五阶韦诺格式与经典的五阶韦诺格式Shu（1998）使用相同数量的单元平均信息，可以得到比经典的同阶韦诺格式更小的绝对数值误差，并且压缩了强激波或接触间断附近的非物理振荡。一些基准测试进行说明这些计划的能力。
A new type of finite difference weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws was designed in Zhu and Qiu (J Comput Phys 318:110–121, 2016), in this continuing paper, we extend such methods to finite volume version in multi-dimensions. There are two major advantages of the new WENO schemes superior to the classical finite volume WENO schemes (Shu, in: Quarteroni (ed) Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, Lecture Notes in Mathematics, CIME subseries, Springer, Berlin, 1998), the first is the associated linear weights can be any positive numbers with only requirement that their summation equals one, and the second is their simplicity and easy extension to multi-dimensions in engineering applications. The new WENO reconstruction is a convex combination of a fourth degree polynomial with two linear polynomials defined on unequal size spatial stencils in a traditional WENO fashion. These new fifth order WENO schemes use the same number of cell average information as the classical fifth order WENO schemes Shu (1998), could get less absolute numerical errors than the classical same order WENO schemes, and compress nonphysical oscillations nearby strong shocks or contact discontinuities. Some benchmark tests are performed to illustrate the capability of these schemes.