Hierarchical basis for stabilized finite element methods for compressible flows
Hierarchical basis for stabilized finite element methods for compressible flows
复制标题
可压缩流稳定有限元方法的层次基础
DOI：
10.1016/j.cma.2003.07.011
复制
发表时间：
2003
影响因子：
7.2
通讯作者：
S. Dey
中科院分区：
文献类型：
--
作者：
C. Whiting;K. Jansen;S. Dey
对Navier-Stokes方程更精确的数值模拟的追求激发了高阶分段多项式基函数的研究，也称为k版本有限元方法，作为以最具成本效益的方式获得这种精度的手段。稳定化有限元方法（例如流线迎风彼得罗夫伽辽金）已被证明可以达到任何多项式阶数基础的最佳收敛速度，并在各种流动（包括湍流应用）上表现良好。我们提出了一个稳定的有限元公式的流体动力学网格实体为基础的分层基函数。实现的线性模型问题，以及Navier-Stokes方程达到理论收敛结果。
The quest for more accurate numerical simulations of the Navier–Stokes equations has motivated the study of high-order piecewise-polynomial basis functions, also known as k-version finite element methods, as a means to attain this accuracy in the most cost effective manner. Stabilized finite element methods (e.g. streamline upwind Petrov Galerkin) have been proven to attain optimal rates of convergence for any polynomial order basis as well as perform well on a variety of flows including turbulence applications. We present a stabilized finite element formulation for fluid dynamics using mesh-entity based hierarchical basis functions. The implementation is shown to attain theoretical convergence results for the linear model problem as well as the Navier–Stokes equations.