A methodology to control numerical dissipation characteristics of velocity based time discontinuous Galerkin space-time finite element method
A methodology to control numerical dissipation characteristics of velocity based time discontinuous Galerkin space-time finite element method
复制标题
基于时间间断伽辽金时空有限元法的速度数值耗散特性控制方法
DOI：
10.1002/nme.7078
复制
发表时间：
2022
影响因子：
2.9
通讯作者：
A. Murakami and S. Sasakawa
中科院分区：
文献类型：
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作者：
V. Sharma;K. Fujisawa;A. Murakami and S. Sasakawa
直接时间积分格式是结构动力学问题有限元模拟的重要组成部分。这种格式应该至少是二阶精度的，无条件稳定的，并且在数值上耗散高频分量。为此，本文在时间不连续Galerkin法的基础上，发展了一种改进的v-ST/FEM时间积分格式。该方法采用非对称三角气泡函数将位移场与速度场联系起来。改进的v-ST/有限元在左(0，0.5)$$中包含两个参数α∈(0，0.5)$\α，在左(-1，{\β}_c\右)$$中包含β∈(−1，βc)$$\β，以控制高频分量的耗散。全面研究了α$$\α$$和β$$\β$$对所提出方法的数值性能的影响。结果表明，当α$$\α$$的值增大时，解中的误差增大。然而，就所有实际目的而言，β$$\Beta$$对所提出方法的精度的影响可以忽略不计。对于α≠为0.0$$\α\ne 0.0$$，修正的v-ST/有限元为二阶精度，对于α=0.0$$\α=0.0$$为三阶精度。通过数值算例验证了改进的v-ST/α方法的数值有效性，并与其他常用方法如梯形法则、HHT-HHT法、Bathe格式的结果进行了比较。
Direct time integration schemes are an integral part of the FEM simulation of structural dynamics problems. Such schemes should be at least second‐order accurate, unconditionally stable, and numerically dissipates the high‐frequency components. To this end, this article develops a time integration scheme, called modified v‐ST/FEM, which is based on the time‐discontinuous Galerkin method. The proposed method employs an unsymmetric triangular bubble function for relating the displacement field to the velocity field. The modified v‐ST/FEM contains two‐parameter α∈(0,0.5)$$ \alpha \in \left(0,0.5\right) $$ and β∈(−1,βc)$$ \beta \in \left(-1,{\beta}_c\right) $$ for controlling the dissipation of high‐frequency components. A comprehensive study of the influence of α$$ \alpha $$ and β$$ \beta $$ on the numerical performance of the proposed method is conducted. It is found that the error in the solution increases when the value of α$$ \alpha $$ increases. However, for all practical purposes, β$$ \beta $$ has a negligible influence on the accuracy of the proposed method. The modified v‐ST/FEM is second‐order accurate for α≠0.0$$ \alpha \ne 0.0 $$, and third‐order accurate for α=0.0$$ \alpha =0.0 $$. The numerical efficacy of the modified v‐ST/FEM is demonstrated by solving some benchmark problems and comparing its result to those obtained by other popular methods such as Trapezoidal rule, HHT‐α$$ \alpha $$, and Bathe's scheme.