Numerical Analysis of Viscoelastic Flow Problems

基于一些线性和非线性本构模型，对粘弹性流动问题的常规混合有限元方法和稳压有限元方法进行了误差分析和数值实验。当使用人工解的方法时，由数学论证建立的误差估计已被数值证实；当使用基准问题“突然收缩渠道流”时，数值涡长与实验值一致。因此，该研究有助于提高数值格式的可靠性。

Error analysis and numerical experiments are performed for conventional mixed finite element methods and pressure stabilized finite element methods of viscoelastic flow problems based on some linear and nonlinear constitutive models. When using methods of manufactured solutions, error estimates established from the mathematical justification have been numerically confirmed; when using a benchmark problem “abrupt contraction channel flow”, the numerical vortex length has been consistent with the experimental one. Therefore, the research has contributed to improvement of the reliability of numerical schemes.