线性化粘弹流体流的自适应亏量校正算法研究（英文）

Adaptive Defect Correction for Linearized Viscoelastic Flow

本文研究粘弹性非牛顿流体的数值计算问题.粘弹性非牛顿流体是介于流体和固体之间的,具有复杂本构关系的物质.由于该问题极其复杂,它的数值模拟非常困难.本文将预估校正方法和自适应有限元方法结合起来研究了线性化粘弹流体流.理论上得到了自适应预估校正方法的可依赖后验误差估计.最后给出一些数值试验验证了自适应预估校正方法对于线性化粘弹流体流的有效性.本文为进一步研究更复杂的粘弹性非牛顿流体奠定了基础.

This paper is concerned with some numerical computation on viscoelastic non- Newtonian fluids. Viscoelastic non-Newtonian fluids can be viewed as the intermediate states between the fluids and the solids. As viscoelastic non-Newtonian fluids is complex, it is very difficult to numerically solve the problem. In this paper, we combine the defect correction method and the adaptive method to study linearized viscoelastic fluid flow. A reliable a posteriori error estimate is derived for the adaptive defect correction method. Numerical experiments are provided which ill-ustrate the utility of the resulting adaptive defect correction method for linearized viscoelastic fluid flow. The obtained results can be viewed as the basis for further research on more complex viscoelastic non-Newtonian fluids.