國立臺南大學應用數學系

講題:Mathematics journeying with rheology:Least-squares finite element methods for viscoelastic fluid flows past a transverse slot problem

講師:Hsueh-Chen Lee

時間:10/18（五）10：00~11：30

地點:格致樓 C201 教室

摘要:The mountains flowed before the Lord.' Thus, the prophetess of the Old Testament sang, beginning an epic song, mathematics journeying with rheology. We develop a numerical method for linear Phan-Thien–Tanner (PTT) viscoelastic fluid flows; in contrast to the Newtonian flows, the problems are associated with fluid viscosity and elasticity. We consider least-squares finite element method with stabilized weights for the viscoelastic model and prove that the LS approximation converges to the linearized solutions of the linear PTT model. An a posteriori error estimator of the LS functional is used for an adaptive weight iteration approach. For numerical experiments we first consider the flow through a planar channel to illustrate our theoretical results. The LS method is then applied to a flow through the slot channel with two depth ratios and the effects of physical parameters are discussed. Numerical solutions of the channel problem indicate that flow characteristics of the viscoelastic polymer solution are described by the results obtained using the method. Furthermore, we present the hole pressure for various Weissenberg numbers, and compare with that derived from the Higashitani–Pritchard (HP) theory. Finally, non-Newtonian fluid flows past a square cline will be presented here.