An Adaptively Refined Least-Squares Finite Element Method for Generalized Newtonian Fluid Flows Using the Carreau Model

Numerical Simulations of Viscoelastic Fluid Flows Using a Least-Squares Finite Element Method Based on Von Mises Stress Criteria

“…Our method couples the LS method (13) with the adaptively refined algorithms presented in [7] for the generalized Newtonian fluid flows. In the work, to capture the flow region of the Oldroyd-B model, we employ the adaptive mesh algorithm in [7], using the grading function of the least-squares solutions such as velocity magnitude as shown in [9]. The LS method with the adaptive algorithm using the grading function of variables.…”

“…To resolve these problems, adaptive LS methods have been extensively used as powerful tools for obtaining more efficient and accurate results [6]- [8]. In [7], an adaptive refined LS approach (ALS) generated using a velocity magnitude is developed to refine the mesh adaptively for the Carreau generalized Newtonian fluid flows. As affected by stress in the viscoelastic fluid problem, the current motion of the fluid is associated with viscosity and elasticity.…”

“…Based on the idea, it is meaningful to use the von Mises stress as a characteristic stress magnitude as a superposition of the polymeric and viscous stresses in viscoelastic fluid flows. To capture the flow region and understand the flow feature, we modify the adaptive mesh algorithm in [7] by using the von Mises stress to refine grid points. To prevent the loss of mass conservation and convergence of numerical schemes when low-order basis functions are used, a LS method involving appropriate mass conservation weights is used in the study.…”

Decoupled algorithm for solving Phan-Thien–Tanner viscoelastic fluid by finite element method

“…In recent years, the least-squares finite element method has been developed for many applications in fluid mechanics [7][8][9][10][11][12][13]. In [7], Bochev and Gunzburger gave a weighted least-squares finite element method for an equivalent first order Stokes system.…”

“…In [7], Bochev and Gunzburger gave a weighted least-squares finite element method for an equivalent first order Stokes system. The least-squares finite element method has also been applied to the Oldroyd-B, Carreau, Giesekus and upperconvected Maxwell models for numerical simulations, see e.g., [4,[11][12][13]. The least-squares finite element method is based on the minimization of a quadratic functional including the residuals of each equation multiplied by a proper weight.…”