Artificial Stress Diffusion in Numerical Simulations of Viscoelastic Fluid Flows

The chapter delves into the complexities of modeling viscoelastic fluids, highlighting the challenges in numerical simulations due to instabilities. It introduces the concept of artificial stress diffusion as a stabilization technique, detailing four variants of diffusion terms. The Oldroyd-B model is used as a prototype for viscoelastic fluid models, and the chapter discusses the implementation of these diffusion terms in finite element methods. Numerical results demonstrate the effectiveness and potential pitfalls of each method, emphasizing the need for careful control of diffusion coefficients. The chapter concludes with a discussion of the practical implications and future directions in this field.