Model Order Reduction for Viscoelastic Fluid Flows

Abstract

The study of viscoelastic fluid flows are very complexdue to the nature of the governing equations making numerical simulations a complex task.A key challenge in such flows is the stabilisation of numerical techniques which is quite often difficult to meetspecially when the Weissenberg number is high.The momentum and continuity equations form an elliptic saddle point problem for velocity and pressure and the constitutive equation is hyperbolic in nature [1]. In such flows, due to the dependency of the viscoelastic stress tensor on velocity gradients, there arises some compatibility issues in the discretisation space between velocity field and viscoelastic stress tensor. There are many improvements in the numerical techniques to treat and maintain the elliptic nature of the momentum equation. Here, we implement discrete elastic viscous split stress-Galerkin (DEVSS-G) [1,2] for smooth interpolation of velocity gradient in the constitutive equation by considering velocity gradient as an additional dependent variable. Also, due to the presence of convection term in the constitutive equation, there can arise spurious numerical oscillations in convection dominated case. So stabilisation techniques like SUPG [2,3] is applied where the test function is modified and more weightage is being put in the upwind direction.