2.1.5 Numerical implementation
The average bulk flow velocity was ramped up at the beginning of the
simulation (within 1 s) to reduce the computational difficulties. The
mechanical parameters of the biofilm were obtained from rheometer tests
(see Section 2.3), including the viscosity and shear modulus. All
parameters are listed in Table 1. To accommodate the incompressibility,
we used traditional Lagrange mixed finite elements (Hughes, 2012). In
particular, we used the quadratic triangular elements for the velocity
and extra stress components, and the linear elements for the pressure
discretization. To alleviate the numerical difficulty caused by the
Oldroyd-B equation, we implemented the Galerkin/Least squares
stabilization (Craven, Rees, & Zimmerman, 2006; Rajagopal & Das,
2016). We also performed model verification and mesh convergence tests
to ensure that the results were not affected by the mesh size (see
Supplementary Information SI). Based on the results, a maximum mesh size
of 50 µm was chosen for this study.