Full-Eulerian Finite-Difference Simulation of Fluid Flow in Hyperelastic Wavy Channel

Fluid flows interacting with deformable wavy channel are simulated by a newly developed full-Eulerian simulation method. A single set of the governing equations for fluid and solid is employed, and a volume-of-fluid (VOF) function is used for describing the multi-component geometry. The stress field is defined by volume-averaging the stresses of the individual components through VOF. The temporal change in the solid deformation is described on the Eulerian frame by updating a left Cauchy-Green deformation tensor. The SMAC method is employed, and a second-order Adams-Bashforth and Crank-Nicolson methods are applied for time-updating the momentum equation. The spatial derivatives are discretized by the second-order central difference, except for the advections of the VOF and the left Cauchy-Green tensor (fifth-order WENO scheme). The full-Eulerian fluid-structure coupling method is applied to a pressure-driven elastic wavy channel of sinusoidal wall geometry to study the interaction between a fluid and elastic object. The elastic walls oscillate as it interacts with the fluid, and the transient phenomenon to steady state is simulated. With a neo-Hookean viscoelastic model as a constitutive law, the obtained numerical results of the elastic wall deformations (for different moduli of elasticity) show good agreements with the theoretical prediction employing the lubrication and steady Stokes approximations. Also, under some pulsating pressure conditions, a nonlinear behavior of the flow rate is studied by varying the amplitude of the pressure difference.