High-order stabilized matrix-free simulation of rotating mixing devices using the Mortar Element Method

Abstract

We present a finite element framework to simulate rotating mixing devices using the Mortar Element Method as a domain decomposition strategy. The model is implemented within a matrix-free Navier-Stokes framework which uses a high-order Continuous Galerkin method. The discretized domain is subdivided into rotor and stator parts. An Arbitrary Lagrangian-Eulerian approach accounts for the relative rotor-stator motion, and stabilization is ensured through the Streamline-Upwind/Petrov-Galerkin and Pressure-Stabilizing Petrov-Galerkin methods. The rotor-stator domains are connected by an interface composed of mortar cells, and continuity is weakly enforced in a Discontinuous Galerkin fashion by accounting for boundary integrals at the rotor-stator interface. Verifications of the convergence order in two-dimensional steady and transient examples report optimal rates. The geometric non-conformity created at the mortar interface due to rotor rotation does not introduce significant error in the solution. A three-dimensional example is used to investigate the model's scalability, which yields ideal strong scaling for large problems. A two-dimensional Rushton impeller example uses a torque analysis to showcase the mesh convergence, and the corresponding velocity profile is in agreement with existing numerical results. In a three-dimensional pitched blade turbine case, the power number curve (Np vs Re) shows good agreement with experimental data for Reynolds number values from 1 to 2000. An energy balance analysis reports a numerical dissipation of 1% for Re=200 and of 10% for Re=2000. By exploiting modern hardware capabilities through matrix-free methods, the proposed model is a robust, accurate, and efficient framework suitable for simulating flows with rotating geometries.