A High Order Stabilized Solver for the Volume Averaged Navier-Stokes Equations

TL;DR

This paper introduces a high-order stabilized finite element solver for volume-averaged Navier-Stokes equations, improving accuracy and robustness in simulating fluid flow in complex solid-fluid systems.

Contribution

The paper develops a novel high-order finite element method with tailored stabilization for volume-averaged Navier-Stokes equations, enhancing stability, mass conservation, and convergence.

Findings

The solver preserves the order of convergence of the finite element discretization.

It effectively prevents oscillations in regions with sharp gradients.

The method accurately simulates pressure drop and mass conservation in packed bed flows.

Abstract

The Volume-Averaged Navier-Stokes equations are used to study fluid flow in the presence of fixed or moving solids such as packed or fluidized beds. We develop a high-order finite element solver using both forms A and B of these equations. We introduce tailored stabilization techniques to prevent oscillations in regions of sharp gradients, to relax the Ladyzhenskaya-Babuska-Brezzi inf-sup condition, and to enhance the local mass conservation and the robustness of the formulation. We calculate the void fraction using the Particle Centroid Method. Using different drag models, we calculate the drag force exerted by the solids on the fluid. We implement the method of manufactured solution to verify our solver. We demonstrate that the model preserves the order of convergence of the underlying finite element discretization. Finally, we simulate gas flow through a randomly packed bed and study the pressure drop and mass conservation properties to validate our model.