A Computationally Efficient Dynamic Grid Motion Approach for Arbitrary Lagrange–Euler Simulations

Abstract

The present article addresses the topic of grid motion computation in Arbitrary Lagrange–Euler (ALE) simulations, where a fluid mesh must be updated to follow the displacements of Lagrangian boundaries. A widespread practice is to deduce the motion for the internal mesh nodes from a parabolic equation, such as the harmonic equation, introducing an extra computational cost to the fluid solver. An alternative strategy is proposed to minimize that cost by changing from the parabolic equation to a hyperbolic equation, implementing an additional time derivative term allowing an explicit solution of the grid motion problem. A fictitious dynamic problem is thus obtained for the grid, with dedicated material parameters to be carefully chosen to enhance the computational efficiency and preserve the mesh quality and the accuracy of the physical problem solution. After reminding the basics of the ALE expression of the Navier–Stokes equations and describing the proposed hyperbolic equation for the grid motion problem, the paper provides the necessary characterization of the influence of the fictitious grid parameters and the analysis of the robustness of the new approach compared to the harmonic reference equation on a significant 2D test case. A 3D test case is finally extensively studied in terms of computational performance to highlight and discuss the benefits of the hyperbolic equation for ALE grid motion.