Verification and Validation of Cylinder Drag: Pressure and Stress Approximations on Curved Boundaries

TL;DR

This paper presents a validation approach for flow simulation algorithms focusing on pressure and stress on curved boundaries, using experiments and finite-element methods to improve accuracy in cylinder drag computations.

Contribution

It introduces a validation technique for boundary stress and pressure calculations, identifies flaws in boundary condition enforcement, and demonstrates improved accuracy with Nitsche's method.

Findings

Finite-element simulations with strong Dirichlet conditions poorly represent drag.

Relaxing boundary conditions with Nitsche's method improves accuracy.

Large domain simulations confirm Lamb's model for low Reynolds numbers.

Abstract

We study a technique for verification of stress and pressure computations on boundaries in flow simulations. We utilize existing experiments to provide validation of the simulations. We show that this approach can reveal critical flaws in simulation algorithms. Using the successful computational algorithms, we examine Lamb's model for cylinder drag at low Reynolds numbers. We comment on a discrepancy observed in an experimental paper, suggesting that the domain size may be a contributing factor. Our simulations on suitably large domains confirm Lamb's model. We highlight a paradox related to imposing Dirichlet (Stokes) boundary conditions on polygonal approximations of the curved surface using finite-element methods that are exactly divergence free. The finite-element simulations provide very poor representations of drag when the boundary conditions are imposed strongly. We demonstrate that relaxing the boundary conditions using Nitsche's method restores high-order approximation.