Lagrangian vs. Eulerian: An Analysis of Two Solution Methods for Free-Surface Flows and Fluid Solid Interaction Problems

As a step towards addressing a scarcity of references on this topic, we compared the Eulerian and Lagrangian Computational Fluid Dynamics (CFD) approaches for the solution of free-surface and Fluid–Solid Interaction (FSI) problems. The Eulerian approach uses the Finite Element Method (FEM) to spatially discretize the Navier–Stokes equations. The free surface is handled via the volume-of-fluid (VOF) and the level-set (LS) equations; an Immersed Boundary Method (IBM) in conjunction with the Nitsche’s technique were applied to resolve the fluid–solid coupling. For the Lagrangian approach, the smoothed particle hydrodynamics (SPH) method is the meshless discretization technique of choice; no additional equations are needed to handle free-surface or FSI coupling. We compared the two approaches for a flow around cylinder. The dam break test was used to gauge the performance for free-surface flows. Lastly, the two approaches were compared on two FSI problems—one with a floating rigid body dropped into the fluid and one with an elastic gate interacting with the flow. We conclude with a discussion of the robustness, ease of model setup, and versatility of the two approaches. The Eulerian and Lagrangian solvers used in this study are open-source and available in the public domain.

Numerical analysis of the flow around a cylinder for the perspective of correlations of the drag coefficient of the ship’s hulls

The flow around cylinder open the path for studying more complex shape bodies like the ship’s hulls. The hydrodynamic properties of the ship’s hulls can be decomposed as combinations of the flow properties of simpler bodies like flat plates, cylinders, ellipses, spheres and ellipsoids. The aim of this study is to describe the flow around a cylinder based on simulations with platforms like Comsol and Ansys that further can be compared with experimental and analytical results. The drag force caused by the flow around cylinders can be combined with the drag force of simple elements like flat plates, ellipses in order to correlate with the drag force of a specific hull of ship. Cylinder is a case that offers with its simplicity the possibility to check the results in all three ways: analytical, computational and experimental. An exhaustive analysis of this shape offers a beginning path for generalizing the external flows like the application of the superposition theory for complex geometries.

Numerical investigation of vortex-induced vibration of an elastically mounted circular cylinder with One-degree of freedom at high Reynolds number using different turbulent models

This study presents numerical investigation for flow around cylinder at Reynolds number = 104 using different turbulent models. Numerical simulations have been conducted for fixed cylinder case at Reynolds number = 104 and for cylinder free to oscillate in cross-flow direction, at Reynolds number O (104), mass–damping ratio = 0.011 and range of frequency ratio wt = 0.4–1.4 using two-dimensional Reynolds-averaged Navier–Stokes equations. In the literature, the study has been conducted using detached eddy simulation, large eddy simulation and direct numerical simulation which are comparatively expensive in terms of computational cost. This study utilizes the Reynolds-averaged Navier–Stokes shear stress transport k-ω and realizable k-ε models to investigate the flow around fixed cylinder and flow around cylinder constrained to oscillate in cross-flow direction only. Hydrodynamic coefficients, vortex mode shape and maximum amplitude ( Ay/ D) extracted from this study are compared with detached eddy simulation, large eddy simulation and direct numerical simulation results. Results obtained using two-dimensional Reynolds-averaged Navier–Stokes shear stress transport k-ω model are encouraging, while realizable k-ε model is unable to capture the entire response branches. In addition, broad range of “lock-in” region is observed due to delay in capturing the transition from upper to lower branch during two-dimensional realizable k-ε analyses.

Numerical investigation of flow around cylinder at Reynolds number = 3900 with large eddy simulation technique: Effect of spanwise length and mesh resolution

Flow around a cylinder at a Reynolds number of 3900 was studied using large eddy simulation with ICEM CFD and Fluent tools for meshing and analysis, respectively. Although this issue has been explored by numerous researchers, a discrepancy still exists in the results, particularly in calculating the angle of separation, recirculation length, and statistics in the wake region behind the cylinder. In addition, the effect of spanwise grid and near-field grid resolution on the wake region needs to be addressed. This study reviews previous work and performs analyses according to the literature recommendations. The effect of spanwise length (4D, 8D, and 16D), mesh resolution in the spanwise direction (1, 10, 20, 40, 60, 80, and 160 elements), and near-field grid on calculating recirculation length, angle of separation, and wake characteristics is investigated. Hydrodynamic values and pressure distribution around the cylinder are analyzed. The wake behind the cylinder is investigated within 10 diameters. This study concluded that compared with spanwise length, mesh resolution in the spanwise direction and near-field grid are more important factors for good-quality results.