Grid Convergence Tests Research Articles

J0206-3-3 超弾性体管内流のオイラー型流体構造連成解析([J0206-3]生命体統合シミュレーション(3))

Abstract An interaction problem between a fluid and elastic walls is solved by a full Eulerian fluid-structure coupling method. The method employs a uniform grid system for both fluid and solid and it does not require any mesh generation or reconstruction, aming at facilitating the practical bio-mechanical fluid-structure analysis. The availability and applicability of the developed method to systems involving complex geometries driven by a pressure gradient are shown through a comparison between the obtained numerical results and theoretical prediction, and a grid convergence test. Further, pulsating flow simulation are performed to demonstrate the effect of the pulsating amplitude on the flow rate.

Computations of flow over a flexible plate using the hybrid Cartesian/immersed boundary method

AbstractA hybrid Cartesian/immersed boundary code is developed and applied to interactions between a flexible plate and a surrounding fluid. The velocities at the immersed boundary (IB) nodes are reconstructed by interpolations along local normal lines to an interface. A new criterion is suggested to distribute the IB nodes near an interface. The suggested criterion guarantees a closed fluid domain by a set of the IB nodes and it is applicable to a zero‐thickness body. To eliminate the pressure interpolation at the IB nodes, the hybrid staggered/non‐staggered grid method is adapted. The developed code is validated by comparisons with other experimental and computational results of flow around an in‐line oscillating cylinder. Good agreements are achieved for velocity profiles and vorticity and pressure contours. As applications to the fluid–structure interaction, oscillations of flexible plate in a resting fluid and flow over a flexible plate are simulated. The elastic deformations of the flexible plate are modelled based on the equations of motion for plates considering the fluid pressure as the external load on the plate. Two non‐dimensional parameters are identified and their effects on the damping of the plate motion are examined. Grid convergence tests are carried out for both cases. Copyright © 2007 John Wiley & Sons, Ltd.

A hybrid Cartesian/immersed boundary method for simulating flows with 3D, geometrically complex, moving bodies

A numerical method is developed for solving the 3D, unsteady, incompressible Navier–Stokes equations in Cartesian domains containing immersed boundaries of arbitrary geometrical complexity moving with prescribed kinematics. The governing equations are discretized on a hybrid staggered/non-staggered grid layout using second-order accurate finite-difference formulas. The discrete equations are integrated in time via a second-order accurate dual-time-stepping, artificial compressibility iteration scheme. Unstructured, triangular meshes are employed to discretize complex immersed boundaries. The nodes of the surface mesh constitute a set of Lagrangian control points used to track the motion of the flexible body. At every instant in time, the influence of the body on the flow is accounted for by applying boundary conditions at Cartesian grid nodes located in the exterior but in the immediate vicinity of the body by reconstructing the solution along the local normal to the body surface. Grid convergence tests are carried out for the flow induced by an oscillating sphere in a cubic cavity, which show that the method is second-order accurate. The method is validated by applying it to calculate flow in a Cartesian domain containing a rigid sphere rotating at constant angular velocity as well as flow induced by a flapping wing. The ability of the method to simulate flows in domains with arbitrarily complex moving bodies is demonstrated by applying to simulate flow past an undulating fish-like body and flow past an anatomically realistic planktonic copepod performing an escape-like maneuver.

The effect of grid topology and density on inviscid hovering rotor solutions

Grid dependence is examined for Euler simulations of multibladed rotors in hover. The numerical simulation of rotor flows poses a unique problem for flow solvers. The solution is extremely sensitive to the accuracy of capture of the vortical wake over several turns; this means that a much finer grid density is required away from the blade than for a fixed-wing case, resulting in excessive run-times. An attempt is made to determine the number of grid points required to obtain practical results, by performing grid convergence tests for O-H and O-C grid topologies and determining the optimum ratio of grid densities in each parametric direction, for two- and four-bladed test cases. An upwind Euler solver is used on O-H and O-C structured grids, generated by transfinite interpolation along with a periodic transformation. It is shown that O-H grids produce more accurate solutions than O-C grids with the same number of points, and that 3 3 105 grid points produce inviscid solutions of sufficient accuracy for initial design. It is also shown that solutions can be improved by choosing optimum ratios of grid density in each parametric direction.