Accurate Cartesian-grid simulations of near-body flows at intermediate Reynolds numbers

Abstract

An accurate Cartesian-grid treatment for intermediate Reynolds number fluid-solid interaction problems is described. We first identify the inability of existing immersed boundary methods to handle intermediate Reynolds number flows to be the discontinuity of the velocity gradient at the interface. We address this issue by generalizing the Boundary Data Immersion Method (BDIM, Weymouth and Yue, J. Comp. Phys., vol. 230, 2011), in which the field equations of each domain are combined analytically, through the addition of a higher order term to the integral formulation. The new method, featuring a second-order convolution, retains the desirable simplicity of direct forcing methods and smoothes the velocity field at the fluid-solid interface while removing its bias. This results in accurate flow predictions and pressure fields without spurious fluctuations, even at high Reynolds number where the method is second order in the L 2 norm. A treatment for sharp corners is also derived that significantly improves the flow predictions near the trailing edge of thin airfoils. The second-order BDIM is applied to unsteady problems relevant to ocean energy extraction as well as animal and vehicle locomotion for Reynolds numbers up to 10 5 .

Unsteady dynamics of rapid perching manoeuvres

“…Previous work has validated this approach for a variety of dynamic rigid-body problems such as accelerating aerofoils (Wibawa et al 2012) and deformingbody problems (Weymouth & Triantafyllou 2013). In Maertens & Weymouth (2015) this method was validated against stationary and flapping aerofoil test cases at moderate Re and found to produce accurate and efficient numerical solutions.…”

“…The Boundary Data Immersion Method (BDIM), a robust immersed boundary method suitable for dynamic fluid-structure interaction problems detailed in Weymouth & Yue (2011) and Maertens & Weymouth (2015), was used for this purpose. Briefly, the full Navier-Stokes equations and the prescribed body kinematics shown in figure 1 are convolved with a kernel of support = 2h, where h is the grid spacing.…”

Performance augmentation mechanism of in-line tandem flapping foils

“…This method has been shown to give accurate results for a variety of problems including towed cylinders (Weymouth 2014), boundary layer instabilities (Maertens & Triantafyllou 2014), vorticity shedding of shrinking cylinders (Weymouth et al 2012) and unsteady dynamics of perching manoeuvres (Polet et al 2015). This method has second-order convergence, and can predict the aerodynamic forces on flapping foils to a high accuracy (Maertens & Weymouth 2015). A Cartesian grid is used, which avoids the difficulties associated with meshing moving boundary problems, and allows a large parameter space to be investigated with relative ease.…”

Shape of retracting foils that model morphing bodies controls shed energy and wake structure

“…The method is well validated for foils with very similar grid spacing and resolution (Maertens & Weymouth 2015), as well as dynamic deforming bodies , 2013. Based on previous convergence studies with 100 grid points per chord length near the foil (Maertens & Weymouth 2015), the resolution is chosen to be 96 points across the chord length of the foil. An adaptive time-stepping scheme was used, with an average step of about 0.1 ∆x U .…”

“…Simulations were performed using the boundary data immersion method, a robust immersed boundary method implemented on a Cartesian-grid, specifically developed for fluid-body interactions (Weymouth & Yue 2011;Maertens & Weymouth 2015). The method is well validated for foils with very similar grid spacing and resolution (Maertens & Weymouth 2015), as well as dynamic deforming bodies , 2013.…”