Abstract
We present a two-way coupled fluid–structure interaction scheme for rigid bodies using a two-population lattice Boltzmann formulation for compressible flows. An arbitrary Lagrangian–Eulerian formulation of the discrete Boltzmann equation on body-fitted meshes is used in combination with polynomial blending functions. The blending function approach localizes mesh deformation and allows treating multiple moving bodies with a minimal computational overhead. We validate the model with several test cases of vortex induced vibrations of single and tandem cylinders and show that it can accurately describe dynamic behavior of these systems. Finally, in the compressible regime, we demonstrate that the proposed model accurately captures complex phenomena such as transonic flutter over an airfoil.
Highlights
The interaction between a fluid and a deformable or moving body is an important area of research in computational mechanics
We present a two-way coupled fluid–structure interaction scheme for rigid bodies using a two-population lattice Boltzmann formulation for compressible flows
lattice Boltzmann method (LBM) arrives at the macroscopic equations of fluid dynamics from a mesoscopic perspective, where the flow is described by discretized particle distribution functions fiðx; tÞ, which are associated with a set of discrete velocities C 1⁄4 fci; i 1⁄4 0; ...; Q À 1g, forming the links of a space-filling lattice
Summary
The interaction between a fluid and a deformable or moving body is an important area of research in computational mechanics. Finite-volume LB schemes[26,27,28] such as the recently proposed DUGKS,[29] finitedifference schemes,[30,31] and finite-elements schemes such as the discontinuous Galerkin LBM32,33 are some of the approaches that are present in the literature While this does allow for non-uniform grids and a flexible CFL number, a partial differential equation for each discrete velocity needs to be solved in order to advect the populations. This typically requires small times steps and repeated non-local evaluation of spatial gradients, which leads to a significant computational overhead and can result in prohibitively high costs.[34]. These transformed discrete velocities cannot be assumed to be integers anymore, and an off-lattice propagation scheme is necessary
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