A novel immersed boundary velocity correction-lattice Boltzmann method and its application to simulate flow past a circular cylinder.

*(English)*Zbl 1173.76395Summary: A novel immersed boundary velocity correction-lattice Boltzmann method is presented and validated in this work by its application to simulate the two-dimensional flow over a circular cylinder. The present approach is inspired from the conventional immersed boundary method (IBM). In the conventional IBM, the effect of rigid body on the surrounding flow is modeled through a forcing term, which is in turn used to correct the surrounding velocity field. It was found that this process is actually an iterative procedure, trying to satisfy the non-slip boundary condition at the solid wall. In this work, a new concept of immersed boundary velocity correction approach is proposed, which directly corrects the velocity to enforce the physical boundary condition. The main advantage of the new method is that it is simple in concept and easy for implementation, and the convergence of numerical computation is faster and more stable than the conventional IBM. One challenging issue of conventional IBM is that some streamlines may pass through the solid body since there is no mechanism to enforce the non-slip condition at the boundary. As shown in the present numerical results, this unphysical phenomenon is avoided in our new method since the non-slip condition is enforced. The present results for the steady and unsteady flows compare very well with available data in the literature.

##### Keywords:

Incompressible flow; immersed boundary method; velocity correction; lattice Boltzmann method; flow around cylinder; Cartesian mesh
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\textit{C. Shu} et al., J. Comput. Phys. 226, No. 2, 1607--1622 (2007; Zbl 1173.76395)

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