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Radial Basis Function (RBF)-based Interpolation and Spreading for the Immersed Boundary Method

Abstract : Immersed boundary methods are efficient tools of growing interest as they allow to use generic CFD codes to deal with complex, moving and deformable geometries, for a reasonable computational cost compared to classical body- conformal or unstructured mesh approaches. In this work, we propose a new immersed boundary method based on a radial basis functions frame- work for the spreading-interpolation procedure. The radial basis function approach allows for dealing with a cloud of scattered nodes around the im- mersed boundary, thus enabling the application of the devised algorithm to any underlying mesh system. The proposed method can also keep into ac- count both Dirichlet and Neumann type conditions. To demonstrate the capabilities of our novel approach, the imposition of Dirichlet boundary con- ditions on a 2D cylinder geometry in a Navier-Stokes CFD solver, and the imposition of Neumann boundary conditions on an adiabatic wall in an un- steady heat conduction problem are considered. One of the most significant advantage of the proposed method lies in its simplicity given by the algo- rithmic possibility of carrying out the interpolation and spreading steps all together, in a single step.
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Francisco Toja-Silva, Julien Favier, Alfredo Pinelli. Radial Basis Function (RBF)-based Interpolation and Spreading for the Immersed Boundary Method. Computers and Fluids, Elsevier, 2014, 105, pp.66-75. ⟨10.1016/j.compfluid.2014.09.026⟩. ⟨hal-01069809⟩

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