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

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.

Francisco Toja-Silva, Julien Favier, Alfredo Pinelli. Radial Basis Function (RBF)-based Interpolation and Spreading for the Immersed Boundary Method. Computers and Fluids, 2014, 105, pp.66-75. ⟨10.1016/j.compfluid.2014.09.026⟩. ⟨hal-01069809⟩

Journal: Computers and Fluids

Date de publication: 10-12-2014

Auteurs:
  • Francisco Toja-Silva
  • Julien Favier
  • Alfredo Pinelli

Digital object identifier (doi): http://dx.doi.org/10.1016/j.compfluid.2014.09.026


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