A semi-implicit immersed boundary methods for flow over sharp bodies

João Rodrigo Andrade¹; Ramon Silva Martins²; Aristeu Silveira Neto³; João Marcelo Vedovoto³

¹ Universidade Federal de Uberlândia / Université Lille 1; ² Universidade Federal do Espírito Santo / Université Lille 1; ³ Universidade Federal de Uberlândia

doi:10.20906/CPS/CILAMCE2017-0361

Resumo

In the present work, the local ghost cell method (LGCM) from Berthelsen and Faltinsen [J. of Comp. Phys., 227, 4354 (2007)] is extended and applied to a semi-implicit temporal integration strategy (SILGCM). The SILGCM is an immersed boundary method for which the boundary conditions are performed directly, it means, by a change in the stencil of the discretized transport equations. The numerical method proposed is applied to the computation of uniform flow over blunt and sharp bodies. This method is investigated by applying the formulation for incompressible laminar flows. Herein, the salient features of the methodology is described with special emphasis on the capacity of computation of flow past sharp bodies. The transport equations are discretized by using the finite differences method, the immersed boundary is represented with a finite number of Lagrangian points, distributed over the solid-fluid interface. A Cartesian grid is used to solve the fluid flow equations. To test the accuracy of this approach, four different benchmark cases are applied. It was shown that the semi-implicit local ghost cell method presents good agreement with analytic, numerical benchmark and experimental data of all simulated cases.

Palavras-chave: immersed boundary method; ghost cell method; Cartesian grid method; thin geometry body; sharp geometry body