Assessment of two immersed boundary methods for flow over thin plates and sharp edges

Abstract

The extension of two different immersed boundary methods is proposed and applied to the numerical computation of uniform flow over blunt and sharp bodies: a directional version of the multi-direct forcing method and a semi-implicit version of the local ghost cell method; the first is an indirect and the second a direct method. These methods are investigated by applying them to incompressible laminar flows. The salient features of the methods are described with special emphasis on the ability to compute flows past thin plates and sharp edges. The transport equations are discretized by using the finite difference method in a Cartesian grid. The immersed boundary is represented by a finite number of Lagrangian points distributed over the solid–fluid interface. In order to test the accuracy of these approaches, three different benchmark cases are assessed. The directional version of the multi-direct forcing method is in good accordance with the flow past blunt bodies. However, it shows some numerical inconsistency when dealing with sharp and thin geometries due to the discontinuity present in the velocity and pressure fields. On the other hand, the semi-implicit version of the local ghost cell method presents good agreement with analytical, numerical and experimental data of all simulated cases.