Treatment of complex geometries with fluid-solid interaction has been one of the challenging issues in CFD because most engineering problems have complex geometries with fluid-solid interaction for the purpose. The unstructured grid method and the immersed boundary method (IBM) are two different approaches that have been developed so far. This paper details the numerical investigation of 2D laminar flow over a backward facing step in hydro-dynamically developing regions (entrance region) as well in the hydro-dynamically developed regions using IBM. Although this flow represents one of the simplest expansion flows, the physics involved are rather complex. For a flow in to an expansion in the form of a step, the boundary layer separates at the step corner, forming a new free shear layer. The present numerical method is based on a finite volume approach on a staggered grid together with a fractional step approach. The momentum forcing and mass source terms are applied on the step to satisfy the no-slip boundary condition and also to satisfy the continuity for the mesh containing the same. The numerically obtained velocity profiles, and stream line plots in the channel with backward facing step shows excellent agreement with the published results in various literatures.
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