Abstract
In this work three branches of Immersed Boundary Methods (IBM) are described and validated for incompressible aerodynamics and fluid-structure interactions. These three approaches are: Cut Cell method, Vortex-Penalization method and Forcing method. Two first techniques are validated for external bluff-body flows and the last one is used for fluid-structure interactions. The paper confirms the ability of this family of numerical schemes for accurate and robust simulation of incompressible flows.
Highlights
In this work three branches of Immersed Boundary Methods (IBM) are described and validated for incompressible aerodynamics and fluid-structure interactions
The Cut-cell methods, called Cartesian grid methods, focus on the discretization of the equations in the mesh cells cut by the immersed boundary
As the boundary conditions are directly imposed, there is no diffusion of the interface fluid-solid. These methods are highly efficient from a computational point of view as it is based on the MAC solver on cartesian grids which has been extensively and successfully used in numerical simulations of turbulent flows, both in the context of direct and Large-Eddy simulations
Summary
We consider a two-dimensional flow past a solid obstacle ΩS ⊂ R2 which is governed by the incompressible Navier-Stokes equations. We denote by ΩF the fluid domain in which the Navier-Stokes equations (2.1)-(2.3) are prescribed so that we have Ω = ΩF ∪ ΩS ∪ ΓS where ΓS = ∂ΩS is the solid boundary. In order to determine the location of each point in the computational domain with respect to the solid boundary ΓS, we use the signed algebraic distance to ΓS, which is given by d : Ω −→ R (x, y) −→ d(x, y). Mesh sizes are defined by : li = xi − xi−1 and hj = yj − yj−1. In order to simplify the notations we denote by dij = d(xi, yj) the algebraic distance of the grid point (xi, yj) to the solid boundary ΓS
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