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Unsteady residual distribution schemes adapted to immersed boundary methods on unstructured grids to account for moving bodies

Abstract : The interest on immersed boundary methods (IBM) increases in Computational Fluid Dynamics because they simplify the mesh generation problem when dealing with the Navier-Stokes equations. To give a few examples, they simplify the simulation of multi-physics flows, the coupling of fluid-solid interactions in situation of large motions or deformations. Nevertheless an accurate treatment of the wall boundary conditions remains an issue of the method. In this work, a penalty term added to the Navier-Stokes equations accounts for the wall boundary conditions and accuracy is recovered using unstructured mesh adaptation. When a penalization technique is used as an IBM, the idea is to extend the velocity field inside the solid body (penalty term) in order to enforce rigid motion of this body. A level set function, the sign distance function to the solids, is used to capture interfaces of the solid bodies. Our numerical simulations are performed on unstructured anisotropic meshes (2D-triangles or 3D-tetrahedra) and we propose to combine our level-set based penalization approach to mesh adaptation [1]. The idea is to conserve the simplicity of the embedded approaches for grid generation process and overcome the difficulty of wall treatments by using mesh adaptation. Mesh adaptations are performed using two criteria, the distance to the level-set 0 (interface of the solid body) and the quality of the flow solution (Hessian of the velocity component or the density). Using some test cases we demonstrate the ability of the proposed method to obtain an accurate solution along with an accurate wall treatment even when the initial mesh does not contain any point on the level-set 0. Residual distribution schemes on unstructured meshes [2] are used to solve the equations: an implicit scheme for steady flows and an explicit one along with a specific splitting algorithm for penalized unsteady flows. Those numerical schemes allow the construction of a high order method with compact stencil to ease parallelism. Validations of the proposed method are performed using static and moving bodies. [1] R. Abgrall, H. Beaugendre, and C. Dobrzynski. An immersed boundary method using unstructured anisotropic mesh adaptation combined with level-sets and penalization techniques. JCP, 257:83–101, 2014. [2] M. Ricchiuto and R. Abgrall. Explicit Runge-Kutta residual distribution schemes for time dependent problems: second order case. JCP, 229(16):5653–5691, 2010.
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Contributor : Héloïse Beaugendre <>
Submitted on : Monday, January 18, 2016 - 10:02:49 AM
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  • HAL Id : hal-01257678, version 1



Héloïse Beaugendre, Léo Nouveau, Cecile Dobrzynski, Remi Abgrall, Mario Ricchiuto. Unsteady residual distribution schemes adapted to immersed boundary methods on unstructured grids to account for moving bodies. 13th US National Congress on Computational Mechanics, Jul 2015, San Diego, United States. ⟨hal-01257678⟩



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