A systematic approach for constructing higher-order immersed boundary and ghost fluid methods for fluid-structure interaction problems.

*(English)*Zbl 1426.76443Summary: A systematic approach is presented for constructing higher-order immersed boundary and ghost fluid methods for CFD in general, and fluid – structure interaction problems in particular. Such methods are gaining popularity because they simplify a number of computational issues. These range from gridding the fluid domain, to designing and implementing Eulerian-based algorithms for challenging fluid – structure applications characterized by large structural motions and deformations or topological changes. However, because they typically operate on non body-fitted grids, immersed boundary and ghost fluid methods also complicate other issues such as the treatment of wall boundary conditions in general, and fluid – structure transmission conditions in particular. These methods also tend to be at best first-order space-accurate at the immersed interfaces. In some cases, they are also provably inconsistent at these locations. A methodology is presented in this paper for addressing this issue. It is developed for inviscid flows and prescribed structural motions. For the sake of clarity, but without any loss of generality, this methodology is described in one and two dimensions. However, its extensions to flow-induced structural motions and three dimensions are straightforward. The proposed methodology leads to a departure from the current practice of populating ghost fluid values independently from the chosen spatial discretization scheme. Instead, it accounts for the pattern and properties of a preferred higher-order discretization scheme, and attributes ghost values as to preserve the formal order of spatial accuracy of this scheme. It is illustrated in this paper by its application to various finite difference and finite volume methods. Its impact is also demonstrated by one- and two-dimensional numerical experiments that confirm its theoretically proven ability to preserve higher-order spatial accuracy, including in the vicinity of the immersed interfaces.

##### MSC:

76M12 | Finite volume methods applied to problems in fluid mechanics |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

##### Keywords:

embedded boundary method; fluid structure interaction; ghost fluid method; higher-order; immersed boundary method; operator matching; surrogate interface##### Software:

SHASTA
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\textit{X. Zeng} and \textit{C. Farhat}, J. Comput. Phys. 231, No. 7, 2892--2923 (2012; Zbl 1426.76443)

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