دانلود رایگان مقاله روش Nitsche unfitted برای تعامل تراکم ناپذیر سازه سیال با مش روی هم افتاده

1. Introduction

The use of Nitsche’s method for the coupling of multiphysics problems in computational mechanics has received increasing attention recently (see, e.g., [1]). Thanks to its flexibility and the mathematical soundness it has been used to design methods for several problems. Examples include XFEM of elasticity, i.e., interface problems on unfitted meshes [2,3], and robust and accurate fictitious domain methods [4]. Nitsche’s method was first applied to fluid– structure interaction problems in the framework of space–time Galerkin methods in [5] and used to design stable loosely coupled fluid–structure interaction methods in [6,7]. The objective of this note is to apply these techniques to design a computational method for fluid–structure interaction on unfitted meshes. The use of fictitious domain or immersed boundary methods for the numerical simulation of fluid–structure interaction problems was pioneered in the works [8–11] and has recently seen a surge of interest in papers such as [12–14].

6. Conclusion

We have introduced a Nitsche type method for incompressible fluid–structure interaction problems with unfitted meshes. The interface is defined as a part of the solid mesh, which is then glued onto the unfitted fluid mesh. The basic ingredients of the method are: • integration of the fluid equations only in the physical domain (cut elements); • Nitsche’s treatment of the interface coupling conditions (kinematic/kinetic coupling); • ghost-penalty stabilization to guarantee robustness. For the space semi-discrete formulation, an a priori error estimate has been derived (Theorem 3.1), which guarantees optimal accuracy with respect to the piecewise affine interpolation used. We have then discussed the stability and accuracy of fully discrete formulations based on implicit and explicit coupling schemes. The numerical results confirmed the theoretical findings. In particular, an overall optimal first-order convergent rate was obtained with the implicit schemes (Algorithm 1) and the explicit coupling scheme with extrapolation/correction (Algorithm 3).