We present a novel isogeometric method, namely the Immersed Boundary-Conformal Method (IBCM), that features a layer of discretization conformal to the boundary while employing a simple background mesh for the remaining domain. In this manner, we leverage the geometric flexibility of the immersed boundary method with the advantages of a conformal discretization, such as intuitive control of mesh resolution around the boundary, higher accuracy per degree of freedom, automatic satisfaction of interface kinematic conditions, and the ability to strongly impose Dirichlet boundary conditions. In the proposed method, starting with a boundary representation of a geometric model, we extrude it to obtain a corresponding conformal layer. Next, a given background B-spline mesh is cut with the conformal layer, leading to two disconnected regions: an exterior region and an interior region. Depending on the problem of interest, one of the two regions is selected to be coupled with the conformal layer through Nitsche's method. Such a construction involves Boolean operations such as difference and union, which therefore require proper stabilization to deal with arbitrarily cut elements. In this regard, we follow our precedent work called the minimal stabilization method [1]. In the end, we solve several 2D benchmark problems to demonstrate improved accuracy and expected convergence with IBCM. Two applications that involve complex geometries are also studied to show the potential of IBCM, including a spanner model and a fiber-reinforced composite model. Moreover, we demonstrate the effectiveness of IBCM in an application that exhibits boundary-layer phenomena.
翻译:我们提出了一个新型的等离子测量方法,即混合边界-正式方法(IBCM),该方法具有与边界一致的分解层,同时对剩余区域使用简单的背景网格。我们以这种方式利用浸入边界方法的几何灵活性,利用分解方法的优点,例如直观地控制边界周围的网状分辨率、更高程度的自由度、界面动态条件的自动满意度以及强力强制实施Drichlet边界条件的能力。在拟议方法中,从几何模型的边界代表开始,我们将其挤压,以获得相应的符合边界层。接着,我们利用一个给定背景的B-线网格网格与符合边界的层隔开,导致两个互连区域:一个外部区域和一个内部区域。根据兴趣问题,选择两个区域中的一个区域与Nitsche 模型方法的相连接。这种构建涉及诸如差异和结合等最起码的操作,因此需要适当稳定地处理任意截断的元素。在这方面,我们用一个背景B-S-S-S-S-S-S-C-C-B-C-C-C-我们用一个预期的准确性标准来展示我们用一个标准化-B-B-CM-B-CM-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-一个标准化-一个比-一个比-一个比-一个比-一个我们研究的标准化-一个比较-一个比较-一个要求一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比较-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个比-一个