A fourth-order finite volume embedded boundary (EB) method is presented for the unsteady Stokes equations. The algorithm represents complex geometries on a Cartesian grid using EB, employing a technique to mitigate the "small cut-cell" problem without mesh modifications, cell merging, or state redistribution. Spatial discretizations are based on a weighted least-squares technique that has been extended to fourth-order operators and boundary conditions, including an approximate projection to enforce the divergence-free constraint. Solutions are advanced in time using a fourth-order additive implicit-explicit Runge-Kutta method, with the viscous and source terms treated implicitly and explicitly, respectively. Formal accuracy of the method is demonstrated with several grid convergence studies, and results are shown for an application with a complex bio-inspired material. The developed method achieves fourth-order accuracy and is stable despite the pervasive small cells arising from complex geometries.
翻译:为不稳定的斯托克斯方程式提出了第四级固定体积嵌入边界法(EB),算法代表了使用EB的笛卡尔网格上复杂的几何,使用了一种技术来缓解“小切细胞”问题,而没有网格修改、细胞合并或州再分配。空间离散是基于一种加权最小方位技术,该技术已扩大到第四级操作者和边界条件,包括执行无差异限制的大致预测。采用第四级添加剂隐含的罗格-库塔方法,及时推进解决办法,并隐含和明确地分别处理粘度和源词。这种方法的形式准确性通过若干网格趋同研究得到证明,并展示了使用复杂的生物激励材料的应用结果。发达方法达到了第四级精确度,尽管复杂的地理模型产生的小细胞十分普遍,但稳定。