使用复合B-SPLINES的局部无差异浸泡有限元素差异方法
Lianxia Li1, Cole Gruninger1, Jae H Lee1
1Department of Mathematics, University of North Carolina, Chapel Hill, NC, USA.
Advances in computational science and engineering
|August 22, 2025
概括
复合B线 (CBS) 内核通过保持体积保存,提高精度和降低计算成本来改善流体结构相互作用模拟. 这些核提供了稳定和高效的模拟,用于在没有额外稳定的情况下变形弹性固体.
科学领域:
- 计算流体动力学 (CFD)
- 流体结构相互作用 (FSI)
- 数字化方法
背景情况:
- 沉浸边界 (IB) 方法依赖于规范化的三角函数来进行流体和固体域之间的信息传输.
- 传统的同位素核在IB方法中往往无法保持无分歧的条件,导致固体力学中的不可压缩性错误.
- 现有的体积稳定技术增加了不可压缩弹性结构中大变形的模拟的复杂性.
研究的目的:
- 在沉浸边界模拟中评估复合B-spline (CBS) 内核的性能.
- 与传统的同位素 (IB 和 B-spline) 核相比,CBS 核的体积保护和精度.
- 在使用大变形时评估是否需要额外的体积稳定.
主要方法:
- 在沉浸式边界框架内实施和测试复合B-spline (CBS) 内核.
- 使用各种流动场景进行了基准测试:弹性带,压力膜,压缩块,库克膜,倾斜通道流量和图雷克-霍恩问题.
- 在脉冲复制器中使用生物假体心流体结构相互作用模型验证了方法.
主要成果:
- 与传统的同位素核相比,CBS核显示出较高的体积保存,因此无需明确的体积稳定.
- 在较粗的网格上使用的CBS芯片的精度与在较细的网格上使用的IB和B线芯片的精度相当.
- 与同位素核相比,CBS核具有较小的网格比率因子,并且对相对网格间距变化不那么敏感.
结论:
- 复合B线核为沉浸式边界模拟流体结构相互作用提供了稳定,准确和高效的替代方案.
- 在CBS内核中固有保持离散无分歧的特性,简化了涉及弹性固体的大变形的模拟.
- 该研究主张使用CBS核来避免复杂的FSI问题中的专用体积稳定处理.
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