复合B-spline调整的三角函数用于沉浸边界方法:无分歧的插值和梯度保持力的扩散力
Cole Gruninger1, Boyce E Griffith1,2,3,4,5,6
1Department of Mathematics, University North Carolina, Chapel Hill, NC, USA.
Journal of computational physics
|January 15, 2026
概括
这项研究提高了沉浸边界 (IB) 方法中的体积保存,使用复合B-spline三角函数. 这种方法通过减少虚流量,改善了流体结构相互作用的模拟,特别是对于封闭的膜.
科学领域:
- 计算流体动力学的流体动力学.
- 流体结构相互作用 流体结构相互作用
- 数学方法 数学方法
背景情况:
- 沉浸边界 (IB) 方法被广泛用于流体结构相互作用 (FSI) 问题.
- 传统的IB方法存在体积保护不良的问题,特别是在压缩,封闭膜的模拟中.
- 这种限制阻碍了生物流和灵活结构等应用中的准确性.
研究的目的:
- 为了增强沉浸边界方法中的体积保存.
- 引入一个计算效率高的方法,使用由复合B-splines衍生的调整的三角函数.
- 为非本地方法提供替代方案,例如无分歧沉浸边界 (DFIB) 方法.
主要方法:
- 采用正则化的三角函数,由由方向依赖多项式度的复合B-splines构建而成.
- 利用张量产品内核,类似于传统IB方法,但具有增强的B-spline属性.
- 保持了IB方法的局部性质,避免了DFIB所需的复杂的Poisson解决方案.
主要成果:
- 复合B-spline调节的三角函数显著改善了体积保护.
- 该方法提供了连续无分歧的速度介质,并正确地将压力跳跃力表示为离散梯度.
- 使用常规复合B-splines的模拟实现了与DFIB相比的体积保存,其中错误主要是由时间渐进的截断.
结论:
- 拟议的方法为IB方法提供了计算效率高且可访问的增强.
- 它通过准确地建模力和插曲速度,有效地消除了假流.
- 这种方法对于大规模的3DFSI模拟特别有利,需要大体积保存.
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