Jacob Bruno, Drawert Brian, Yi Tau-Mu, Petzold Linda
Department of Mechanical Engineering, University of California-Santa Barbara, Santa Barbara, California, 93106, USA.
Department of Computer Science, University of North Carolina at Asheville, Asheville, North Carolina, 28804, USA.
Eng Anal Bound Elem. 2021 Jul 1;128:274-289. doi: 10.1016/j.enganabound.2021.04.006. Epub 2021 Apr 22.
We present a new weakly-compressible smoothed particle hydrodynamics (SPH) method capable of modeling non-slip fixed and moving wall boundary conditions. The formulation combines a boundary volume fraction (BVF) wall approach with the transport-velocity SPH method. The resulting method, named SPH-BVF, offers detection of arbitrarily shaped solid walls on-the-fly, with small computational overhead due to its local formulation. This simple framework is capable of solving problems that are difficult or infeasible for standard SPH, namely flows subject to large shear stresses or at moderate Reynolds numbers, and mass transfer in deformable boundaries. In addition, the method extends the transport-velocity formulation to reaction-diffusion transport of mass in Newtonian fluids and linear elastic solids, which is common in biological structures. Taken together, the SPH-BVF method provides a good balance of simplicity and versatility, while avoiding some of the standard obstacles associated with SPH: particle penetration at the boundaries, tension instabilities and anisotropic particle alignments, that hamper SPH from being applied to complex problems such as fluid-structure interaction in a biological system.
我们提出了一种新的弱可压缩光滑粒子流体动力学（SPH）方法，该方法能够对无滑移固定壁和移动壁边界条件进行建模。该公式将边界体积分数（BVF）壁方法与输运速度SPH方法相结合。由此产生的方法，称为SPH-BVF，能够实时检测任意形状的固体壁，由于其局部公式，计算开销很小。这个简单的框架能够解决标准SPH难以解决或无法解决的问题，即承受大剪切应力或中等雷诺数的流动，以及可变形边界中的质量传递。此外，该方法将输运速度公式扩展到牛顿流体和线性弹性固体中质量的反应扩散输运，这在生物结构中很常见。综合来看，SPH-BVF方法在简单性和通用性之间取得了良好的平衡，同时避免了与SPH相关的一些标准障碍：边界处的粒子穿透、张力不稳定性和各向异性粒子排列，这些障碍阻碍了SPH应用于复杂问题，如生物系统中的流固相互作用。
