发表机构
MPI-CB; UZH（马克斯·普朗分子生物细胞遗传学研究所; 苏黎世大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种无网格数值求解器，可求解含可变形界面的体-面耦合问题，经生长球质量守恒、不可压缩Navier-Stokes流体耦合反应-扩散等算例验证，还实现了生物形态发生的双向耦合模拟。
AI 中文摘要
在诸多系统中，可变形表面或界面与周围体流体之间的相互作用，与移动表面内的固有时空动态耦合，实例包括肿瘤生长、生物组织形态发生、心脏力学、多相表面活性剂化学、增材制造、衣物磨损以及反应性燃烧流等。求解此类问题既需要几何计算算法来跟踪和解析表面，也需要数值方法来求解表面及周围体相中的耦合控制方程。本文针对此类具有可变形界面的体-面耦合问题，提出了一种完全无网格的数值求解器。该求解器隐式跟踪表面，基于耦合周围流体相的应力平衡求解动态表面几何。我们展示了生长球上质量守恒情形的收敛性，求解了耦合表面内非线性反应-扩散动态的不可压缩Navier-Stokes流体的体-面耦合问题，最后展示了生物形态发生模型，同时求解动态表面形状与弯曲表面上的场，并实现双向耦合。
英文摘要
In many systems, the interaction between a deformable surface or interface and the surrounding bulk fluid is coupled with intrinsic spatiotemporal dynamics within the moving surface. Examples include tumor growth, biological tissue morphogenesis, cardiac mechanics, multi-phase surfactant chemistry, additive manufacturing, clothing wear-and-tear, and reactive combustion flows. Solving such problems requires both geometric computing algorithms to track and resolve the surface and numerical methods to solve the coupled governing equations in the surface and the surrounding bulk phase. Here, we present a fully meshfree numerical solver for such coupled bulk-surface problems with deformable interfaces. The presented solver tracks the surface implicitly, solving for the dynamic surface geometry based on stress balance coupled to surrounding fluid phases. We show convergence for a mass-conserving case on a growing sphere and solve bulk-surface problems with incompressible Navier-Stokes fluids coupled to in-surface nonlinear reaction-diffusion dynamics. Finally, we show a model of biological morphogenesis, solving simultaneously for the dynamic surface shape and the fields on the curved surface with two-way coupling.
