Problem
Research questions and friction points this paper is trying to address.
deformable interface
spatiotemporal dynamics
coupled bulk-surface problems
A meshfree solver for coupled bulk-surface problems with self-organizing surface geometry
🤖 AI Summary
本文提出了一种无网格数值求解器，用于解决具有自组织表面几何的可变形界面与周围流体耦合的问题，通过隐式跟踪表面并求解应力平衡。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
meshfree solver
coupled bulk-surface problems
self-organizing surface geometry
implicit surface tracking
stress balance
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