一种用于材料点方法中简单且准确的Neumann热边界施加的虚拟热流方法
A Virtual Heat Flux Method for Simple and Accurate Neumann Thermal Boundary Imposition in the Material Point Method
AI总结：
本文提出了一种虚拟热流方法，用于在材料点方法中高效且准确地施加Neumann型热边界条件，通过构建虚拟流场简化计算过程，提升热力学模拟的精度和稳定性。
摘要：
在材料点方法（MPM）中，准确施加Neumann型热边界条件，特别是对流热流边界条件，仍然是一个重大挑战，因为复杂演变材料边界与固定背景网格之间存在固有不一致性。本文介绍了一种新的虚拟热流方法（VHFM），以克服这一限制。核心思想是构建一个围绕物理边界周围的虚拟流场，该流场恰好满足所规定的边界条件。这将弱形式中的表面积分转换为等效且易于计算的体积积分。因此，VHFM消除了显式边界跟踪、专用边界粒子或复杂表面重建的需要。提出了一个统一的公式，展示了该方法向一般标量、向量和张量Neumann条件的简单扩展。通过一系列数值基准测试，包括1D瞬态分析、2D和3D弯曲边界以及具有大旋转和复杂移动几何的问题，严格验证了VHFM的准确性、鲁棒性和收敛性。结果表明，VHFM的准确性与符合节点法相当，并显著优于传统粒子法。其简单性、计算效率和鲁棒性使其成为将准确的热边界条件整合到热力学和其它多物理场MPM框架中的有吸引力的解决方案。
英文摘要：
In the Material Point Method (MPM), accurately imposing Neumann-type thermal boundary conditions, particularly convective heat flux boundaries, remains a significant challenge due to the inherent nonconformity between complex evolving material boundaries and the fixed background grid. This paper introduces a novel Virtual Heat Flux Method (VHFM) to overcome this limitation. The core idea is to construct a virtual flux field on an auxiliary domain surrounding the physical boundary, which exactly satisfies the prescribed boundary condition. This transforms the surface integral in the weak form into an equivalent, and easily computed, volumetric integral. Consequently, VHFM eliminates the need for explicit boundary tracking, specialized boundary particles, or complex surface reconstruction. A unified formulation is presented, demonstrating the method's straightforward extension to general scalar, vector, and tensor Neumann conditions. The accuracy, robustness, and convergence of VHFM are rigorously validated through a series of numerical benchmarks, including 1D transient analysis, 2D and 3D curved boundaries, and problems with large rotations and complex moving geometries. The results show that VHFM achieves accuracy comparable to conforming node-based imposition and significantly outperforms conventional particle-based approaches. Its simplicity, computational efficiency, and robustness make it an attractive solution for integrating accurate thermal boundary conditions into thermo-mechanical and other multiphysics MPM frameworks.
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