稳定、紧凑且直接的虚拟单元重构：嵌入式边界方法的非迭代方法
Stable, Compact, and Direct Ghost-Cell Reconstruction: A Non-Iterative Approach for Embedded-Boundary Methods
- Khalifa University of Science and Technology（Khalifa 科学与技术大学）
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AI总结：
提出一种直接、解析、非迭代的虚拟单元重构框架，用于嵌入式边界方法，通过拓扑排序和混合虚拟单元实现稳定紧凑的边界条件施加，并验证于圆柱和翼型绕流。
AI中文摘要：
针对笛卡尔网格嵌入式边界方法，开发了一种直接、解析且非迭代的虚拟单元重构框架。解析表达式直接在嵌入式边界上施加Dirichlet和Neumann边界条件，消除了中间像点重构、矩阵求逆以及几何相关重构权重的预计算或存储。对于所考虑的笛卡尔模板，相邻虚拟单元之间的依赖关系形成有向无环图。拓扑排序将虚拟单元划分为依赖层级，允许逐级重构而无需迭代更新。该公式与混合虚拟单元（HGC）相结合，其中心可位于嵌入式边界的任一侧。这种布置满足先前针对标量平流推导的线性重构稳定性准则，同时保留紧凑的最近邻笛卡尔模板。扩展模板的经典虚拟单元公式（CGC_ES）作为保持稳定性的参考，以区分重构稳定性和模板紧凑性的影响。相同的解析关系直接在嵌入式边界上提供解值和空间梯度，使得无需单独的表面重构或滤波即可评估压力力、壁面应力、阻力和升力。对圆柱和翼型绕流的模拟表明，对于所考虑的非线性不可压缩Navier-Stokes情形，线性准则仍是重构稳定性的有用指标。当准则被违反时，经典虚拟单元重构会产生虚假振荡，而CGC_ES和HGC保持稳定。HGC还以紧凑的最近邻模板满足稳定性要求。
英文摘要：
A direct, analytical, non-iterative ghost-cell reconstruction framework is developed for Cartesian-grid embedded-boundary methods. Analytical expressions impose Dirichlet and Neumann boundary conditions directly at the embedded boundary, eliminating intermediate image-point reconstruction, matrix inversion, and precomputation or storage of geometry-dependent reconstruction weights. For the Cartesian stencil considered, dependencies among neighboring ghost cells form a directed acyclic graph. A topological ordering partitions ghost cells into dependency levels, permitting level-by-level reconstruction without iterative updates. The formulation is combined with hybrid ghost cells (HGC), whose centers may lie on either side of the embedded boundary. This placement satisfies the linear reconstruction-stability criterion previously derived for scalar advection while retaining a compact nearest-neighbour Cartesian stencil. An extended-stencil classical ghost-cell formulation (CGC_ES) serves as a stability-preserving reference, distinguishing the effects of reconstruction stability and stencil compactness. The same analytical relations provide solution values and spatial gradients directly on the embedded boundary, enabling evaluation of pressure forces, wall stresses, drag, and lift without separate surface reconstruction or filtering. Simulations of flow past a circular cylinder and an airfoil show that the linear criterion remains a useful indicator of reconstruction stability for the nonlinear incompressible Navier-Stokes cases considered. Classical ghost-cell reconstruction develops spurious oscillations when the criterion is violated, whereas CGC_ES and HGC remain stable. HGC additionally satisfies the stability requirement with a compact nearest-neighbour stencil.
