发表机构
Institut Pprime, CNRS - Université de Poitiers（普里姆研究所，法国国家科学研究中心-普瓦捷大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种高阶虚拟点浸入边界法，结合辅助微分方程在非贴体网格上施加时域阻抗壁面条件，经多种算例验证具有高阶收敛性并缓解切向网格不稳定性。
AI 中文摘要
在线性化欧拉方程框架下，将虚拟点浸入边界方法与辅助微分方程耦合，以在不符合笛卡尔网格的壁面上施加局部反应阻抗条件。虚拟点重构采用法向模板方法：利用椭圆最小二乘流体节点云沿局部壁面法向构建高阶多项式，然后通过一维拉格朗日插值外推到虚拟点。阻抗被建模为质量-弹簧-阻尼振荡器，通过每个虚拟点的两个辅助状态变量在时间上推进，并在每个龙格-库塔阶段与重构耦合。该方法在平坦浸入壁面、反射声脉冲的圆柱壁面以及散射谐波单极子的圆柱上，与精确和半解析参考解进行了验证。测量到曲壁上的收敛阶约为三阶，平壁上的收敛阶约为四阶半；与精确谐波参考解的交叉检查表明，针对半解析参考解观察到的持续偏移是该参考解的特性，而非耦合求解器的特性。对线性化半离散算子的谱稳定性分析进一步表明，法向模板重构减少但未消除当浸入壁面与网格相切时出现的已知不稳定性。
英文摘要
A ghost-point immersed boundary method is coupled with auxiliary differential equations to impose a locally-reacting impedance condition on a wall that does not conform to a Cartesian grid, in the framework of the linearized Euler equations. The ghost-point reconstruction follows the normal-stencil approach: an elliptical least squares cloud of fluid nodes is used to build a high-order polynomial along the local wall normal, which is then extrapolated onto the ghost points by one-dimensional La grange interpolation. The impedance, modeled as a massspringdamper oscillator, is advanced in time through two auxiliary state variables per ghost point, coupled to the reconstruction at every RungeKutta stage. The method is validated against exact and semi-analytical references on a flat immersed wall, a cylindrical wall reflecting an acoustic pulse, and a cylinder scattering a harmonic monopole. Convergence orders ranging from about three on the curved wall to about four and a half on the flat wall are measured, and a cross-check against an exact harmonic reference shows that a persistent offset observed against a semi-analytical reference is a property of that ref erence rather than of the coupled solver. A spectral stability analysis of the linearized semi-discrete operator further shows that the normal-stencil reconstruction reduces, without eliminating, a known instability that occurs when the immersed wall becomes tangent to the grid.
Comments21 pages, 10 figures
