一种混合型CFD离散误差估计方法及其应用

A Hybrid CFD Discretization Error Estimation Method and Its Application

  • 摘要: 针对计算流体力学(CFD)中离散误差估计问题,提出一种融合伴随理论与Richardson外推法的混合误差估计方法。传统Richardson外推依赖多套一致加密网格,成本高且难以反映局部误差;伴随方法可进行局部估计,但其精度受限于内嵌密网格的近似求解。本方法通过伴随误差估计识别流动敏感区域,指导网格自适应加密,自动生成系列网格,再结合Richardson外推获得网格无关解,实现离散误差定量评估。将该方法应用于CHN-T1运输机跨声速算例,经两次自适应加密得到粗、中、细网格,外推结果与官方参考解及高分辨率网格结果吻合良好,阻力系数误差在2 counts以内。该方法降低了人工网格生成成本,实现了高效、自动化的误差估计,为复杂外形CFD模拟的验证与确认提供了有效工具。

     

    Abstract: A hybrid error estimation method integrating adjoint theory and Richardson extrapolation is proposed to address the discretization error estimation issue in computational fluid dynamics (CFD). Conventional Richardson extrapolation relies on multiple consistently refined grids, which is costly and struggles to capture local error effects. While the adjoint method enables local error estimation, its accuracy is constrained by approximate solutions on an embedded fine grid. The present approach identifies flow-sensitive regions through adjoint-based error estimation, guides adaptive mesh refinement to automatically generate a series of grids, and subsequently employs Richardson extrapolation to obtain a grid-independent solution, thereby achieving quantitative assessment of discretization errors. Applied to a transonic case of the CHN-T1 transport aircraft, coarse, medium, and fine grids are generated via two adaptive refinement steps. The extrapolated results show good agreement with official reference data and high-resolution grid solutions, with a drag coefficient error within 2 counts. This method reduces the manual cost of grid generation and enables efficient, automated error estimation, providing an effective tool for the verification and validation of CFD simulations for complex geometries.

     

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