基于自适应直角网格的二维全速势方程有限体积解法A finite volume method for 2D Full-Potential equation on adaptive Cartesian grids

为满足亚声速和跨声速飞机概念设计中快速气动计算的需求，研究和发展一种基于自适应直角网格的非线性全速势方程有限体积解法。要点如下。（1）在几何自适应直角网格的基础上，使用结合单元融合的网格切割算法处理物面边界，提出一种修正非贴体切割网格的方法。（2）采用隐式格式结合GM RES算法求解该非线性位流方程，针对流场的自适应来捕捉激波。（3）采用镜像法处理物面边界处的无穿透条件，并提出解析的方法来修正镜像单元的值。（4）针对直角网格的特点，提出在库塔线上插入库塔单元的方法施加库塔条件。NACA0012翼型绕流的算例结果表明，该方法用于亚声速和跨声速气动计算能得到令人满意的结果，且自动化程度高、收敛速度快。

A finite volume method for 2D Full-Potential equation on adaptive Cartesian grids

In order to meet the requirements of rapid calculation of subsonic and transonic aerodynamics in aircraft conceptual design,a finite volume method for solving the full potential equation on adaptive Cartesian grids is proposed in this paper.This method has the following characteristics,(1) Cut-cell method is applied to process the surface boundary with cell-merging algorithm on geometry-adaptation Cartesian grids,and then the cut-cells on the wall boundary are modified for better body-fitted quality.(2) An implicit scheme with GMRES algorithm is employed to solve the nonlinear potential equation,and shock wave is captured by a solution-adaptation algorithm.(3) It uses ghost-cell method to treat the no penetration condition,and suggests a analytic method to modify the velocity-potential of ghost-cells.(4) According to the characteristics of the Cartesian grids,the Kutta condition is applied by appending Kutta-cells on the Kutta line.The numerical results of a NACA0012 airfoil show that the proposed method can provide satisfactory accuracy and rapid convergence in subsonic and transonic flow simulations with highly automatic grid treatment,indicating its valuable application in aircraft conceptual design.