A finite volume method for full-potential equation on adaptive Cartesian grids

In order to meet the requirements of fast computation of subsonic and transonic aerodynamics in aircraft conceptual design, a finite volume method (FVM) for solving the full potential equation on adaptive Cartesian grids is proposed in this paper. The proposed method employs a Cut-cell technique to process the surface boundary with cell-merging algorithm on geometry-adaptation Cartesian grids, while the cut-cells on the wall boundary are modified to achieve a higher body-fitted quality. An implicit scheme with GMRES algorithm is employed to solve the nonlinear potential equation. The ghost-cell method is used to treat the non-penetration condition, and suggests an analytic method to modify the velocity-potential of ghost-cells for better accuracy. According to the characteristics of the Cartesian grids, the Kutta condition is applied by specially computing the gradients on Kutta-faces without directly assigning the potential jump to the cells adjacent the Kutta line, which can significantly improve the solution converging speed. The feasibility and accuracy of the proposed method are validated by simulating sub/transonic flow around a NACA0012 airfoil. The results demonstrate a fast convergence history with highly automatic grid treatment and suggest its potential application in aircraft conceptual design.