A fast and automatic full-potential finite volume solver on Cartesian grids for unconventional configurations

Abstract To meet the requirements of fast and automatic computation of subsonic and transonic aerodynamics in aircraft conceptual design, a novel finite volume solver for full potential flows on adaptive Cartesian grids is developed in this paper. Cartesian grids with geometric adaptation are firstly generated automatically with boundary cells processed by cell-cutting and cell-merging algorithms. The nonlinear full potential equation is discretized by a finite volume scheme on these Cartesian grids and iteratively solved in an implicit fashion with a generalized minimum residual (GMRES) algorithm. During computation, solution-based mesh adaptation is also applied so as to capture flow features more accurately. An improved ghost-cell method is proposed to implement the non-penetration wall boundary condition where the velocity-potential of a ghost cell is modified by an analytic method instead. 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 cells adjacent wake faces, which can significantly improve the solution converging speed. The feasibility and accuracy of the proposed method are validated by several typical cases of sub/transonic flows around an ONERA M6 wing, a DLR-F4 wing-body, and an unconventional figuration of a blended wing body (BWB). The validation cases demonstrate a fast convergence with fully automatic grid treatment and computation, and the results suggest its capacity in application for aircraft conceptual design.

[1]  Gediminas Adomavicius,et al.  A Parallel Multilevel Method for Adaptively Refined Cartesian Grids with Embedded Boundaries , 2000 .

[2]  J. Bonet,et al.  An alternating digital tree (ADT) algorithm for 3D geometric searching and intersection problems , 1991 .

[3]  Antony Jameson,et al.  Progress in Finite-Volume Calculations for Wing-Fuselage Combinations , 1980 .

[4]  M. Hafez,et al.  Artificial Compressibility Methods for Numerical Solutions of Transonic Full Potential Equation , 1979 .

[5]  Terry L. Holst,et al.  Transonic flow computations using nonlinear potential methods , 2000 .

[6]  Forrester T. Johnson,et al.  THIRTY YEARS OF DEVELOPMENT AND APPLICATION OF CFD AT BOEING COMMERCIAL AIRPLANES, SEATTLE , 2005 .

[7]  Marcus S. Day,et al.  Embedded Boundary Algorithms for Solving the Poisson Equation on Complex Domains , 1998 .

[8]  Richard H. Burkhart,et al.  A new approach to the solution of boundary value problems involving complex configurations , 1986 .

[9]  Antony Jameson,et al.  Numerical Calculation of Transonic Potential Flow about Wing-Body Combinations , 1979 .

[10]  M. Berger,et al.  Robust and efficient Cartesian mesh generation for component-based geometry , 1998 .

[11]  Martin Spieck,et al.  State-of-the-Art and Future Trends in Multidisciplinary Design Optimization , 2007 .

[12]  Derek M. Causon,et al.  Calculation of compressible flows about complex moving geometries using a three‐dimensional Cartesian cut cell method , 2000 .

[13]  A. Jameson,et al.  A finite volume method for transonic potential flow calculations , 1977 .

[14]  Ivan E. Sutherland,et al.  Reentrant polygon clipping , 1974, Commun. ACM.

[15]  D. P. Young,et al.  A locally refined rectangular grid finite element method: application to computational fluid dynamics and computational physics , 1990 .

[16]  A. Jameson.  Iterative solution of transonic flows over airfoils and wings, including flows at mach 1 , 1974 .

[17]  William H. Mason,et al.  On the Use of the Potential Flow Model for Aerodynamic Design at Transonic Speeds , 1995 .