A Blended Continuation Method for Solving Steady Inviscid Flow

被引：0
作者：
Qiao L. [1 ]
Bai J. [1 ]
Qiu Y. [1 ]
Hua J. [1 ,2 ]
Xu J. [1 ]
机构：
[1] Northwestern Polytechnical University, School of Aeronautics, Xi'an
[2] China Aeronautical Establishment, Aviation Industry Corporation of China, Beijing
来源：
Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University | 2018年 / 36卷 / 01期
关键词：
Computational fluid dynamics; Equation continuation; Euler equations; Implicit scheme; Newton-Raphson method; Steady flow;
D O I：
10.1051/jnwpu/20183610057
中图分类号：
学科分类号：
摘要：
Steady flow field solving is wieldly used in aircraft aerodynamic design, efficiency of steady flow field solving has great influnence on efficiency of aircraft aerodynamic design. A continuation method that blended Laplacian operator and pseudo time marching method for solving steady inviscid flow problem is proposed. In steady flow problem, the field is usually initialized as an uniform field before starting iteration. This resulted in the fact that the initial residual in only nonzero on wall boundary. Based on this feature, Laplacian operator is introduced to accelarate convergence at the starting stage of nonlinear solving. At the ending stage of nonlinear solving, the blended continuation term is biased to pseduo time marching method to avoid over dissipation graduately. To establish a complete continuation method, the starting, evolution and termination method are also described. At last, the proposed continuation method is implemented in a finite element solver, and tested aginst GAMM channel and NACA0012 foil subsonic and transonic cases. Numerical test results confirmed that the blended continuation method could get an efficency improvement about 1/3 to 1/4 comparing with stand alone Laplacian continuation and much more better than pure pseudo time marching method. © 2018, Editorial Board of Journal of Northwestern Polytechnical University. All right reserved.
引用
收藏
页码：57 / 65
页数：8
相关论文
共 18 条
  • [1] Gong Y., Zhang W., Liu Y., Reaserching How Initial Value if Internal Iteration Impacts on Computational Efficieny in Unsteady Flow Solving, Journal of Northwestern Polytechnical University, 34, 1, pp. 11-17, (2016)
  • [2] Geuzaine P., Newton-Krylov Strategy for Compressible Turbulent Flows on Unstructured Meshes, AIAA Journal, 39, 3, pp. 528-531, (2001)
  • [3] Dennis J., Schnabel R., Numerical Methods for Unconstrained Optimization and Nonlinear Equations, (1996)
  • [4] Brown D.A., Zingg D.W., Advances in Homotopy Continuation Methods in Computational Fluid Dynamics
  • [5] Lyra P.R.M., Morgan K., A Review and Comparative Study of Upwind Biased Schemes for Compressible Flow Computation. PartⅢ: Multidimensional Extension on Unstructured Grids, Archives of Computational Methods in Engineering, 9, 3, pp. 207-256, (2002)
  • [6] Kelley C.T., Liao L.Z., Qi L., Et al., Projected Pseudotransient Continuation, SIAM Journal on Numerical Analysis, 46, 6, pp. 3071-3083, (2008)
  • [7] Young D.P., Melvin R.G., Bieterman M.B., Et al., Global Convergence of Inexact Newton Methods for Transonic Flow, International Journal for Numerical Methods in Fluids, 11, 8, pp. 1075-1095, (1990)
  • [8] Hicken J., Buckley H., Osusky M., Et al., Dissipation-Based Continuation: a Globalization for Inexact-Newton Solvers
  • [9] Pollock S., A Regularized Newton-Like Method for Nonlinear PDE, Numerical Functional Analysis and Optimization, 36, 11, pp. 1493-1511, (2015)
  • [10] Persson P.O., Peraire J., Sub-Cell Shock Capturing for Discontinuous Galerkin Methods
12