Efficient Gridless Method Using Constrained Weights Optimization for Two-Dimensional Unsteady Inviscid Flows at Low Angles of Attack
Publication: Journal of Aerospace Engineering
Volume 30, Issue 5
Abstract
An accurate and efficient gridless method is presented for calculation of unsteady flows at low and high reduced frequencies. A central gridless scheme is applied to solve unsteady flow equations in the arbitrary Lagrangian-Eulerian formulation. Taylor series least squares are used to discretize spatial derivatives at each node. Constrained weights optimization is proposed using a blend of second and fourth differences artificial dissipation terms. The proposed scheme leads to a faster gridless method with simple formulations and a reduction in flux computations. For time advancement, explicit and implicit dual-time methods are used. The segment spring analogy is applied to control/treat smoothness of the dynamic clouds and nodes movement. The capability and accuracy of the method are examined by comparing results of a multielement airfoil in steady flows and some test cases in unsteady flows with those from a finite-volume method and experimental data for low angles of attack at the prestall region. Results show a good agreement with the experimental data. Moreover, it is shown that the constraint weights optimization on the fast gridless method increases the efficiency and accuracy of the approach.
Get full access to this article
View all available purchase options and get full access to this article.
References
Batina, J. T. (1990). “Unsteady Euler airfoil solutions using unstructured dynamic meshes.” AIAA J., 28(8), 1381–1388.
Batina, J. T. (1993). “A gridless Euler/Navier-Stokes solution algorithm for complex-aircraft applications.” Proc., 31st Aerospace Sciences Meeting, American Institute of Aeronautics and Astronautics, Reno, NV.
Bertsekas, D. P. (1996). Constrained optimization and Lagrange multiplier method, Academic, New York.
Blazek, J. (2015). Computational fluid dynamics: Principles and applications, Butterworth-Heinemann, Amsterdam, Netherlands.
Blom, F. J. (2000). “Considerations on the spring analogy.” Int. J. Numer. Methods Fluids, 32(6), 647–668.
Cai, X. W., Tan, J. J., Ma, X. J., Zhang, M., and Wang, H. S. (2013). “Application of hybrid Cartesian grid and gridless approach to moving boundary flow problems.” Int. J. Numer. Methods Fluids., 72(9), 994–1013.
Ghosh, A., and Deshpande, S. (1995). “Least squares kinetic upwind method for inviscid compressible flows.” Proc., 12th Computational Fluid Dynamics Conf., American Institute of Aeronautics and Astronautics, Reston, VA, 1001–1011.
Hadidoolabi, M. (2005). “Unsteady compressible flow simulation for 3D moving bodies using unstructured grids.” Dept. of Aerospace Engineering, Amirkabir Univ. of Technology, Tehran, Iran.
Hashemi, M., and Jahangirian, A. (2011). “An efficient implicit mesh less method for compressible flow calculations.” Int. J. Numer. Methods Fluids, 67(6), 754–770.
Jahangirian, A., and Hadidoolabi, M. (2005). “Unstructured moving grids for implicit calculation of unsteady compressible viscous flows.” Int. J. Numer. Methods Fluids, 47(10–11), 1107–1113.
Jaisankar, S., Shivashankar, K., and Rao, S. R. (2007) “A grid-free central scheme for inviscid compressible flows.” Proc., 18th AIAA Computational Fluid Dynamics Conf., American Institute of Aeronautics and Astronautics, Reston, VA.
Jameson, A. (1995). “Analysis and design of numerical schemes for gas dynamics. 1: Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence.” Int. J. Comput. Fluid Dyn., 4(3–4), 171–218.
Jameson, A., and Mavriplis, D. (1986). “Finite volume solution of the two-dimensional Euler equations on a regular triangular mesh.” AIAA J., 24(4), 611–618.
Katz, A., and Jameson, A. (2009). “A comparison of various meshless schemes within a unified algorithm.” Proc., 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, American Institute of Aeronautics and Astronautics, Reston, VA.
Katz, A., and Jameson, A. (2010). “Meshless scheme based on alignment constraints.” AIAA J., 48(11), 2501–2511.
Kennett, D., Timme, S., Angulo, J., and Badcock, K. (2013). “An implicit meshless method for application in computational fluid dynamics.” Int. J. Numer. Methods Fluids, 71(8), 1007–1028.
Landon, R., and Davis, S. (1982). “Compendium of unsteady aerodynamic measurements.”, Advisory Group for Aerospace Research and Development, London.
Liszka, T., and Orkisz, J. (1980). “The finite difference method at arbitrary irregular grids and its application in applied mechanics.” Comput. Struct., 11(1), 83–95.
Löhner, R., Sacco, C., Oñate, E., and Idelsohn, S. (2002). “A finite point method for compressible flow.” Int. J. Numer. Methods Eng., 53(8), 1765–1779.
Ma, Z., Wang, H., and Pu, S. (2015). “A parallel meshless dynamic cloud method on graphic processing units for unsteady compressible flows past moving boundaries.” Comput. Methods Appl. Mech. Eng., 285, 146–165.
Morinishi, K. (2001). “Effective accuracy and conservation consistency of gridless type solver.” Computational fluid dynamics 2000, Springer, Berlin, 325–330.
Ortega, E., Oñate, E., Idelsohn, S., and Flores, R. (2013). “A meshless finite point method for three-dimensional analysis of compressible flow problems involving moving boundaries and adaptivity.” Int. J. Numer. Methods Fluids, 73(4), 323–343.
Ramesh, V., Vivek, S., and Deshpande, S. (2011). “Kinetic meshless methods for unsteady moving boundaries.” Meshfree methods for partial differential equations V, Springer, Berlin, 189–206.
Tota, P. V., and Wang, Z. J. (2007). “Meshfree Euler solver using local radial basis functions for inviscid compressible flows.” Proc., 18th AIAA Computational Fluid Dynamics Conf., American Institute of Aeronautics and Astronautics, Reston, VA.
Tuncer, I. H., and Platzer, M. F. (1996). “Thrust generation due to airfoil flapping.” AIAA J., 34(2), 324–331.
van den Berg, B. (1979). “Boundary layer measurements on a two-dimensional wing with flap.”, National Aerospace Laboratory, Amsterdam, Netherlands.
Wang, H., Chen, H., and Periaux, J. (2010). “A study of gridless method with dynamic clouds of points for solving unsteady CFD problems in aerodynamics.” Int. J. Numer. Methods Fluids, 64(1), 98–118.
Wang, H., and Periaux, J. (2013). “A fast meshless method coupled with artificial dissipation for solving 2D Euler equations.” Comput. Fluids, 71, 83–90.
Zhou, X., and Xu, H. (2010). “Gridless method for unsteady flows involving moving discrete points and its applications.” Eng. Appl. Comput. Fluid Mech., 4(2), 276–286.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 30 • Issue 5 • September 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Jun 23, 2016
Accepted: Mar 9, 2017
Published online: Jun 13, 2017
Published in print: Sep 1, 2017
Discussion open until: Nov 13, 2017
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.