Moving Mesh Method for Pitching Naca0012 Airfoil

Abstract

Abstract: We give discretization for fluid system in integral form with arbitrary moving velocity on unstructured meshes, where re-mapping step in ALE method to interpolate flow variables between old mesh and new one can be avoided. We give three kinds of velocity for different part of computational domain, and apply the scheme to pitching Naca0012 airfoil with moving boundary. It shows that the scheme is efficient and accurate.

Key words: compressible fluid system, moving boundary, pitching Naca0012, adaptive moving mesh method

CLC Number:

O351

ZENG Xianyang, NI Guoxi. Moving Mesh Method for Pitching Naca0012 Airfoil[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 33(3): 266-272.

References

[1] 李德元, 等.二维非定常流体力学数值方法[M]. 北京:科学出版社,1987.
[2] NEUMANN V, RICHTMYER R D. A method for the numerical calculations of hydrodynamics shocks[J]. J Appl Phys, 1950, 21:232-254.
[3] HIRT C W, NICHOLS B D. An arbitrary Lagrangian Eulerian computing method for all flow speed[J]. J Comput Phys, 1997,135:203-216.
[4] LIPNIKOV K, SHASHKOV M. The error-minimization-based strategy for moving mesh methods[J]. Comm Comput Phys, 2006, 1:53-81.
[5] CHEN G X, TANG H Z, JIANG S. Second order accurate Godunov scheme for multicompoment flows on moving triangular meshes[J]. J Sci Comput, 2008,34:64-86.
[6] TANG H Z, TANG T. Adaptive mesh methods for one-and two-dimensional hyperbolic conservation laws[J]. SIAM J Numer Anal, 2003, 41:487-515.
[7] JIN C Q, XU K. A unified moving grid gas-kinetic method in Eulerian space for viscous flow computation[J]. J Comput Phys, 2007, 222:155-175.
[8] NI G X, JIANG S, XU K. Efficient kinetic scheme for steady and unsteady flow simulation on unstructured grid[J]. J Comput Phys, 2008, 227:3015-3031.
[9] NI G X, JIANG S, XU K. Remapping-free ALE-type kinetic method for flow computations[J]. J Comput Phys,2009,228:3154-3171.
[10] XU X, NI G. A high-order moving mesh kinetic scheme based on WENO reconstruction for compressible flows[J].Chinese J Comput Phys, 2013,30(4):509-514.
[11] BERGER M J,OLIGER J. Adaptive mesh refinement for hyperbolic partial differential equations[J]. J Comput Phys, 2007, 53:155-175.
[12] SHU S, YUE X, ZHOU Z, et al. Approximation and two-level algorithm for finite volume schemes for diffusion equations with structured AMR[J]. Chinese J Comput Phys, 2014, 31(4):390-402.
[13] ZHOU C. An approach of adaptive mesh refinement/unrefinement based on prediction-correction for unsteady flows[J].Chinese J Comput Phys,2013,30(5):633-641.
[14] CAO W M, HUANG W Z, RUSSEL R D. An r-adaptive finite element method based upon moving mesh PDEs[J]. J Comput Phys, 1999,149:221-244.
[15] FIX G J. Free boundary problems:Theory and applications[M]. Fasano A, Primicerio M. Ed. Pitman, Boston, 1983.
[16] LI Z L, ITO K. The immersed interface method-numerical solutions of PDEs involving interfaces and irregular domains[M]. Society for Industry and Applied Mathematics, 2006.
[17] SHYY W, UDAYKUMAR H S, RAO M M, et al. Computational fluid dynamics with moving boundaries[M]. Taylor and Francis, Washington DC (1996).
[18] SUN M, YADA K, JAGADEESH G, et al. A study of shock wave interaction with a rotating cylinder[J]. Shock Waves, 2003,12:479-485.
[19] TORO E F. Riemann solvers and numerical methods for fluid dynamics[M]. 2nd ed. Springer, 1999.