YANG Yu-wei, YU Jia-lei, ZHANG Ya-ping, LI Xing-gang, QIU Xiao-pu. Numerical Solution of the 2D Compressible Euler Equations Based on the Unstructured Adaptive Grids[J]. Applied Mathematics and Mechanics, 2016, 37(9): 981-992. doi: 10.21656/1000-0887.370077
 Citation: YANG Yu-wei, YU Jia-lei, ZHANG Ya-ping, LI Xing-gang, QIU Xiao-pu. Numerical Solution of the 2D Compressible Euler Equations Based on the Unstructured Adaptive Grids[J]. Applied Mathematics and Mechanics, 2016, 37(9): 981-992.

# Numerical Solution of the 2D Compressible Euler Equations Based on the Unstructured Adaptive Grids

##### doi: 10.21656/1000-0887.370077
Funds:  The National Natural Science Foundation of China（61262070；61462097）
• Rev Recd Date: 2016-07-07
• Publish Date: 2016-09-15
• A numerical method for the solution of the 2D Euler equations based on the unstructured adaptive grids was proposed. The finite-volume method was used to carry out the space discretization, and the flux was calculated with Jamson’s central scheme, which was suitable for the calculation of arbitrary polygons. In order to get the stationary solution, an explicit 4-step Runge-Kutta iterative method was adopted to do the time-domain integral. According to the gradients of the flow field parameters, the refining edges were determined. Under this refining criterion, the mesh distribution was reasonably improved. With the proposed method the 2D Euler equations were solved for the simulation of the NACA0012 airfoil. The numerical results show the correctness and validity of the present method.
•  [1] 范绪箕, 董葳. 计算流体力学在飞行器研制中的应用[J]. 民用飞机设计与研究, 2004(4): 2-11.(FAN Xu-ji, DONG Wei. Application of computational fluid dynamics in aircraft development[J]. Civil Aircraft Design And Research,2004(4): 2-11.(in Chinese)) [2] 孙少鹏, 杨岞生. 非结构网格生成技术的研究[J]. 空气动力学学报, 1996,14(1): 19-25.(SUN Shao-peng, YANG Zuo-sheng. Research on unstructured grid generation technology[J]. Acta Aerodynamica Sinica,1996,14(1): 19-25.(in Chinese)) [3] Connell S D, Holmes D. A 3D unstructured adaptive multigrid scheme for the Euler equations[C]// 11th Computational Fluid Dynamics Conference . Orlando, FL, USA, 1993: AIAA-93-3339. [4] 王平, 朱自强. 二维非结构网格的生成及其Euler方程解[J]. 北京航空航天大学学报, 2000,26(2): 190-193.(WANG Ping, ZHU Zi-qiang. Generation of 2D unstructured grid and the Euler solution on it[J]. Journal of Beijing University of Aeronautics and Astronautics,2000,26(2): 190-193.(in Chinese)) [5] Shang H M, Chen Y S. Unstructured adaptive grid method for reacting flow computation[C]//33rd Joint Propulsion Conference and Exhibit.Seattle, WA, USA, 1997: AIAA 97-3183. [6] Blazek J. Computational Fluid Dynamics: Principles and Applications [M]. UK: Elsevier, 2001. [7] Northrup S A, Groth C P T. Parallel implicit adaptive mesh refinement for unsteady fully-compressible reactive flows[C]//21st AIAA Computational Fluid Dynamics Conference.San Diego, CA, 2013: AIAA- 2013-2433. [8] L?hner R, Baum J D. Adaptive h-refinement on 3D unstructured grids for transient problems[J]. International Journal for Numerical Methods in Fluids,1992,14(12): 1407-1419. [9] Godunov S K. A finite difference method for the computation of discontinuous solutions of the equations of fluid dynamics. Mat. Sb.47[J]. Mathematics of the USSR-Sbornik,1959: 271-306. [10] 尹河. 在非结构自适应网格上对二维Euler方程进行数值模拟[D]. 博士学位论文. 西安: 西北工业大学, 2001.(YIN He. Numerical simulation of two dimensional Euler equations on unstructured adaptive meshes[D]. PhD Thesis. Xi’an: Northwestern Polytechnical University, 2001.(in Chinese)) [11] 董程栋. Euler方程的自适应叉树结构直角网格算法的研究[J]. 博士学位论文. 南京: 南京航空航天大学, 1999.(DONG Cheng-dong. Euler equation of the adaptive cross tree structure of the right angle grid algorithm[D]. PhD Thesis. Nanjing: Nanjing University of Aeronautics & Astronautics, 1999.(in Chinese)) [12] 黄明恪. Jameson有限体积法对非结构网格推广的改进[J]. 空气动力学报, 1999,17(1): 15-20.(HUANG Ming-ke. Improvement of the extension of Jameson’s finite volume method to unstructured meshes[J]. Acta Aerodynamics Sinica,1999,17(1): 15-20.(in Chinese)) [13] Rodriguez I, Lehmkuhl O, Borrell R, Oliva A. Direct numerical simulation of a NACA0012 in full stall[J]. International Journal of Heat and Fluid Flow,2013,43: 194-203. [14] Forestieri G, Guardone A, Isola D, Marulli F, Quaranta G. Numerical simulation of compressible vertical flows using a conservative unstructured-grid adaptive scheme[J].Communications in Computational Physics,2012,12(3): 866-884. [15] Collaboration E , Bryan G L, Norman M L, et al. Enzo: an adaptive mesh refinement code for astrophysics[J].Astrophysical Journal Supplement,2013. doi: 10.1088/0067-0049/211/2/19.

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142