Numerical solutions of 2-D steady compressible natural convection using high-order flux reconstruction

作     者：Yaojie Yu Feng Liu Tingbo Zhou Chao Gao Ya Liu 

作者机构：National Key Laboratory of Aerodynamic Design and Research Northwestern Polytechnical UniversityXi’an 710072 China Department of Mechanical and Aerospace EngineeringUniversity of California Irvine Irvine CA 92697 USA Facility Design and Instrumentation Institute China Aerodynamics Research and Development CenterMianyang 621000 China 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2019年第35卷第2期

页      面：401-410页

核心收录：

学科分类：08[工学] 0802[工学-机械工程] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 0702[理学-物理学] 

主　　题：Flux reconstruction Preconditioning method Low Mach flows Natural convection 

摘      要：Low Mach number flows are common and typical in industrial applications. When simulating these flows, performance of traditional compressible flow solvers can deteriorate in terms of both efficiency and accuracy. In this paper, a new high-order numerical method for two-dimensional(2-D)state low Mach number flows is proposed by combining flux reconstruction(FR)and preconditioning. Firstly, a Couette flow problem is used to assess the efficiency and accuracy of preconditioned FR. It is found that the FR scheme with preconditioning is much more efficient than the original FR scheme. Meanwhile,this improvement still preserves the numerical accuracy. Using this new method and without the Boussinesq assumption,classic natural convection is directly simulated for cases of small and large temperature differences. For the small temperature difference, a p and h refinement study is conducted to verify the grid convergence and accuracy. Then, the influence of the Rayleigh number (Ra) is analyzed. By comparing with the reference results, the numerical results of preconditioned FR is very close to that calculated by incompressible solvers. Furthermore, a large temperature difference test case is calculated and analyzed, indicating this method is not limited by the Boussinesq assumption and is also applicable to heat convection with large temperature differences.