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

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Abstract

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.

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Authors and Affiliations

  1. National Key Laboratory of Aerodynamic Design and Research, Northwestern Polytechnical University, Xi’an, 710072, China

    Yaojie Yu, Chao Gao & Ya Liu

  2. Department of Mechanical and Aerospace Engineering, University of California, Irvine, Irvine, CA, 92697, USA

    Feng Liu

  3. Facility Design and Instrumentation Institute, China Aerodynamics Research and Development Center, Mianyang, 621000, China

    Tingbo Zhou

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  1. Yaojie Yu
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Correspondence to Tingbo Zhou.

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Yu, Y., Liu, F., Zhou, T. et al. Numerical solutions of 2-D steady compressible natural convection using high-order flux reconstruction. Acta Mech. Sin. 35, 401–410 (2019). https://doi.org/10.1007/s10409-018-00835-w

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