A high-order scheme based on lattice Boltzmann flux solver for viscous compressible flow simulations

doi:10.1007/s10483-022-2913-7

Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (10): 1601-1614.doi: https://doi.org/10.1007/s10483-022-2913-7

• Articles • Previous Articles Next Articles

A high-order scheme based on lattice Boltzmann flux solver for viscous compressible flow simulations

Jian QIN^1,2,3, Jie WU^1,2,3, Chao MA^1,2,3

1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
2. Key Laboratory of Unsteady Aerodynamics and Flow Control, Ministry of Industry and Information Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
3. Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received:2022-03-19 Revised:2022-08-08 Published:2022-10-25
Contact: Jie WU, E-mail: wuj@nuaa.edu.cn
Supported by:
the National Natural Science Foundation of China (No. 12072158), the Natural Science Foundation of Jiangsu Province (No. BK20191271), and the Research Fund of Key Laboratory of Computational Aerodynamics, AVIC Aerodynamics Research Institute (No. YL2022XFX0402)

Abstract

Abstract: In this paper, a high-order scheme based on the lattice Boltzmann flux solver (LBFS) is proposed to simulate viscous compressible flows. The flux reconstruction (FR) approach is adopted to implement the spatial discretization. The LBFS is employed to compute the inviscid flux by using the local reconstruction of the lattice Boltzmann equation solutions from macroscopic flow variables. Meanwhile, a switch function is used in LBFS to adjust the magnitude of the numerical viscosity. Thus, it is more beneficial to capture both strong shock waves and thin boundary layers. Moreover, the viscous flux is computed according to the local discontinuous Galerkin method. Some typical compressible viscous problems, including manufactured solution case, lid-driven cavity flow, supersonic flow around a cylinder and subsonic flow over a NACA0012 airfoil, are simulated to demonstrate the accuracy and robustness of the proposed FR-LBFS.

Key words: high-order method, flux reconstruction, lattice Boltzmann flux solver (LBFS), viscous compressible flow

2010 MSC Number:

76N15

Jian QIN, Jie WU, Chao MA. A high-order scheme based on lattice Boltzmann flux solver for viscous compressible flow simulations. Applied Mathematics and Mechanics (English Edition), 2022, 43(10): 1601-1614.

TrendMD

References

[1] HARTEN, A., ENGQUIST, B., OSHER, S., and CHAKRAVARTHY, S. R. Uniformly high order accurate essentially non-oscillatory schemes, III. Journal of Computational Physics, 71, 231-303(1987)
[2] HU, C. and SHU, C. W. Weighted essentially non-oscillatory schemes on triangular meshes. Journal of Computational Physics, 150, 97-127(1999)
[3] REED, W. H. and HILL, T. R. Triangular mesh methods for the neutron transport equation. Technical Report LA-UR-73-479, Los Alamos Scientif Laboratory (1973)
[4] KOPRIVA, D. A. and KOLIAS, J. H. A conservative staggered-grid Chebyshev multidomain method for compressible flows. Journal of Computational Physics, 125, 244-261(1996)
[5] HUYNH, H. T. A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods. 18th AIAA Computational Fluid Dynamics Conference, 2007-4079(2007)
[6] HESTHAVEN, J. S. and WARBURTON, T. Nodal Discontinuous Galerkin Methods, Springer (2008)
[7] WANG, Z. J. and GAO, H. A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids. Journal of Computational Physics, 228, 8161-8186(2009)
[8] YU, M., WANG, Z. J., and LIU, Y. On the accuracy and efficiency of discontinuous Galerkin, spectral difference and correction procedure via reconstruction methods. Journal of Computational Physics, 259, 70-95(2014)
[9] JAMESON, A., VINCENT, P. E., and CASTONGUAY, P. On the non-linear stability of flux reconstruction schemes. Journal of Scientific Computing, 50, 434-445(2012)
[10] VINCENT, P. E., CASTONGUAY, P., and JAMESON, A. A new class of high-order energy stable flux reconstruction schemes. Journal of Scientific Computing, 47, 50-72(2011)
[11] ROE, P. L. Approximate Riemann solvers, parameter vectors, and difference schemes. Journal of Computational Physics, 43, 357-372(1981)
[12] LIOU, M. S. and STEFFEN, C. J. A new flux splitting scheme. Journal of Computational Physics, 107, 23-39(1993)
[13] HARTEN, A., LAX, P. D., and VAN LEER, B. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Review, 25, 35-61(1983)
[14] KITAMURA, K., SHIMA, E., and ROE, P. L. Evaluation of Euler fluxes for hypersonic heating computations. AIAA Journal, 48, 763-776(2010)
[15] ALEXANDER, F. J., CHEN, S., and STERLING, J. Lattice Boltzmann thermos hydrodynamics. Physical Review E, 47, 2249(1993)
[16] SHI, W., SHYY, W., and MEI, R. Finite-difference-based lattice Boltzmann method for inviscid compressible flows. Numerical Heat Transfer, Part B:Fundamentals, 40, 1-21(2001)
[17] KATAOKA, T. and TSUTAHARA, M. Lattice Boltzmann method for the compressible Euler equations. Physical Review E, 69, 056702(2004)
[18] JI, C. Z., SHU, C., and ZHAO, N. A lattice Boltzmann method-based flux solver and its application to solver shock tube problem. Modern Physics Letters B, 23, 313-316(2009)
[19] YANG, L. M., SHU, C., and WU, J. Development and comparative studies of three non-free parameter lattice Boltzmann models for simulation of compressible flows. Advances in Applied Mathematics and Mechanics, 4, 454-472(2012)
[20] YANG, L. M., SHU, C., and WU, J. A moment conservation-based non-free parameter compressible lattice Boltzmann model and its application for flux evaluation at cell interface. Computers and Fluids, 79, 190-199(2013)
[21] YANG, L. M., SHU, C., and WU, J. A hybrid lattice Boltzmann flux solver for simulation of viscous compressible flows. Advances in Applied Mathematics and Mechanics, 8, 887-910(2016)
[22] XU, K. A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method. Journal of Computational Physics, 171, 289-335(2001)
[23] XU, K. Regularization of the Chapman-Enskog expansion and its description of shock structure. Physics of Fluids, 14, 17-20(2002)
[24] GUO, Z. L. and SHU, C. Lattice Boltzmann Method and its Applications in Engineering, World Scientific Publishing, 365-404(2013)
[25] COCKBURN, B. and SHU, C. W. The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM Journal on Numerical Analysis, 35, 2440-2463(1998)
[26] WITHERDEN, F. D., FARRINGTON, A. M., and VINCENT, P. E. PyFR:an open source framework for solving advection-diffusion type problems on streaming architectures using the flux reconstruction approach. Computer Physics Communications, 185, 3028-3040(2014)
[27] PERSSON, P. O. and PERAIRE, J. Sub-cell shock capturing for discontinuous Galerkin methods. 44th AIAA Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, 2006-112(2006)
[28] LASKOWSKI W., RUEDA-RAMIREZ, A. M., RUBIO, G., VALERO, E., and FERRER, E. Advantages of static condensation in implicit compressible Navier-Stokes DGSEM solvers. Computers and Fluids, 209, 104646(2020)
[29] GHIA, U., GHIA, K. N., and SHIN, C. T. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics, 48, 387-411(1982)
[30] ERTURK, E., CORKE, T. C., and GOKCOL, C. Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers. International Journal for Numerical Methods in Fluids, 48, 747-774(2005)
[31] TAKAHASHI, S., NONOMURA, T., and FUKUDA, K. A numerical scheme based on an immersed boundary method for compressible turbulent flows with shocks applications to two-dimensional flows around cylinders. Journal of Applied Mathematics, 10, 1155-1175(2014)
[32] BHARADWAJ, A. and GHOSH, S. Data reconstruction at surface in immersed-boundary methods. Computers & Fluids, 196, 104236(2019)
[33] JAWAHAR, P. and KAMATH, H. A high-resolution procedure for Euler and Navier-Stokes computations on unstructured grids. Journal of Computational Physics, 164, 165-203(2000)
[34] BRISTEAU, M. O., GLOWINSKI, R., PERIAUX, J., and VIANDVIAND, H. Numerical Simulation of Compressible Navier-Stokes Flows, John Wiley, London (1987)

A high-order scheme based on lattice Boltzmann flux solver for viscous compressible flow simulations

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 1

Recommended Articles

Metrics

Comments