Volume 8, Issue 6
A Hybrid Lattice Boltzmann Flux Solver for Simulation of Viscous Compressible Flows

L. M. Yang, C. Shu & J. Wu

Adv. Appl. Math. Mech., 8 (2016), pp. 887-910.

Published online: 2018-05

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  • Abstract

In this paper, a hybrid lattice Boltzmann flux solver (LBFS) is proposed for simulation of viscous compressible flows. In the solver, the finite volume method is applied to solve the Navier-Stokes equations. Different from conventional Navier-Stokes solvers, in this work, the inviscid flux across the cell interface is evaluated by local reconstruction of solution using one-dimensional lattice Boltzmann model, while the viscous flux is still approximated by conventional smooth function approximation. The present work overcomes the two major drawbacks of existing LBFS [28–31], which is used for simulation of inviscid flows. The first one is its ability to simulate viscous flows by including evaluation of viscous flux. The second one is its ability to effectively capture both strong shock waves and thin boundary layers through introduction of a switch function for evaluation of inviscid flux, which takes a value close to zero in the boundary layer and one around the strong shock wave. Numerical experiments demonstrate that the present solver can accurately and effectively simulate hypersonic viscous flows.

  • Keywords

Lattice Boltzmann flux solver, hybrid, 1D lattice Boltzmann model, switch function.

  • AMS Subject Headings

76M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-8-887, author = {L. M. Yang , and C. Shu , and Wu , J.}, title = {A Hybrid Lattice Boltzmann Flux Solver for Simulation of Viscous Compressible Flows}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {6}, pages = {887--910}, abstract = {

In this paper, a hybrid lattice Boltzmann flux solver (LBFS) is proposed for simulation of viscous compressible flows. In the solver, the finite volume method is applied to solve the Navier-Stokes equations. Different from conventional Navier-Stokes solvers, in this work, the inviscid flux across the cell interface is evaluated by local reconstruction of solution using one-dimensional lattice Boltzmann model, while the viscous flux is still approximated by conventional smooth function approximation. The present work overcomes the two major drawbacks of existing LBFS [28–31], which is used for simulation of inviscid flows. The first one is its ability to simulate viscous flows by including evaluation of viscous flux. The second one is its ability to effectively capture both strong shock waves and thin boundary layers through introduction of a switch function for evaluation of inviscid flux, which takes a value close to zero in the boundary layer and one around the strong shock wave. Numerical experiments demonstrate that the present solver can accurately and effectively simulate hypersonic viscous flows.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1172}, url = {http://global-sci.org/intro/article_detail/aamm/12122.html} }
TY - JOUR T1 - A Hybrid Lattice Boltzmann Flux Solver for Simulation of Viscous Compressible Flows AU - L. M. Yang , AU - C. Shu , AU - Wu , J. JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 887 EP - 910 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2015.m1172 UR - https://global-sci.org/intro/article_detail/aamm/12122.html KW - Lattice Boltzmann flux solver, hybrid, 1D lattice Boltzmann model, switch function. AB -

In this paper, a hybrid lattice Boltzmann flux solver (LBFS) is proposed for simulation of viscous compressible flows. In the solver, the finite volume method is applied to solve the Navier-Stokes equations. Different from conventional Navier-Stokes solvers, in this work, the inviscid flux across the cell interface is evaluated by local reconstruction of solution using one-dimensional lattice Boltzmann model, while the viscous flux is still approximated by conventional smooth function approximation. The present work overcomes the two major drawbacks of existing LBFS [28–31], which is used for simulation of inviscid flows. The first one is its ability to simulate viscous flows by including evaluation of viscous flux. The second one is its ability to effectively capture both strong shock waves and thin boundary layers through introduction of a switch function for evaluation of inviscid flux, which takes a value close to zero in the boundary layer and one around the strong shock wave. Numerical experiments demonstrate that the present solver can accurately and effectively simulate hypersonic viscous flows.

L. M. Yang, C. Shu & J. Wu. (2020). A Hybrid Lattice Boltzmann Flux Solver for Simulation of Viscous Compressible Flows. Advances in Applied Mathematics and Mechanics. 8 (6). 887-910. doi:10.4208/aamm.2015.m1172
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