A D3Q19 hybrid recursive regularized pressure based lattice-Boltzmann method (HRR-P LBM) is assessed for the simulation of complex transonic flows. Mass and momentum conservation equations are resolved through a classical LBM solver coupled with a finite volume resolution of entropy equation for a complete compressible solver preserving stability, accuracy, and computational costs. An efficient treatment for wall and open boundaries is coupled with a grid refinement technique and extended to the HRR-P LBM in the scope of compressible aerodynamics. A Vreman subgrid turbulence model and an improved coupling of immersed boundary method with turbulence wall model on Cartesian grid accounts for unresolved scales by large-eddy simulation. The validity of the present method for transonic applications is investigated through various test cases with increasing complexity starting from an inviscid flow over a 10% bump and ending with a turbulent flow over a ONERA M6 three-dimensional wing.

1.
S.
Chen
and
G. D.
Doolen
, “
Lattice Boltzmann method for fluid flows
,”
Annu. Rev. Fluid Mech.
30
,
329
364
(
1998
).
2.
Z.
Guo
and
C.
Shu
,
Lattice Boltzmann Method and its Applications in Engineering
(
World Scientific
,
2013
), Vol.
3
.
3.
T.
Krüger
,
H.
Kusumaatmaja
,
A.
Kuzmin
,
O.
Shardt
,
G.
Silva
, and
E. M.
Viggen
,
The Lattice Boltzmann Method: Principles and Practice
(
Springer
,
2016
).
4.
S.
Succi
,
The Lattice Boltzmann Equation: For Complex States of Flowing Matter
(
Oxford University Press
,
2018
).
5.
Y.
Feng
,
P.
Boivin
,
J.
Jacob
, and
P.
Sagaut
, “
Hybrid recursive regularized lattice Boltzmann simulation of humid air with application to meteorological flows
,”
Phys. Rev. E
100
,
023304
(
2019
).
6.
C. G.
Coreixas
, “High-order extension of the recursive regularized lattice Boltzmann method,” Ph.D. thesis (
Institut National Polytechnique de Toulouse
,
2018
).
7.
N.
Frapolli
, “
Entropic lattice Boltzmann models for thermal and compressible flows
,” Ph.D. thesis (
ETH Zurich
,
2017
).
8.
Y.
Feng
,
P.
Sagaut
, and
W.-Q.
Tao
, “
A compressible lattice Boltzmann finite volume model for high subsonic and transonic flows on regular lattices
,”
Comput. Fluids
131
,
45
55
(
2016
).
9.
G.
Farag
,
S.
Zhao
,
T.
Coratger
,
P.
Boivin
,
G.
Chiavassa
, and
P.
Sagaut
, “
A pressure-based regularized lattice-Boltzmann method for the simulation of compressible flows
,”
Phys. Fluids
32
,
066106
(
2020
).
10.
S.
Hosseini
,
A.
Abdelsamie
,
N.
Darabiha
, and
D.
Thévenin
, “
Low-Mach hybrid lattice Boltzmann-finite difference solver for combustion in complex flows
,”
Phys. Fluids
32
,
077105
(
2020
).
11.
S. A.
Hosseini
,
A.
Eshghinejadfard
,
N.
Darabiha
, and
D.
Thévenin
, “
Weakly compressible lattice Boltzmann simulations of reacting flows with detailed thermo-chemical models
,”
Comput. Math. Appl.
79
,
141
158
(
2020
).
12.
M.
Tayyab
,
S.
Zhao
,
Y.
Feng
, and
P.
Boivin
, “
Hybrid regularized lattice-Boltzmann modelling of premixed and non-premixed combustion processes
,”
Combust. Flame
211
,
173
184
(
2020
).
13.
M.
Tayyab
,
S.
Zhao
, and
P.
Boivin
, “
Lattice-Boltzmann modelling of a turbulent bluff-body stabilized flame
,”
Phys. Fluids
33
,
031701
(
2021
).
14.
P.
Boivin
,
M.
Tayyab
, and
S.
Zhao
, “
Benchmarking a lattice-Boltzmann solver for reactive flows: Is the method worth the effort for combustion?
,”
Phys. Fluids
33
,
071703
(
2021
).
15.
L.
Merlier
,
J.
Jacob
, and
P.
Sagaut
, “
Lattice-Boltzmann large-eddy simulation of pollutant dispersion in street canyons including tree planting effects
,”
Atmos. Environ.
195
,
89
103
(
2018
).
16.
L.
Merlier
,
J.
Jacob
, and
P.
Sagaut
, “
Lattice-Boltzmann large-eddy simulation of pollutant dispersion in complex urban environment with dense gas effect: Model evaluation and flow analysis
,”
Build. Environ.
148
,
634
652
(
2019
).
17.
I.
Cheylan
,
S.
Zhao
,
P.
Boivin
, and
P.
Sagaut
, “
Compressible pressure-based lattice-Boltzmann applied to humid air with phase change
,”
Appl. Therm. Eng.
191
,
116868
(
2021
).
18.
Y.
Feng
,
P.
Boivin
,
J.
Jacob
, and
P.
Sagaut
, “
Hybrid recursive regularized thermal lattice Boltzmann model for high subsonic compressible flows
,”
J. Comput. Phys.
394
,
82
99
(
2019
).
19.
G.
Farag
,
T.
Coratger
,
G.
Wissocq
,
S.
Zhao
,
P.
Boivin
, and
P.
Sagaut
, “
A unified hybrid lattice-Boltzmann method for compressible flows: Bridging between pressure-based and density-based methods
,”
Phys. Fluids
33
,
086101
(
2021
).
20.
D.
Casalino
,
A. F.
Ribeiro
,
E.
Fares
, and
S.
Nölting
, “
Lattice–Boltzmann aeroacoustic analysis of the LAGOON landing-gear configuration
,”
AIAA J.
52
,
1232
1248
(
2014
).
21.
A.
Sengissen
,
J.-C.
Giret
,
C.
Coreixas
, and
J.-F.
Boussuge
, “
Simulations of lagoon landing-gear noise using lattice Boltzmann solver
,”
AIAA Paper No. 2015-2993
,
2015
, p.
2993
.
22.
N. I.
Prasianakis
and
I. V.
Karlin
, “
Lattice Boltzmann method for thermal flow simulation on standard lattices
,”
Phys. Rev. E
76
,
016702
(
2007
).
23.
C.-H.
Liu
,
K.-H.
Lin
,
H.-C.
Mai
, and
C.-A.
Lin
, “
Thermal boundary conditions for thermal lattice Boltzmann simulations
,”
Comput. Math. Appl.
59
,
2178
2193
(
2010
).
24.
N.
Frapolli
,
S.
Chikatamarla
, and
I.
Karlin
, “
Multispeed entropic lattice Boltzmann model for thermal flows
,”
Phys. Rev. E
90
,
043306
(
2014
).
25.
G. D.
Ilio
,
D.
Chiappini
,
S.
Ubertini
,
G.
Bella
, and
S.
Succi
, “
Fluid flow around naca 0012 airfoil at low-Reynolds numbers with hybrid lattice Boltzmann method
,”
Comput. Fluids
166
,
200
208
(
2018
).
26.
Y.
Feng
,
S.
Guo
,
J.
Jacob
, and
P.
Sagaut
, “
Solid wall and open boundary conditions in hybrid recursive regularized lattice Boltzmann method for compressible flows
,”
Phys. Fluids
31
,
126103
(
2019
).
27.
J.
Latt
,
C.
Coreixas
,
J.
Beny
, and
A.
Parmigiani
, “
Efficient supersonic flow simulations using lattice Boltzmann methods based on numerical equilibria
,”
Philos. Trans. R. Soc. A
378
,
20190559
(
2020
).
28.
S.
Guo
,
Y.
Feng
,
J.
Jacob
,
F.
Renard
, and
P.
Sagaut
, “
An efficient lattice Boltzmann method for compressible aerodynamics on d3q19 lattice
,”
J. Comput. Phys.
418
,
109570
(
2020
).
29.
K.
Hejranfar
and
A.
Ghaffarian
, “
A high-order accurate unstructured spectral difference lattice Boltzmann method for computing inviscid and viscous compressible flows
,”
Aerosp. Sci. Technol.
98
,
105661
(
2020
).
30.
M. H.
Saadat
,
F.
Bösch
, and
I. V.
Karlin
, “
Lattice Boltzmann model for compressible flows on standard lattices: Variable Prandtl number and adiabatic exponent
,”
Phys. Rev. E
99
,
013306
(
2019
).
31.
M. H.
Saadat
,
B.
Dorschner
, and
I.
Karlin
, “
Extended lattice Boltzmann model
,”
Entropy
23
,
475
(
2021
).
32.
L.
Yang
,
C.
Shu
, and
J.
Wu
, “
A hybrid lattice Boltzmann flux solver for simulation of 3d compressible viscous flows
,” in
Proceedings of the Eighth International Conference on Computational Fluid Dynamics
(
ICCFD
,
Chengdu, China
,
2014
), pp.
14
18
.
33.
Y.
Feng
,
S.
Guo
,
J.
Jacob
, and
P.
Sagaut
, “
Grid refinement in the three-dimensional hybrid recursive regularized lattice Boltzmann method for compressible aerodynamics
,”
Phys. Rev. E
101
,
063302
(
2020
).
34.
O.
Filippova
and
D.
Hänel
, “
Grid refinement for lattice-BGK models
,”
J. Comput. Phys.
147
,
219
228
(
1998
).
35.
D.
Lagrava
,
O.
Malaspinas
,
J.
Latt
, and
B.
Chopard
, “
Advances in multi-domain lattice Boltzmann grid refinement
,”
J. Comput. Phys.
231
,
4808
4822
(
2012
).
36.
J.
Jacob
,
O.
Malaspinas
, and
P.
Sagaut
, “
A new hybrid recursive regularised Bhatnagar–Gross–Krook collision model for lattice Boltzmann method-based large eddy simulation
,”
J. Turbul.
19
,
1051
1076
(
2018
).
37.
J.
Degrigny
,
S.-G.
Cai
,
J.-F.
Boussuge
, and
P.
Sagaut
, “
Improved wall model treatment for aerodynamic flows in LBM
,”
Comput. Fluids
227
,
105041
(
2021
).
38.
S.-G.
Cai
,
J.
Degrigny
,
J.-F.
Boussuge
, and
P.
Sagaut
, “
Coupling of turbulence wall models and immersed boundaries on Cartesian grids
,”
J. Comput. Phys.
429
,
109995
(
2021
).
39.
P. L.
Bhatnagar
,
E. P.
Gross
, and
M.
Krook
, “
A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems
,”
Phys. Rev.
94
,
511
525
(
1954
).
40.
G.
Farag
,
S.
Zhao
,
G.
Chiavassa
, and
P.
Boivin
, “
Consistency study of lattice-Boltzmann schemes macroscopic limit
,”
Phys. Fluids
33
,
037101
(
2021
).
41.
Y.
Feng
,
P.
Sagaut
, and
W.
Tao
, “
A three dimensional lattice model for thermal compressible flow on standard lattices
,”
J. Comput. Phys.
303
,
514
529
(
2015
).
42.
J.
Latt
and
B.
Chopard
, “
Lattice Boltzmann method with regularized pre-collision distribution functions
,”
Math. Comput. Simul.
72
,
165
168
(
2006
).
43.
O.
Malaspinas
, “
Increasing stability and accuracy of the lattice Boltzmann scheme: Recursivity and regularization
,” arXiv:1505.06900 (
2015
).
44.
G.
Wissocq
and
P.
Sagaut
, “
Hydrodynamic limits and numerical errors of isothermal lattice Boltzmann schemes
,” arXiv:2104.14217, [physics.flu-dyn] (
2021
).
45.
S.
Zhao
,
G.
Farag
,
P.
Boivin
, and
P.
Sagaut
, “
Toward fully conservative hybrid lattice Boltzmann methods for compressible flows
,”
Phys. Fluids
32
,
126118
(
2020
).
46.
P.
Sagaut
,
Large Eddy Simulation for Incompressible Flows: An Introduction
(
Springer Science and Business Media
,
2006
).
47.
B.
Vreman
,
B.
Geurts
, and
H.
Kuerten
, “
Large-eddy simulation of the turbulent mixing layer
,”
J. Fluid Mech.
339
,
357
390
(
1997
).
48.
A.
Vreman
, “
An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications
,”
Phys. Fluids
16
,
3670
3681
(
2004
).
49.
E.
Garnier
,
N.
Adams
, and
P.
Sagaut
,
Large Eddy Simulation for Compressible Flows
(
Springer Science and Business Media
,
2009
).
50.
S.-G.
Cai
and
P.
Sagaut
, “
Explicit wall models for large eddy simulation
,”
Phys. Fluids
33
,
041703
(
2021
).
51.
S. R.
Allmaras
and
F. T.
Johnson
, “
Modifications and clarifications for the implementation of the Spalart-Allmaras turbulence model
,” in Proceedings of the
Seventh International Conference on Computational Fluid Dynamics (ICCFD7)
(
ICCFD
,
Big Island
,
HI
,
2012
), pp.
1
11
.
52.
E.
Hewitt
and
R. E.
Hewitt
, “
The Gibbs-Wilbraham phenomenon: An episode in Fourier analysis,” Arch. Hist.
Exact Sci.
21
,
129
160
(
1979
).
53.
A.
Jameson
, “
Origins and further development of the Jameson–Schmidt–Turkel scheme
,”
AIAA J.
55
,
1487
1510
(
2017
).
54.
T. J.
Poinsot
and
S.
Lelef
, “
Boundary conditions for direct simulations of compressible viscous flows
,”
J. Comput. Phys.
101
,
104
129
(
1992
).
55.
H.
Xu
and
P.
Sagaut
, “
Analysis of the absorbing layers for the weakly-compressible lattice Boltzmann methods
,”
J. Comput. Phys.
245
,
14
42
(
2013
).
56.
S.
Wilhelm
,
J.
Jacob
, and
P.
Sagaut
, “
An explicit power-law-based wall model for lattice Boltzmann method–Reynolds-averaged numerical simulations of the flow around airfoils
,”
Phys. Fluids
30
,
065111
(
2018
).
57.
F.
Capizzano
, “
Turbulent wall model for immersed boundary methods
,”
AIAA J.
49
,
2367
2381
(
2011
).
58.
Y.
Tamaki
,
M.
Harada
, and
T.
Imamura
, “
Near-wall modification of Spalart–Allmaras turbulence model for immersed boundary method
,”
AIAA J.
55
,
3027
3039
(
2017
).
59.
J.
Fürst
, “
On the implicit density based OpenFOAM solver for turbulent compressible flows
,”
EPJ Web Conf.
143
,
02027
(
2017
).
60.
M.
Allahyari
,
K.
Yousefi
,
V.
Esfahanian
, and
M.
Darzi
, “
A block–interface approach for high–order finite–difference simulations of compressible flows
,”
J. Appl. Fluid Mech.
14
,
345
359
(
2021
).
61.
A.
Karbalaei
and
K.
Hejranfar
, “
A central difference finite volume lattice Boltzmann method for simulation of 2d inviscid compressible flows on triangular meshes
,”
in Proceedings of the ASME International Mechanical Engineering Congress and Exposition
(American Society of Mechanical Engineers,
2018
), Vol.
52101
, p.
V007T09A025
.
62.
M. H.
Djavareshkian
and
M. A.
Jahdi
, “
Shock-capturing method using characteristic-based dissipation filters in pressure-based algorithm
,”
Acta Mech.
209
,
99
113
(
2010
).
63.
N.
Frapolli
,
S. S.
Chikatamarla
, and
I. V.
Karlin
, “
Entropic lattice Boltzmann model for gas dynamics: Theory, boundary conditions, and implementation
,”
Phys. Rev. E
93
,
063302
(
2016
).
64.
L.
Ramírez
,
X.
Nogueira
,
P.
Ouro
,
F.
Navarrina
,
S.
Khelladi
, and
I.
Colominas
, “
A higher-order Chimera method for finite volume schemes
,”
Arch. Comput. Methods Eng.
25
,
691
706
(
2018
).
65.
V. G.
Ferreira
,
R. A.
de Queiroz
,
M. A. C.
Candezano
,
G. A.
Lima
,
L.
Corrêa
,
C. M.
Oishi
, and
F. L.
Santos
, “
Simulation results and applications of an advection bounded scheme to practical flows
,”
Comput. Appl. Math.
31
,
591
616
(
2012
).
66.
J. J.
van der Vegt
and
H.
Van der Ven
, “
Discontinuous Galerkin finite element method with anisotropic local grid refinement for inviscid compressible flows
,”
J. Comput. Phys.
141
,
46
77
(
1998
).
67.
N.
Frapolli
,
S.
Chikatamarla
, and
I.
Karlin
, “
Theory, analysis, and applications of the entropic lattice Boltzmann model for compressible flows
,”
Entropy
22
,
370
(
2020
).
68.
V.
Schmitt
, “
Pressure distributions on the onera m6-wing at transonic Mach numbers, experimental data base for computer program assessment
,”
Report No. AGARD AR-138
,
1979
.
69.
E. F.
Toro
,
Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction
(
Springer Science and Business Media
,
2009
).
You do not currently have access to this content.