A new pressure-based lattice-Boltzmann method (HRR-p) is proposed for the simulation of flows for Mach numbers ranging from 0 to 1.5. Compatible with nearest-neighbor lattices (e.g., D3Q19), the model consists of a predictor step comparable to classical athermal lattice-Boltzmann methods, appended with a fully local and explicit correction step for the pressure. Energy conservation—for which the Hermitian quadrature is not accurate enough on such a lattice—is solved via a classical finite volume MUSCL-Hancock scheme based on the entropy equation. The Euler part of the model is then validated for the transport of three canonical modes (vortex, entropy, and acoustic propagation), while its diffusive/viscous properties are assessed via thermal Couette flow simulations. All results match the analytical solutions with very limited dissipation. Last, the robustness of the method is tested in a one-dimensional shock tube and a two-dimensional shock–vortex interaction.
REFERENCES
1.
R.
Löhner
, “Towards overcoming the LES crisis
,” Int. J. Comput. Fluid Dyn.
33
, 87
(2019
).2.
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
).3.
C.
Lin
and K. H.
Luo
, “Mesoscopic simulation of nonequilibrium detonation with discrete Boltzmann method
,” Combust. Flame
198
, 356
(2018
).4.
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
).5.
S.
Chen
and G. D.
Doolen
, “Lattice Boltzmann method for fluid flows
,” Annu. Rev. Fluid Mech.
30
, 329
–364
(1998
).6.
X.
Shan
, X.-F.
Yuan
, and H.
Chen
, “Kinetic theory representation of hydrodynamics: A way beyond the Navier–Stokes equation
,” J. Fluid Mech.
550
, 413
(2006
).7.
X.
Shan
et al., “General solution of lattices for Cartesian lattice Bhatanagar-Gross-Krook models
,” Phys. Rev. E
81
, 036702
(2010
).8.
Q.
Li
, K.
Luo
, Q.
Kang
, Y.
He
, Q.
Chen
, and Q.
Liu
, “Lattice Boltzmann methods for multiphase flow and phase-change heat transfer
,” Prog. Energy Combust. Sci.
52
, 62
–105
(2016
).9.
T.
Krüger
, H.
Kusumaatmaja
, A.
Kuzmin
, O.
Shardt
, G.
Silva
, and E. M.
Viggen
, The Lattice Boltzmann Method: Principles and Practice
(Springer
, 2016
).10.
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
).11.
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
).12.
Y.
Feng
, M.
Tayyab
, and P.
Boivin
, “A lattice-Boltzmann model for low-Mach reactive flows
,” Combust. Flame
196
, 249
–254
(2018
).13.
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
).14.
F.
Renard
, Y.
Feng
, J.
Boussuge
, and P.
Sagaut
, “Improved compressible hybrid lattice Boltzmann method on standard lattice for subsonic and supersonic flows
,” arXiv:2002.03644 (2020
).15.
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
(2018
).16.
T.
Astoul
, G.
Wissocq
, J.
Boussuge
, A.
Sengissen
, and P.
Sagaut
, “Analysis and reduction of spurious noise generated at grid refinement interfaces with the lattice Boltzmann method
,” J. Comput. Phys.
109645
(2020
).17.
G.
Wissocq
, P.
Sagaut
, and J.-F.
Boussuge
, “An extended spectral analysis of the lattice Boltzmann method: Modal interactions and stability issues
,” J. Comput. Phys.
380
, 311
–333
(2019
).18.
C.
Coreixas
, G.
Wissocq
, G.
Puigt
, J. F.
Boussuge
, and P.
Sagaut
, “Recursive regularization step for high-order lattice Boltzmann methods
,” Phys. Rev. E
96
, 033306
(2017
).19.
C.
Coreixas
, B.
Chopard
, and J.
Latt
, “Comprehensive comparison of collision models in the lattice Boltzmann framework: Theoretical investigations
,” Phys. Rev. E
100
, 033305
(2019
).20.
R.
Zhang
, X.
He
, and S.
Chen
, “Interface and surface tension in incompressible lattice Boltzmann multiphase model
,” Comput. Phys. Commun.
129
, 121
–130
(2000
).21.
T.
Lee
and C.-L.
Lin
, “A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio
,” J. Comput. Phys.
206
, 16
–47
(2005
).22.
X.
He
, S.
Chen
, and R.
Zhang
, “A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh–Taylor instability
,” J. Comput. Phys.
152
, 642
–663
(1999
).23.
R.
Zhang
, X.
He
, G.
Doolen
, and S.
Chen
, “Surface tension effects on two-dimensional two-phase Kelvin–Helmholtz instabilities
,” Adv. Water Resour.
24
, 461
–478
(2001
).24.
X.
He
, R.
Zhang
, S.
Chen
, and G.
Doolen
, “On the three-dimensional Rayleigh–Taylor instability
,” Phys. Fluids
11
, 1143
–1152
(1999
).25.
Y.
Cao
, “Variable property-based lattice Boltzmann flux solver for thermal flows in the low Mach number limit
,” Int. J. Heat Mass Transfer
103
, 254
–264
(2016
).26.
O.
Filippova
and D.
Hänel
, “A novel lattice BGK approach for low Mach number combustion
,” J. Comput. Phys.
158
, 139
–160
(2000
).27.
O.
Filippova
and D.
Haenel
, “A novel numerical scheme for reactive flows at low Mach numbers
,” Comput. Phys. Commun.
129
, 267
–274
(2000
).28.
M.
Ashna
and M.
Rahimian
, “LMB simulation of head-on collision of evaporating and burning droplets in coalescence regime
,” Int. J. Heat Mass Transfer
109
, 520
–536
(2017
).29.
T.
Lee
, C.-L.
Lin
, and L.-D.
Chen
, “A lattice Boltzmann algorithm for calculation of the laminar jet diffusion flame
,” J. Comput. Phys.
215
, 133
–152
(2006
).30.
T.
Inamuro
, T.
Ogata
, S.
Tajima
, and N.
Konishi
, “A lattice Boltzmann method for incompressible two-phase flows with large density differences
,” J. Comput. Phys.
198
, 628
–644
(2004
).31.
S.
Mukherjee
and J.
Abraham
, “A pressure-evolution-based multi-relaxation-time high-density-ratio two-phase lattice-Boltzmann model
,” Comput. Fluids
36
, 1149
–1158
(2007
).32.
K.
Connington
, M.
Miskin
, T.
Lee
, H.
Jaeger
, and J.
Morris
, “Lattice Boltzmann simulations of particle-laden liquid bridges: Effects of volume fraction and wettability
,” Int. J. Multiphase Flow
76
, 32
–46
(2015
).33.
T.
Lee
, “Effects of incompressibility on the elimination of parasitic currents in the lattice Boltzmann equation method for binary fluids
,” Comput. Math. Appl.
58
, 987
–994
(2009
).34.
A.
Fakhari
, M.
Geier
, and T.
Lee
, “A mass-conserving lattice Boltzmann method with dynamic grid refinement for immiscible two-phase flows
,” J. Comput. Phys.
315
, 434
–457
(2016
).35.
K.
Sahu
and S.
Vanka
, “A multiphase lattice Boltzmann study of buoyancy-induced mixing in a tilted channel
,” Comput. Fluids
50
, 199
–215
(2011
).36.
K.
Connington
and T.
Lee
, “Lattice Boltzmann simulations of forced wetting transitions of drops on superhydrophobic surfaces
,” J. Comput. Phys.
250
, 601
–615
(2013
).37.
T.
Lee
and L.
Liu
, “Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces
,” J. Comput. Phys.
229
, 8045
–8063
(2010
).38.
L.
Amaya-Bower
and T.
Lee
, “Single bubble rising dynamics for moderate Reynolds number using lattice Boltzmann method
,” Comput. Fluids
39
, 1191
–1207
(2010
).39.
R.
Abadi
and M.
Rahimian
, “Hybrid lattice Boltzmann finite difference model for simulation of phase change in a ternary fluid
,” Int. J. Heat Mass Transfer
127
, 704
–716
(2018
).40.
E.
Reyhanian
, M.
Rahimian
, and S.
Farsid Chini
, “Investigation of 2D drop evaporation on a smooth and homogeneous surface using lattice Boltzmann method
,” Int. Commun. Heat Mass Transfer
89
, 64
–72
(2018
).41.
H.
Safari
, M.
Rahimian
, and M.
Krafczyk
, “Extended lattice Boltzmann method for simulation of thermal phase change in two-phase fluid flow
,” Phys. Rev. E
88
, 013304
(2013
).42.
H.
Safari
, M.
Rahimian
, and M.
Krafczyk
, “Consistent simulation of droplet evaporation based on phase-field multiphase lattice Boltzmann method
,” Phys. Rev. E
90
, 033305
(2014
).43.
M.
Mohammadi-Shad
and T.
Lee
, “Phase-field lattice Boltzmann modelling of boiling using a sharp-interface energy solver
,” Phys. Rev. E
96
, 013306
(2017
).44.
R.
Knikker
, “A comparative study of high-order variable-property segregated algorithms for unsteady low Mach number flows
,” Int. J. Numer. Methods Fluids
66
, 403
–427
(2011
).45.
N.
Kwatra
, J.
Su
, J.
Grétarsson
, and R.
Fedkiw
, “A method for avoiding the acoustic time step restriction in compressible flow
,” J. Comput. Phys.
228
, 4146
–4162
(2009
).46.
K.
Nerinckx
, J.
Vierendeels
, and E.
Dick
, “Mach-uniformity through the coupled pressure and temperature correction algorithm
,” J. Comput. Phys.
206
, 597
–623
(2005
).47.
G.
Hauke
, A.
Landaberea
, I.
Garmendia
, and J.
Canales
, “A segregated method for compressible flow computation Part I: Isothermal compressible flows
,” Int. J. Numer. Methods Fluids
47
, 271
–323
(2005
).48.
G.
Hauke
, A.
Landaberea
, I.
Garmendia
, and J.
Canales
, “A segregated method for compressible flow computation. Part II: General divariant compressible flows
,” Int. J. Numer. Methods Fluids
49
, 183
–209
(2005
).49.
M.
Darwish
, F.
Moukalled
, and B.
Sekar
, “A unified formulation of the segregated class of algorithms for multifluid flow at all speeds
,” Numer. Heat Transfer, Part B
40
, 99
–137
(2001
).50.
F.
Moukalled
and M.
Darwish
, “Pressure-based algorithms for multifluid flow at all speeds—Part I: Mass conservation formulation
,” Numer. Heat Transfer, Part B
45
, 495
–522
(2004
).51.
A.
Chorin
, “A numerical method for solving incompressible viscous flow problems
,” J. Comput. Phys.
2
, 12
–26
(1967
).52.
A.
Chorin
, “Numerical solution of the Navier-Stokes equations
,” Math. Comput.
22
, 745
–762
(1968
).53.
C.
Hirt
and B.
Nichols
, “Adding limited compressibility to incompressible hydrocodes
,” J. Comput. Phys.
34
, 390
–400
(1980
).54.
P.
Madsen
and H.
Schäffer
, “A discussion of artificial compressibility
,” Coastal Eng.
53
, 93
–98
(2006
).55.
W.
Kim
and S.
Menon
, “An unsteady incompressible Navier-Stokes solver for large eddy simulation of turbulent flows
,” Int. J. Numer. Methods Fluids
31
, 983
–1017
(1999
).56.
A.
Kajzer
and J.
Pozorski
, “Application of the entropically damped artificial compressibility model to direct numerical simulation of turbulent channel flow
,” Comput. Math. Appl.
76
, 997
–1013
(2018
).57.
A.
Toutant
, “Numerical simulations of unsteady viscous incompressible flows using general pressure equation
,” J. Comput. Phys.
374
, 822
–842
(2018
).58.
X.
He
, G. D.
Doolen
, and T.
Clark
, “Comparison of the lattice Boltzmann method and the artificial compressibility method for Navier–Stokes equations
,” J. Comput. Phys.
179
, 439
–451
(2002
).59.
P.
Asinari
, T.
Ohwada
, E.
Chiavazzo
, and A.
Di Rienzo
, “Link-wise artificial compressibility method
,” J. Comput. Phys.
231
, 5109
–5143
(2012
).60.
T.
Lee
and C.-L.
Lin
, “Pressure evolution lattice-Boltzmann-equation method for two-phase flow with phase change
,” Phys. Rev. E
67
, 056703
(2003
).61.
S.
Karni
, “Hybrid multifluid algorithms
,” SIAM J. Sci. Comput.
17
, 1019
–1039
(1996
).62.
R.
Abgrall
and S.
Karni
, “Computations of compressible multifluids
,” J. Comput. Phys.
169
, 594
–623
(2001
).63.
A.
Toutant
, “General and exact pressure evolution equation
,” Phys. Lett. A
381
, 3739
–3742
(2017
).64.
J.
Jacob
and P.
Sagaut
, “Wind comfort assessment by means of large eddy simulation with lattice Boltzmann method in full scale city area
,” Build. Environ.
139
, 110
–124
(2018
).65.
P. J.
Dellar
, “An interpretation and derivation of the lattice Boltzmann method using strang splitting
,” Comput. Math. Appl.
65
, 129
–141
(2013
).66.
Y.-L.
Feng
, S.-L.
Guo
, W.-Q.
Tao
, and P.
Sagaut
, “Regularized thermal lattice Boltzmann method for natural convection with large temperature differences
,” Int. J. Heat Mass Transfer
125
, 1379
–1391
(2018
).67.
S.
Marié
, D.
Ricot
, and P.
Sagaut
, “Comparison between lattice Boltzmann method and Navier–Stokes high order schemes for computational aeroacoustics
,” J. Comput. Phys.
228
, 1056
–1070
(2009
).68.
D.
Fabre
, L.
Jacquin
, and J.
Sesterhenn
, “Linear interaction of a cylindrical entropy spot with a shock
,” Phys. Fluids
13
, 2403
–2422
(2001
).69.
70.
E. F.
Toro
, Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction
(Springer Science & Business Media
, 2009
).71.
O.
Inoue
and Y.
Hattori
, “Sound generation by shock–vortex interactions
,” J. Fluid Mech.
380
, 81
–116
(1999
).© 2020 Author(s).
2020
Author(s)
You do not currently have access to this content.
