A conservation-moment-based implicit finite volume lattice Boltzmann method for steady nearly incompressible flows

Nourgaliev, 2003, The lattice Boltzmann equation method: theoretical interpretation, numerics and implications, Int. J. Multiph. Flow, 29, 117, 10.1016/S0301-9322(02)00108-8 Chen, 1998, Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech., 30, 329, 10.1146/annurev.fluid.30.1.329 McNamara, 1988, Use of the Boltzmann equation to simulate lattice-gas automata, Phys. Rev. Lett., 61, 2332, 10.1103/PhysRevLett.61.2332 Cao, 1997, Physic symmetry and lattice symmetry in the lattice Boltzmann method, Phys. Rev. E, 55, R21, 10.1103/PhysRevE.55.R21 Guo, 2003, Explicit finite-difference lattice Boltzmann method for curvilinear coordinates, Phys. Rev. E, 67, 10.1103/PhysRevE.67.066709 Reider, 1995, Accuracy of discrete-velocity BGK models for the simulation of the incompressible Navier-Stokes equations, Comput. Fluids, 24, 459, 10.1016/0045-7930(94)00037-Y Ubertini, 2003, Lattice Boltzmann method on unstructured grids: further developments, Phys. Rev. E, 68, 10.1103/PhysRevE.68.016701 Stiebler, 2006, An upwind discretization scheme for the finite volume lattice Boltzmann method, Comput. Fluids, 35, 814, 10.1016/j.compfluid.2005.09.002 Patil, 2009, Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh, J. Comput. Phys., 228, 5262, 10.1016/j.jcp.2009.04.008 Li, 2013, A stable, low diffusion up-wind scheme for unstructured finite volume lattice Boltzmann method, 3 Li, 2016, Finite volume lattice Boltzmann method for nearly incompressible flows on arbitrary unstructured meshes, Commun. Comput. Phys., 20, 301, 10.4208/cicp.211015.040316a Li, 2016, An implicit block LUSGS finite volume lattice Boltzmann scheme for steady flows on arbitrary unstructured meshes, J. Comput. Phys., 327, 503, 10.1016/j.jcp.2016.09.038 Lee, 2001, A characteristic Galerkin method for discrete Boltzmann equation, J. Comput. Phys., 171, 336, 10.1006/jcph.2001.6791 Lee, 2003, An Eulerian description of the streaming process in the lattice Boltzmann equation, J. Comput. Phys., 185, 445, 10.1016/S0021-9991(02)00065-7 Li, 2005, Least-squares finite-element scheme for the lattice Boltzmann method on an unstructured mesh, Phys. Rev. E, 72, 10.1103/PhysRevE.72.046711 Li, 2017, High order spectral difference lattice Boltzmann method for incompressible hydrodynamics, J. Comput. Phys., 345, 618, 10.1016/j.jcp.2017.05.039 Tölke, 1998, Implicit discretization and nonuniform mesh refinement approaches for FD discretizations of LBGK models, Int. J. Mod. Phys. C, 09, 1143, 10.1142/S0129183198001059 Huang, 2015, A fully implicit method for lattice Boltzmann equations, SIAM J. Sci. Comput., 37, S291, 10.1137/140975346 Li, 2017, A matrix-free, implicit finite volume lattice Boltzmann method for steady flows, Comput. Fluids, 148, 157, 10.1016/j.compfluid.2017.02.019 Gol'Din, 1964, A quasi-diffusion method of solving the kinetic equation, USSR Comput. Math. Math. Phys., 4, 136, 10.1016/0041-5553(64)90085-0 Alcouffe, 1977, Diffusion synthetic acceleration methods for the diamond-differenced discrete-ordinates equations, Nucl. Sci. Eng., 64, 344, 10.13182/NSE77-1 Winkler, 1985, Implicit adaptive-grid radiation hydrodynamics, 145 Larsen, 1988, A grey transport acceleration method for time-dependent radiative transfer problems, J. Comput. Phys., 78, 459, 10.1016/0021-9991(88)90060-5 Mason, 1981, Implicit moment particle simulation of plasmas, J. Comput. Phys., 41, 233, 10.1016/0021-9991(81)90094-2 Brackbill, 1982, An implicit method for electromagnetic plasma simulation in two dimensions, J. Comput. Phys., 46, 271, 10.1016/0021-9991(82)90016-X Zhu, 2016, Implicit unified gas-kinetic scheme for steady state solutions in all flow regimes, J. Comput. Phys., 315, 16, 10.1016/j.jcp.2016.03.038 Taitano, 2014, Moment-based acceleration for neutral gas kinetics with BGK collision operator, J. Comput. Theor. Transp., 43, 83, 10.1080/00411450.2014.910228 Chacón, 2017, Multiscale high-order/low-order (holo) algorithms and applications, J. Comput. Phys., 330, 21, 10.1016/j.jcp.2016.10.069 Li, 2018, A gas-kinetic BGK scheme for the finite volume lattice Boltzmann method for nearly incompressible flows, Comput. Fluids, 162, 126, 10.1016/j.compfluid.2017.12.008 He, 1997, Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation, Phys. Rev. E, 56, 6811, 10.1103/PhysRevE.56.6811 Qian, 1992, Lattice BGK models for Navier-Stokes equation, Europhys. Lett., 17, 479, 10.1209/0295-5075/17/6/001 d'Humières, 1994, Generalized lattice-Boltzmann equations, Rarefied gas dynamics: theory and simulations, Prog. Astronaut. Aeronaut., 450 Lallemand, 2000, Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability, Phys. Rev. E, 61, 6546, 10.1103/PhysRevE.61.6546 Jameson, 1987, Lower-upper implicit schemes with multiple grids for the Euler equations, AIAA J., 25, 929, 10.2514/3.9724 Sharov, 1997, Reordering of 3D hybrid unstructured grids for vectorized LUSGS Navier-Stokes computations, AIAA Pap., 97, 2102 Luo, 2000, A fast, matrix-free implicit method for computing low Mach number flows on unstructured grids, Int. J. Comput. Fluid Dyn., 14, 133, 10.1080/10618560008940720 Li, 2013, A new matrix-free, high efficient preconditioned LUSGS method for low Mach axisymmetric flows on unstructured mesh, 3 Li, 2014, An implicit gas kinetic BGK scheme for high temperature equilibrium gas flows on unstructured meshes, Comput. Fluids, 93, 100, 10.1016/j.compfluid.2014.01.015 Roe, 1981, Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys., 43, 357, 10.1016/0021-9991(81)90128-5 Li, 2017, On convergence accelerations of the DUGKS for steady nearly incompressible flows Blazek, 2005 Kovasznay, 1948, Laminar flow behind a two-dimensional grid, Proc. Camb. Philos. Soc., 44, 58, 10.1017/S0305004100023999 Schlichting, 2000 Chen, 2012, A unstructured nodal spectral-element method for the Navier-Stokes equations, Commun. Comput. Phys., 10.4208/cicp.070111.140711a Watari, 2003, Two-dimensional thermal model of the finite-difference lattice Boltzmann method with high spatial isotropy, Phys. Rev. E, 67, 10.1103/PhysRevE.67.036306 Feng, 2015, A three dimensional lattice model for thermal compressible flow on standard lattices, J. Comput. Phys., 303, 514, 10.1016/j.jcp.2015.09.011 Feng, 2016, A compressible lattice Boltzmann finite volume model for high subsonic and transonic flows on regular lattices, Comput. Fluids, 131, 45, 10.1016/j.compfluid.2016.03.009 Shizgal, 1981, A Gaussian quadrature procedure for use in the solution of the Boltzmann equation and related problems, J. Comput. Phys., 41, 309, 10.1016/0021-9991(81)90099-1 Yang, 1995, Numerical solutions of the nonlinear model Boltzmann equations, Proc. R. Soc. Lond. Ser. A, 448, 55, 10.1098/rspa.1995.0003 Mieussens, 2000, Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries, J. Comput. Phys., 162, 429, 10.1006/jcph.2000.6548 Guo, 2004, Preconditioned lattice-Boltzmann method for steady flows, Phys. Rev. E, 70, 10.1103/PhysRevE.70.066706 De Rosis, 2017, Preconditioned lattice Boltzmann method for steady flows: A noncascaded central-moments-based approach, Phys. Rev. E, 96, 10.1103/PhysRevE.96.063308 Hejranfar, 2018, Preconditioned WENO finite-difference lattice Boltzmann method for simulation of incompressible turbulent flows, Comput. Math. Appl., 76, 1427, 10.1016/j.camwa.2018.06.036