Implementation of a high-order compact finite-difference lattice Boltzmann method in generalized curvilinear coordinates

[1]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[2]  D. Tritton Experiments on the flow past a circular cylinder at low Reynolds numbers , 1959, Journal of Fluid Mechanics.

[3]  A. S. Grove,et al.  An experimental investigation of the steady separated flow past a circular cylinder , 1964, Journal of Fluid Mechanics.

[4]  S. Dennis,et al.  Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100 , 1970, Journal of Fluid Mechanics.

[5]  E. Berger,et al.  Periodic Flow Phenomena , 1972 .

[6]  H. B. Keller,et al.  Viscous flow past circular cylinders , 1973 .

[7]  F. White Viscous Fluid Flow , 1974 .

[8]  R. Hirsh,et al.  Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique , 1975 .

[9]  R. Bouard,et al.  Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Part 1. Steady flow , 1977, Journal of Fluid Mechanics.

[10]  R. L. Sorenson,et al.  Automatic mesh-point clustering near a boundary in grid generation with elliptic partial differential equations , 1979 .

[11]  U. Ghia,et al.  High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method , 1982 .

[12]  S. Lele Compact finite difference schemes with spectral-like resolution , 1992 .

[13]  James D. Sterling,et al.  Accuracy of Discrete-Velocity BGK Models for the Simulation of the Incompressible Navier-Stokes Equations , 1993, comp-gas/9307003.

[14]  D. Gottlieb,et al.  The Stability of Numerical Boundary Treatments for Compact High-Order Finite-Difference Schemes , 1993 .

[15]  Li-Shi Luo,et al.  Some Progress in Lattice Boltzmann Method. Part I. Nonuniform Mesh Grids , 1996 .

[16]  L. Luo,et al.  Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation , 1997 .

[17]  L. Luo,et al.  Lattice Boltzmann Model for the Incompressible Navier–Stokes Equation , 1997 .

[18]  Ernst Rank,et al.  Implicit discretization and nonuniform mesh refinement approaches for FD discretizations of LBGK Models , 1998 .

[19]  Hudong Chen VOLUMETRIC FORMULATION OF THE LATTICE BOLTZMANN METHOD FOR FLUID DYNAMICS : BASIC CONCEPT , 1998 .

[20]  Wei Shyy,et al.  On the Finite Difference-Based Lattice Boltzmann Method in Curvilinear Coordinates , 1998 .

[21]  Chaoqun Liu,et al.  Preconditioned Multigrid Methods for Unsteady Incompressible Flows , 1997 .

[22]  Miguel R. Visbal,et al.  Further development of a Navier-Stokes solution procedure based on higher-order formulas , 1999 .

[23]  Miguel R. Visbal,et al.  High-Order-Accurate Methods for Complex Unsteady Subsonic Flows , 1999 .

[24]  S. Chou,et al.  Finite-volume lattice Boltzmann method. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  Jeffrey L. Young,et al.  Practical aspects of higher-order numerical schemes for wave propagation phenomena , 1999 .

[26]  D. Wolf-Gladrow Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction , 2000 .

[27]  Luo Li-Shi,et al.  Theory of the lattice Boltzmann method: Lattice Boltzmann models for non-ideal gases , 2001 .

[28]  R. Smith,et al.  An edge-based method for the incompressible Navier—Stokes equations on polygonal meshes , 2001 .

[29]  Taehun Lee,et al.  A characteristic Galerkin method for discrete Boltzmann equation , 2001 .

[30]  W. Shyy,et al.  A multi‐block lattice Boltzmann method for viscous fluid flows , 2002 .

[31]  Miguel R. Visbal,et al.  On the use of higher-order finite-difference schemes on curvilinear and deforming meshes , 2002 .

[32]  D. Calhoun A Cartesian Grid Method for Solving the Two-Dimensional Streamfunction-Vorticity Equations in Irregular Regions , 2002 .

[33]  Zhaoli Guo,et al.  Explicit finite-difference lattice Boltzmann method for curvilinear coordinates. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Jianzhong Lin,et al.  Discontinuous Galerkin spectral element lattice Boltzmann method on triangular element , 2003 .

[35]  S. Succi,et al.  Lattice Boltzmann method on unstructured grids: further developments. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Michihisa Tsutahara,et al.  Two-dimensional thermal model of the finite-difference lattice Boltzmann method with high spatial isotropy. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Taehun Lee,et al.  An Eulerian description of the streaming process in the lattice Boltzmann equation , 2003 .

[38]  Z. J. Wang,et al.  A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow , 2003 .

[39]  Victor Sofonea,et al.  Viscosity of finite difference lattice Boltzmann models , 2003 .

[40]  E. Erturk,et al.  Numerical solutions of 2‐D steady incompressible driven cavity flow at high Reynolds numbers , 2004, ArXiv.

[41]  A. Xu Finite-difference lattice-Boltzmann methods for binary fluids. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  Taro Imamura,et al.  Acceleration of steady-state lattice Boltzmann simulations on non-uniform mesh using local time step method , 2005 .

[43]  E. LeBoeuf,et al.  Least-squares finite-element scheme for the lattice Boltzmann method on an unstructured mesh. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  Taro Imamura,et al.  Flow Simulation Around an Airfoil by Lattice Boltzmann Method on Generalized Coordinates , 2005 .

[45]  Zhaoli Guo,et al.  Finite difference-based lattice Boltzmann simulation of natural convection heat transfer in a horizontal concentric annulus , 2006 .

[46]  Ernst Rank,et al.  High‐order finite elements applied to the discrete Boltzmann equation , 2006 .

[47]  Manfred Krafczyk,et al.  An upwind discretization scheme for the finite volume lattice Boltzmann method , 2006 .

[48]  Long Wu,et al.  Finite Difference Lattice Boltzmann Method for Incompressible Navier-Stokes Equation Using Acceleration Modification , 2007 .

[49]  M. Hafez,et al.  Improved Numerical Simulations of Incompressible Flows Based on Viscous/Inviscid Interaction Procedures , 2007 .

[50]  Pierre Lallemand,et al.  On lattice Boltzmann scheme, finite volumes and boundary conditions , 2008, 2306.15291.

[51]  Dhiraj V. Patil,et al.  Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh , 2009, J. Comput. Phys..

[52]  Manfred Krafczyk,et al.  Second order interpolation of the flow field in the lattice Boltzmann method , 2009, Comput. Math. Appl..

[53]  Pierre Sagaut,et al.  Lattice Boltzmann method with selective viscosity filter , 2009, J. Comput. Phys..

[54]  R. M. C. So,et al.  Stochastic finite difference lattice Boltzmann method for steady incompressible viscous flows , 2010, J. Comput. Phys..

[55]  Tony W. H. Sheu,et al.  A differentially interpolated direct forcing immersed boundary method for predicting incompressible Navier-Stokes equations in time-varying complex geometries , 2010, J. Comput. Phys..

[56]  Manfred Krafczyk,et al.  A lattice Boltzmann approach for free-surface-flow simulations on non-uniform block-structured grids , 2010, Comput. Math. Appl..

[57]  Taehun Lee,et al.  A spectral-element discontinuous Galerkin lattice Boltzmann method for nearly incompressible flows , 2011, J. Comput. Phys..

[58]  J. Wu,et al.  A solution-adaptive lattice Boltzmann method for two-dimensional incompressible viscous flows , 2011, J. Comput. Phys..

[59]  Kazem Hejranfar,et al.  Implementing a high‐order accurate implicit operator scheme for solving steady incompressible viscous flows using artificial compressibility method , 2011 .

[60]  Martin Geier,et al.  Multi-thread implementations of the lattice Boltzmann method on non-uniform grids for CPUs and GPUs , 2011, Comput. Math. Appl..

[61]  A. N. Gorban,et al.  Add-ons for Lattice Boltzmann Methods: Regularization, Filtering and Limiters , 2013 .

[62]  Kazem Hejranfar,et al.  A high‐order compact finite‐difference lattice Boltzmann method for simulation of steady and unsteady incompressible flows , 2014 .