An immersed boundary-gas kinetic flux solver for simulation of incompressible flows

Xu, 2001, A gas-kinetic BGK scheme for the Navier–Stokes equations and its connection with artificial dissipation and Godunov method, J Comput Phys, 171, 289, 10.1006/jcph.2001.6790 Bhatnagar, 1954, A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems, Phys Rev, 94, 511, 10.1103/PhysRev.94.511 Xu, 1998, Gas-kinetic schemes for the unsteady compressible flow simulations, VKI Fluid Dyn Lect Ser, 1998(3) Sun, 2015, Explicit formulations of gas-kinetic flux solver for simulation of incompressible and compressible viscous flows, J Comput Phys, 300, 492, 10.1016/j.jcp.2015.07.060 Peskin, 1977, Numerical analysis of blood flow in the heart, J Comput Phys, 25, 220, 10.1016/0021-9991(77)90100-0 Wu, 2009, Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications, J Comput Phys, 228, 1963, 10.1016/j.jcp.2008.11.019 Goldstein, 1993, Modeling a no-slip flow boundary with an external force field, J Comput Phys, 105, 354, 10.1006/jcph.1993.1081 Mohd-Yusof, 1997, Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries, Annu Res Briefs, Cent Turbul Res, 317 Fadlun, 2000, Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations, J Comput Phys, 161, 35, 10.1006/jcph.2000.6484 Balaras, 2004, Modeling complex boundaries using an external force field on fixed Cartesian grids in large-eddy simulations, Comput Fluids, 33, 375, 10.1016/S0045-7930(03)00058-6 Uhlmann, 2005, An immersed boundary method with direct forcing for the simulation of particulate flows, J Comput Phys, 209, 448, 10.1016/j.jcp.2005.03.017 Wang, 2009, Immersed boundary method for the simulation of 2D viscous flow based on vorticity–velocity formulations, J Comput Phys, 228, 1504, 10.1016/j.jcp.2008.10.038 Feng, 2004, The immersed boundary-lattice Boltzmann method for solving fluid–particles interaction problems, J Comput Phys, 195, 602, 10.1016/j.jcp.2003.10.013 Feng, 2005, Proteus: a direct forcing method in the simulations of particulate flows, J Comput Phys, 202, 20, 10.1016/j.jcp.2004.06.020 Niu, 2006, A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows, Phys Lett A, 354, 173, 10.1016/j.physleta.2006.01.060 Ye, 1999, An Accurate Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries, J Comput Phys, 156, 209, 10.1006/jcph.1999.6356 Shu, 2007, A novel immersed boundary velocity correction–lattice Boltzmann method and its application to simulate flow past a circular cylinder, J Comput Phys, 226, 1607, 10.1016/j.jcp.2007.06.002 Wang, 2015, An immersed boundary-lattice Boltzmann flux solver and its applications to fluid–structure interaction problems, J Fluids Struct, 54, 440, 10.1016/j.jfluidstructs.2014.12.003 Shu, 2014, Development of Lattice Boltzmann Flux Solver for Simulation of Incompressible Flows, Adv Appl Math Mech, 6, 436, 10.4208/aamm.2014.4.s2 Su, 2007, An immersed boundary technique for simulating complex flows with rigid boundary, Compute Fluids, 36, 313, 10.1016/j.compfluid.2005.09.004 Le, 2008, An implicit-forcing immersed boundary method for simulating viscous flows in irregular domains, Comput Methods Appl Mech Eng, 197, 2119, 10.1016/j.cma.2007.08.008 Yuan, 2015, An immersed-boundary method based on the gas kinetic BGK scheme for incompressible viscous flow, J Comput Phys, 296, 184, 10.1016/j.jcp.2015.04.052 Xu, 2003, Lattice Boltzmann method and gas-kinetic BGK scheme in the low-Mach number viscous flow simulations, J Comput Phys, 190, 100, 10.1016/S0021-9991(03)00255-9 Xu, 2010, A unified gas-kinetic scheme for continuum and rarefied flows, J Comput Phys, 229, 7747, 10.1016/j.jcp.2010.06.032 Peskin, 2002, The immersed boundary method, Acta Numer, 11, 479, 10.1017/S0962492902000077 Suzuki, 2011, Effect of internal mass in the simulation of a moving body by the immersed boundary method, Comput Fluids, 49, 173, 10.1016/j.compfluid.2011.05.011 Dennis, 1970, Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100, J Fluid Mech, 42, 471, 10.1017/S0022112070001428 Shukla, 2007, Very high-order compact finite difference schemes on non-uniform grids for incompressible Navier–Stokes equations, J Comput Phys, 224, 1064, 10.1016/j.jcp.2006.11.007 Braza, 1986, Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder, J Fluid Mech, 165, 79, 10.1017/S0022112086003014 Benson, 1989, A viscous splitting algorithm applied to low Reynolds number flows round a circular cylinder, J Fluids Struct, 3, 439, 10.1016/S0889-9746(89)80026-X Ding, 2004, Simulation of incompressible viscous flows past a circular cylinder by hybrid FD scheme and meshless least square-based finite difference method, Comput Methods Appl Mech Eng, 193, 727, 10.1016/j.cma.2003.11.002 Imamura, 2004, Flow simulation around an airfoil using lattice Boltzmann method on generalized coordinates, AIAA paper, 244 Lockard, 2002, Evaluation of PowerFLOW for aerodynamic applications, J Stat Phys, 107, 423, 10.1023/A:1014539411062 DÜTsch, 1998, Low-Reynolds-number flow around an oscillating circular cylinder at low Keulegan-Carpenter numbers, J Fluid Mech, 360, 249, 10.1017/S002211209800860X Yang, 2006, An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries, J Comput Phys, 215, 12, 10.1016/j.jcp.2005.10.035 Zhong, 2013, Experimental investigation of freely falling thin disks. Part 1. The flow structures and Reynolds number effects on the zigzag motion, J Fluid Mech, 716, 228, 10.1017/jfm.2012.543 Lee, 2013, Experimental investigation of freely falling thin disks. Part 2. Transition of three-dimensional motion from zigzag to spiral, J Fluid Mech, 732, 77, 10.1017/jfm.2013.390 Ren, 2012, A stream function–vorticity formulation‐based immersed boundary method and its applications, Int J Numer Methods Fluids, 70, 627, 10.1002/fld.2705 Wan, 2006, Direct numerical simulation of particulate flow via multigrid FEM techniques and the fictitious boundary method, Int J Numer Methods Fluids, 51, 531, 10.1002/fld.1129