PHYSALIS: A new method for particle flow simulation. III: Convergence analysis of two-dimensional flows. We study the convergence property of PHYSALIS when it is applied to incompressible particle flows in two-dimensional space. PHYSALIS is a recently proposed iterative method which computes the solution without imposing the boundary conditions on the particle surfaces directly. Instead, a consistency equation based on the local (near particle) representation of the solution is used as the boundary conditions. One of the important issues needs to be addressed is the convergence properties of the iterative procedure. In this paper, we present the convergence analysis using Laplace and biharmonic equations as two model problems. It is shown that convergence of the method can be achieved but the rate of convergence depends on the relative locations of the cages. The results are directly related to potential and Stokes flows. However, they are also relevant to Navier-Stokes flows, heat conduction in composite media, and other problems.

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  1. Vincent, Stéphane; Brändle de Motta, Jorge César; Sarthou, Arthur; Estivalezes, Jean-Luc; Simonin, Olivier; Climent, Eric: A Lagrangian VOF tensorial penalty method for the DNS of resolved particle-laden flows (2014)
  2. Wang, Lian-Ping; Ayala, Orlando; Gao, Hui; Andersen, Charles; Mathews, Kevin L.: Study of forced turbulence and its modulation by finite-size solid particles using the lattice Boltzmann approach (2014)
  3. Liu, Qianlong: Directly resolving particles in an electric field: local charge, force, torque, and applications (2012)
  4. Bertoluzza, Silvia; Ismail, Mourad; Maury, Bertrand: Analysis of the fully discrete fat boundary method (2011)
  5. Liu, Qianlong: Physalis method for heterogeneous mixtures of dielectrics and conductors: accurately simulating one million particles using a PC (2011)
  6. Sugiyama, Kazuyasu; Ii, Satoshi; Takeuchi, Shintaro; Takagi, Shu; Matsumoto, Yoichiro: A full Eulerian finite difference approach for solving fluid-structure coupling problems (2011)
  7. Xu, Ying; Subramaniam, Shankar: Effect of particle clusters on carrier flow turbulence: A direct numerical simulation study (2010)
  8. Luo, Xian; Maxey, Martin R.; Karniadakis, George Em: Smoothed profile method for particulate flows: Error analysis and simulations (2009)
  9. Wang, Zeli; Fan, Jianren; Cen, Kefa: Immersed boundary method for the simulation of 2D viscous flow based on vorticity-velocity formulations (2009)
  10. Xia, Zhenhua; Connington, Kevin W.; Rapaka, Saikiran; Yue, Pengtao; Feng, James J.; Chen, Shiyi: Flow patterns in the sedimentation of an elliptical particle (2009)
  11. Zhang, Quan; Prosperetti, Andrea: Pressure-driven flow in a two-dimensional channel with porous walls (2009)
  12. Ardekani, A.M.; Rangel, R.H.; Joseph, D.D.: Two spheres in a free stream of a second-order fluid (2008)
  13. Gao, Hui; Han, Jie; Jin, Yan; Wang, Lian-Ping: Modelling microscale flow and colloid transport in saturated porous media (2008)
  14. Perrin, A.; Hu, H.H.: An explicit finite difference scheme with spectral boundary conditions for particulate flows (2008)
  15. Ardekani, A.M.; Rangel, R.H.; Joseph, D.D.: Motion of a sphere normal to a wall in a second-order fluid (2007)
  16. Ayala, Orlando; Grabowski, Wojciech W.; Wang, Lian-Ping: A hybrid approach for simulating turbulent collisions of hydrodynamically-interacting particles (2007)
  17. Luo, Kun; Wang, Zeli; Fan, Jianren: A modified immersed boundary method for simulations of fluid-particle interactions (2007)
  18. Xu, Sheng; Wang, Z.Jane: An immersed interface method for simulating the interaction of a fluid with moving boundaries (2006)
  19. Pan, Tsorng-Whay; Glowinski, Roland; Joseph, Daniel D.: Simulating the dynamics of fluid-cylinder interactions (2005)
  20. Zhang, Z.; Prosperetti, A.: A second-order method for three-dimensional particle simulation (2005)

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