Eulerian–Lagrangian grid coupling and penalty methods for the simulation of multiphase flows interacting with complex objects

Our purpose is to develop an efficient coupling between incompressible multiphase flows and fixed or moving obstacles of complex shape. The flow is solved on a fixed Cartesian grid and the solid objects are represented by surface elements. Our strategy is based on two main originalities: the generation and management of the objects are ensured by computer graphics software and front-tracking methods, while the coupling between the flow and the obstacle grids is ensured by a fictitious domain approach and new high-order penalty techniques. Several validation problems are presented to demonstrate the interest and accuracy of the method. Copyright © 2007 John Wiley & Sons, Ltd.

[1]  J. Caltagirone,et al.  Numerical modelling of solid particle motion using a new penalty method , 2005 .

[2]  R. Glowinski,et al.  A distributed Lagrange multiplier/fictitious domain method for particulate flows , 1999 .

[3]  B. Maury.  Regular Article: Direct Simulations of 2D Fluid-Particle Flows in Biperiodic Domains , 1999 .

[4]  Seungwon Shin,et al.  Modeling three-dimensional multiphase flow using a level contour reconstruction method for front tracking without connectivity , 2002 .

[5]  Jean-Paul Caltagirone,et al.  A hybrid linking approach for solving the conservation equations with an adaptive mesh refinement method , 2006 .

[6]  S. Osher,et al.  A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method) , 1999 .

[7]  Boo Cheong Khoo,et al.  An immersed interface method for viscous incompressible flows involving rigid and flexible boundaries , 2006, J. Comput. Phys..

[8]  Philippe Angot,et al.  A general fictitious domain method with immersed jumps and multilevel nested structured meshes , 2007, J. Comput. Phys..

[9]  J. Caltagirone,et al.  A One-Cell Local Multigrid Method for Solving Unsteady Incompressible Multiphase Flows , 2000 .

[10]  P. Angot,et al.  A Fictitious domain approach with spread interface for elliptic problems with general boundary conditions , 2007 .

[11]  Grégoire Pianet,et al.  Local penalty methods for flows interacting with moving solids at high Reynolds numbers , 2007 .

[12]  Khodor Khadra,et al.  Fictitious domain approach for numerical modelling of Navier–Stokes equations , 2000 .

[13]  C. Peskin.  The immersed boundary method , 2002, Acta Numerica.