Multidomain Finite Element Computations: Application to Multiphasic Problems

Abstract : Contents: Introduction. A classification of multidomain approaches. Notations. Functional and discrete spaces. Bubble space. Element length definition. Characterization of different phases. The level set or signed distance functions. Mesh adaptation. Displacement of the level set function. The reinitialization. Convective reinitialization. The local distance function. Parameters of reinitialized and truncated convective equations. Stabilized finite element formulations. Multidomain Navier-Stokes equations. Weak formulation of incompressible Navier-Stokes equations. Stable multiscale variational approach for Navier-Stokes equations. The fine scale subproblem. The coarse scale subproblem. Time advancing. Matrix formulation of the problem. Stabilized weak formulation for convection equation. Multiphasic problems with fluid-air and fluid-fluid interface. Two-dimensional Zalesak's problem. Gravitational flow. The surface tension. Immersion of solid bodies in fluid. Immersed body having an imposed velocity. Velocity-pressure formulation for solid bodies in a fluid. Weak formulation of fluid/solid system. Discrete formulation and Uzawa algorithm. Lagrangian particle displacement. A sphere in a shear flow. Two rigid spheres in stokes flow. Influence of mesh. Particle displacements