A dual grid, dual level set based cut cell immersed boundary approach for simulation of multi-phase flow

A numerical methodology based on dual grid dual level set function is presented for simulating 2D multiphase flows through complex geometries on a non-body fitted Cartesian computational grid. A Cut Cell based immersed boundary method (IBM) is used to sharply resolve complex geometries. The cut cells near the immersed boundary are identified using a fictitious level set function. The governing equations are discretized using the finite volume method (FVM) on a m × n staggered grid. The dynamics of fluid-fluid interface is tracked by an other level set function defined on dual grid (2m × 2n). The use of dual grid arrangement for fictitious level set function results in an accurate calculation of diffusion and advection fluxes at the cut cell near the immersed boundary. A module by module validation of the developed numerical methodology is carried out with several test cases. Two single phase flow problems corresponds to Poiseuille flow and flow through a convergent-divergent section while the two multiphase problems selected are the standard Young's Laplace law test - semicircular fluid rod on a horizontal surface - and the bubble rise phenomenon in an inclined channel. The obtained results show an excellent agreement with those derived analytically or taken from literature. Furthermore, the performance study carried out on the present model shows that the method is between first and second order accurate.