2020/11/02 by Jun-Jie Huang, Jun‐Jie Huang, Huang, Jun-Jie · 1 citation
Engineering · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Heat Transfer #Fluid Dynamics and Thin Films #Lattice Boltzmann Simulation Studies #physics.comp-ph #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.2011.00814
arxiv created 2020/11/02 · openalex publication_date 2020/11/02 · arxiv updated 2020/11/03 · openalex created_date 2020/11/09 · openalex updated_date 2026/07/28
The general pressure equation (GPE) is a new method proposed recently by Toutant (J. Comput. Phys., 374:822-842 (2018)) for incompressible flow simulation. It circumvents the Poisson equation for the pressure and performs better than the classical artificial compressibility method. Here it is generalized for two-phase incompressible viscous flows with variable density and viscosity. First, the pressure evolution equation is modified to account for the density variation. Second, customized discretizations are proposed to deal with the viscous stress terms with variable viscosity. Besides, additional terms related to the bulk viscosity are included to stabilize the simulation. The interface evolution and surface tension effects are handled by a phase-field model coupled with the GPE-based flow equations. The pressure and momentum equations are discretized on a stagger grid using the second order centered scheme and marched in time using the third order total variation diminishing Runge-Kutta scheme. Several unsteady two-phase problems in two dimensional, axisymmetric and three dimensional geometries at intermediate density and viscosity ratios were simulated and the results agreed well with those obtained by other incompressible solvers and/or the lattice-Boltzmann method (LBM) simulations. Similar to the LBM, the proposed GPE-based method is fully explicit and easy to be parallelized. Although slower than the LBM, it requires much less memory than the LBM. Thus, it can be a good alternative to simulate two-phase flows with limited memory resource.