A hybrid scheme based on finite element/volume methods for two immiscible fluid flows

Abstract

SUMMARYWe have successfully extended our implicit hybrid finite element/volume (FE/FV) solver to flows involving two immiscible fluids. The solver is based on the segregated pressure correction or projection method on staggered unstructured hybrid meshes. An intermediate velocity field is first obtained by solving the momentum equations with the matrix-free implicit cell-centered FV method. The pressure Poisson equation is solved by the node-based Galerkin FE method for an auxiliary variable. The auxiliary variable is used to update the velocity field and the pressure field. The pressure field is carefully updated by taking into account the velocity divergence field. This updating strategy can be rigorously proven to be able to eliminate the unphysical pressure boundary layer and is crucial for the correct temporal convergence rate. Our current staggered-mesh scheme is distinct from other conventional ones in that we store the velocity components at cell centers and the auxiliary variable at vertices. The fluid interface is captured by solving an advection equation for the volume fraction of one of the fluids. The same matrix-free FV method, as the one used for momentum equations, is used to solve the advection equation. We will focus on the interface sharpening strategy to minimize the smearing of the interface over time. We have developed and implemented a global mass conservation algorithm that enforces the conservation of the mass for each fluid.

Numerical Modeling and Experimental Validation of Free Surface Flow Problems

“…Particularly, the interface or free surface is smartly identified at variable φ enforcing the volume preservation of a fluid chunk. This technique, called later Interface-Sharpening/Global Mass Conservation (IS-GMC), was used for simulating the free surface together with an Arbitrary Lagrangian-Eulerian (ALE) method for the mesh movement of rigid bodies in order to calculate mooring forces [6] and, it was also mixed with an hybrid FEM/FVM solver for the NS equations [225] with a turbulence model.…”

Experimental validation of computational fluid dynamics for solving isothermal and incompressible viscous fluid flow

“…Novel approaches have been proposed for advancing meshing algorithms as well as developing better solvers for fluid dynamics [75][76][77][78]. Also novel developments exist in hybrid methods as in [79][80][81] leading to research codes as in [82] as well as incorporating semi-analytical methods [83] or by modeling jump conditions on element boundaries in [84][85][86]. All these different theoretical approaches and various numerical implementations indicate that a computational method accepted by all communities is unlikely to occur in the near future.…”

A hybrid incremental projection method for thermal-hydraulics applications

“…The first use of a predominantly finite volume scheme with a continuous Galerkin pressure-Poisson operator appeared in the work of Bell, et al [2], albeit using structured meshes with explicit advection, and a time-step strictly constrained by CF L < 1. More recently, Aliabadi and co-workers have developed a method [33][34][35] that is similar to that presented here, although they use a more complex pressure update.…”