An effective preconditioning strategy for volume penalized incompressible/low Mach multiphase flow solvers

Abstract

The volume penalization (VP) or the Brinkman penalization (BP) method is a diffuse interface method for simulating multiphase fluid-structure interaction (FSI) problems in ocean engineering and/or phase change problems in thermal sciences. The method relies on a penalty factor (which is inversely related to body's permeability $\kappa$) that must be large to enforce rigid body velocity in the solid domain. When the penalty factor is large, the discrete system of equations becomes stiff and difficult to solve numerically. In this paper, we propose a projection method-based preconditioning strategy for solving volume penalized (VP) incompressible and low-Mach Navier-Stokes equations. The projection preconditioner enables the monolithic solution of the coupled velocity-pressure system in both single phase and multiphase flow settings. In this approach, the penalty force is treated implicitly, which is allowed to take arbitrary large values without affecting the solver's convergence rate or causing numerical stiffness/instability. It is made possible by including the penalty term in the pressure Poisson equation. Solver scalability under grid refinement is demonstrated. A manufactured solution in a single phase setting is used to determine the spatial accuracy of the penalized solution. Second-order pointwise accuracy is achieved for both velocity and pressure solutions. Two multiphase fluid-structure interaction (FSI) problems from the ocean engineering literature are also simulated to evaluate the solver's robustness and performance. The proposed solver allows us to investigate the effect of $\kappa$ on the motion of the contact line over the surface of the immersed body. It also allows us to investigate the dynamics of the free surface of a solidifying metal

References in corpus (13)

• Hydrodynamics of Suspensions of Passive and Active Rigid Particles: A Rigid Multiblob Approach
• A robust incompressible Navier-Stokes solver for high density ratio multiphase flows
• An Immersed Boundary Method for Rigid Bodies
• A DLM immersed boundary method based wave-structure interaction solver for high density ratio multiphase flows
• The inertial sea wave energy converter (ISWEC) technology: device-physics, multiphase modeling and simulations
• Simulating water-entry/exit problems using Eulerian-Lagrangian and fully-Eulerian fictitious domain methods within the open-source IBAMR library
• Comparison of wave-structure interaction dynamics of a submerged cylindrical point absorber with three degrees of freedom using potential flow and computational fluid dynamics models
• Efficient Variable-Coefficient Finite-Volume Stokes Solvers
• A sharp interface Lagrangian-Eulerian method for rigid-body fluid-structure interaction
• A hybrid immersed boundary method for dense particle-laden flows
• Volume penalization for inhomogeneous Neumann boundary conditions modeling scalar flux in complicated geometry
• A one-sided direct forcing immersed boundary method using moving least squares
• Critique on "Volume penalization for inhomogeneous Neumann boundary conditions modeling scalar flux in complicated geometry"

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• Consistent continuum equations and numerical benchmarks for a perturbation-based, variable-coefficient acoustofluidic solver
• Simulating acoustically-actuated flows in complex microchannels using the volume penalization technique