A volume-of-fluid ghost-cell immersed boundary method for multiphase flows with contact line dynamics

A diffuse domain method for two-phase flows with large density ratio in complex geometries

“…With being the static contact angle, the contact line of the droplet recedes if or spreads if , and eventually reaches an equilibrium with the interface intersecting the solid cylinder at an angle of . In the absence of gravity, the equilibrium state of the droplet can be obtained analytically by carving the cylinder out of a circle (Liu & Ding 2015; O'Brien & Bussmann 2018); see figure 7. The distance between the centres of the droplet and the cylinder, , and the diameter of the circle, , can be computed by solving where The exact solution is given by and .…”

“…2018), extended finite element methods (Fries & Belytschko 2010), immersed boundary methods (Schneider 2015; Stein, Guy & Thomases 2017), immersed interface methods (Li 2003; Chen, Li & Lin 2007; Gong et al. 2018; O'Brien & Bussmann 2018) and the volume penalty method (Shirokoff & Nave 2014; De Stefano, Nejadmalayeri & Vasilyev 2016), where the complex geometry is embedded in a larger, regular domain with a test function being used to enforce the boundary conditions at solid–fluid interfaces. Other methods include boundary integral methods (Biros, Ying & Zorin 2004; Mittal et al.…”

“…Many numerical methods have been developed for solving multiphase flows in complex geometries. Examples are fictitious domain methods (Glowinski et al 2001;Zhang et al 2018), extended finite element methods (Fries & Belytschko 2010), immersed boundary methods (Schneider 2015;Stein, Guy & Thomases 2017), immersed interface methods (Li 2003;Chen, Li & Lin 2007;Gong et al 2018;O'Brien & Bussmann 2018) and the volume penalty method (Shirokoff & Nave 2014;De Stefano, Nejadmalayeri & Vasilyev 2016), where the complex geometry is embedded in a larger, regular domain with a test function being used to enforce the boundary conditions at solid-fluid interfaces. Other methods include boundary integral methods (Biros, Ying & Zorin 2004;Mittal et al 2008), which explicitly incorporate the boundary conditions in the reformulated equations, front-tracking methods (Tryggvason et al 2001;Zolfaghari, Izbassarov & Muradoglu 2017) and arbitrary Eulerian-Lagrangian methods (Hu, Patankar & Zhu 2001;Gilmanov & Sotiropoulos 2005;Anjos et al 2013) that utilize a separate Lagrangian mesh to track the complex boundary and either smear the boundary conditions across several mesh points or explicitly enforce the boundary conditions on the Lagrangian mesh that cuts across the Eulerian mesh using body forces or modified discretizations.…”

On the estimation of unsteady aerodynamic forces and wall spectral content with immersed boundary conditions

“…The main idea of discrete forcing immersed boundary methods is to create the effect of an object in the flow through the application of source terms in nearwall regions cells, named IB forcing points. As depicted in figure 1, near-wall solid [24,38] or fluid cells [64,25,5,65] can be chosen as forcing points. Moreover, in the particular framework of finite-volume methods, the forcing can also be achieved through the direct manipulation of the numerical fluxes at the faces between solid and fluid cells [7,51].…”

Macroscopic and mesoscopic simulation of viscoelastic free surface flow in gas‐assisted injection moulding process

“…The free surface problems that abound in many industrial production processes, including CIM and GAIM, are usually addressed with interface tracking methods such as smoothed particle hydrodynamics (SPH), phase field, volume of fluid (VOF), level set (LS), and CLSVOF (coupled level set and volume of fluid) methods . Among these methods, the CLSVOF method combines the advantages of the LS and VOF methods and compensates for the disadvantages of individual methods.…”