Marker-Based, 3-D Adaptive Cartesian Grid Method for Multiphase Flow around Irregular Geometries

Abstract

Computational simulations of multiphase flow are challenging because many practical applications require adequate resolution of not only interfacial physics associated with moving boundaries with possible topological changes, but also around three-dimensional, irregular solid geometries. In this paper, we focus on the simulations of fluid/fluid dynamics around complex geometries, based on an Eulerian-Lagrangian framework. The approach uses two independent but related grid layouts to track the interfacial and solid boundary conditions, and is capable of capturing interfacial as well as multiphase dynamics. In particular, the stationary Cartesian grid with time dependent, local adaptive refinement is utilized to handle the computation of the transport equations, while the interface shape and movement are treated by marker-based triangulated surface meshes which freely move and interact with the Cartesian grid. The markers are also used to identify the location of solid boundaries and enforce the no-slip condition there. Issues related to the contact line treatment, topological changes of multiphase fronts during merger or breakup of objects, and necessary data structures and solution techniques are also highlighted. Selected test cases including spacecraft fuel tank flow management, and movement and rupture of interfaces associated with liquid plug flow are presented.

A computational study of droplet evaporation with fuel vapor jet ejection induced by localized heat sources

“…This approach is much easier to implement and ensures the conservation properties without expensive curvature computation. 25 During the evaporation process, the liquid is transformed to the vapor, and the difference of enthalpy is used for the evaporation energy. The critical modeling issues are (1) how to compute the 2015) amount of the mass transfer and (2) how to treat the latent heat, because they are directly related to the vapor concentration, phase boundary movement, and the resulting temperature distribution.…”

“…24 As a rational compromise, the Eulerian-Lagrangian method (e.g., the immersed boundary method) utilizes a separate set of Lagrangian moving mesh associated with a marker/tag system representing the interface, which is overlaid on stationary Eulerian grids to compute the flow fields. 25 As such, the interface representation is achieved with high accuracy and does not require modifications to the computational grid of the field equations. Within some high order interpolation errors, the explicit tracking of the interface results in higher fidelity for the same level of grid resolution, in comparison with Eulerian methods at the same level of computational cost.…”

Analysis of the diffuse-domain method for solving PDEs in complex geometries

“…However, most of these methods typically require tools not frequently available in standard finite element and finite difference software packages. Examples of such approaches include the extended and composite finite element methods (e.g., [31,12,23,13,32,55,7,4]), immersed interface methods (e.g., [40,43,60,44,65]), virtual node methods with embedded boundary conditions (e.g., [3,73,34]), matched interface and boundary methods (e.g., [71,68,69,67,72]), modified finite volume/embedded boundary/cut-cell methods/ghost-fluid methods (e.g., [27,36,19,25,26,35,47,70,48,37,46,64,49,9,10,52,53,33,63]). In another approach, known as the fictitious domain method (e.g., [28,29,56,45]), the original system is either augmented with equations for Lagrange multipliers to enforce the boundary conditions, or the penalty method is used to enforce the boundary condi-tions weakly.…”

A Computational Study of Internal Flows in a Heated Water-Oil Emulsion Droplet

“…Therefore, the computation of line integral form is used with normal and tangential direction of interface elements instead of direct curvature computation because it is much easier, and maintains conservation without expensive curvature computation. 8 The single set of conservation equations for mass, momentum, and energy for the entire flow in Eqs. (3)- (5) are solved using a projection method, where an intermediate velocity field is computed and projected into a divergencefree space.…”

“…It utilizes a separate set of Lagrangian moving meshes representing the interface, which is overlaid on a stationary Eulerian grid to compute the flow fields. 8 In this approach, the interface can be represented accurately due to explicit interface tracking by surface meshes, and it does not require modifications to the computational grid of the field equations. It is known that the interface tracking and surface tension computations are more accurate and efficient in Eulerian-Lagrangian method than Eulerian method at the same level of grid resolutions.…”