Abstract
We introduce an improved conservative direct re-initialization (ICDR) method (for two-phase flow problems) as a new and efficient geometrical re-distancing scheme. The ICDR technique takes advantage of two mass-conserving and fast re-distancing schemes, as well as a global mass correction concept to reduce the extent of the mass loss/gain in two- and three-dimensional (2D and 3D) problems. We examine the ICDR method, at the first step, with two 2D benchmarks: the notched cylinder and the swirling flow vortex problems. To do so, we (for the first time) extensively analyze the dependency of the regenerated interface quality on both time-step and element sizes. Then, we quantitatively assess the results by employing a defined norm value, which evaluates the deviation from the exact solution. We also present a visual assessment by graphical demonstration of original and regenerated interfaces. In the next step, we investigate the performance of the ICDR in three-dimensional (3D) problems. For this purpose, we simulate drop deformation in a simple shear flow field. We describe our reason for this choice and show that, by employing the ICDR scheme, the results of our analysis comply with the existing numerical and experimental data in the literature.
Highlights
Besides the mentioned methods, which consist of solving a partial differential equation (PDE) as the re-initialization step, hybrid techniques are employed to improve the mass conservation
We examine the viability of the ICDR method
We show that the new re-initialization algorithm is applicable for structured and unstructured meshes
Summary
The level set (LS) method has been a popular and efficient means to capture interfaces in different two-phase (or multi-phase) flow fields since being introduced by Osher and Sethian [1]. Guermon et al [19] extended the artificial compression and viscosity method to integrate the level set and the re-initialization equations By employing their approach, one equation covers the interface advection and the re-initialization steps. Besides the mentioned methods, which consist of solving a partial differential equation (PDE) as the re-initialization step, hybrid techniques are employed to improve the mass conservation. A mass-conserving re-distancing scheme was proposed by Mut et al [24] that employs unstructured triangular and tetrahedral meshes for two- and three-dimensional (2D and 3D) problems, respectively Their technique, which we name the Mut method, comprises an iterative element-wise mass correction, followed by an averaging process between the nodes in a narrow band.
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