Tetra-marching procedure for high order Level Contour Reconstruction Method

Abstract

Direct numerical simulation of the multiphase flow on a fixed Eulerian grid became increasingly popular due to its simplicity and robustness. Lately, there have been efforts to construct hybrids from existing well-known methods including VOF, Level Set, and Front Tracking with the intention of overcoming the inherent drawbacks of each method. The Level Contour Reconstruction Method is one of the hybrid type methods, which combines the Front Tracking and Level Set characteristics. By introducing a high order interpolation kernel during interface reconstruction, we could reconstruct the interface very accurately and smoothly compared to linear interpolation of a given distance function field. The high order reconstruction procedure can be undertaken, generally, with the same rectangular shaped Eulerian grid structure as the flow computation. With this rectangular shaped grid, there can be more than two lines in a single cell during the reconstruction. In this paper, we introduce the tetramarching reconstruction procedure which can eliminate ambiguity of drawing contour lines between multiple edge points in a single cell during high order reconstruction. We tested several benchmarking simulations of interface evolution and found that high order reconstruction with a tetra-marching procedure enables the fidelity of the reconstructed interface, which is continuous and smooth even with a highly distorted interface.

The Local Front Reconstruction Method for direct simulation of two- and three-dimensional multiphase flows

“…The LFRM cannot differentiate multiple interfaces in a single reconstruction cell since we still use the basic concept of the Level Set method to handle topological changes of the interface. This procedure is readily applicable to three-dimensions and a detailed procedure can be found in [33].…”

“…A more detailed description of the LCRM can be found in [30][31][32][33]. The version used for comparison with the LFRM in Section 3 is the high-order tetra-marching LCRM.…”

“…Recently, the tetra-marching procedure was used by Yoon and Shin [33] for improved handling of the interface structure during the interface reconstruction with the high-order LCRM. With a rectangular shaped reconstruction grid as in the original 2D LCRM (Fig.…”

“…In order to describe the interface structure and the reconstruction procedure of the LFRM more effectively, we first give a brief description of the 2D and 3D LCRM followed by a detailed explanation of the LFRM. The Level Contour Reconstruction Method has been explained in detail in previous papers [30][31][32][33][34][35].…”

“…The high order LCRM [32] was introduced to increase the accuracy and smoothness of the reconstructed interface by exactly imposing the zero contour level condition of the distance function using a high order spline kernel. Recently, the tetra-marching procedure [33] was implemented in order to eliminate the ambiguity in drawing lines between multiple edge crossing points in a single cell during the high order Level Contour Reconstruction.…”