Adaptive interface-Mesh un-Refinement (AiMuR) based sharp-interface level-set-method for two-phase flow

Adaptive interface-Mesh un-Refinement (AiMuR) based Sharp-Interface Level-Set-Method (SI-LSM) is proposed for both uniform and non-uniform Cartesian-Grid. The AiMuR involves interface location based dynamic un-refinement (with merging of the four control volumes) of the Cartesian grid away from the interface. The un-refinement is proposed for the interface solver only. A detailed numerical methodology is presented for the AiMuR and ghost-fluid method based SI-LSM. Advantage of the novel as compared to the traditional SI-LSM is demonstrated with a detailed qualitative as well as quantitative performance study, involving the SI-LSMs on both coarse grid and fine grid, for three sufficiently different two-phase flow problems: dam break, breakup of a liquid jet and drop coalescence. A superior performance of AiMuR based SI-LSM is demonstrated - the AiMuR on a coarser non-uniform grid (NUcAiMuR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$NU_{c}^{AiMuR}$$\end{document}) is almost as accurate as the traditional SI-LSM on a uniform fine grid (Uf\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_{f}$$\end{document}) and takes a computational time almost same as that by the traditional SI-LSM on a uniform coarse grid (Uc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_{c}$$\end{document}). The AMuR is different from the existing Adaptive Mesh Refinement (AMR) as the former involves only mesh un-refinement while the later involves both refinement and un-refinement of the mesh. Moreover, the proposed computational development is significant since the present adaptive un-refinement strategy is much simpler to implement as compared to that for the commonly used adaptive refinement strategies. The proposed numerical development can be extended to various other multi-physics, multi-disciplinary and multi-scale problems involving interfaces.