An adaptive mesh front tracking method for phase change problems

Purpose: This purpose of this study is to propose and test an adaptive grid scheme for modeling phase change problems. Design/methodology/approach: Appealing to literature related to solving hydrogeology problems and classic moving boundary methodologies, a novel adaptive mesh scheme for Stefan melting problems is proposed. This scheme uses a local adaptive mesh. A set of nodes attached to the moving melt front advances along prescribed directions. All other nodes in the domain retain fixed locations. When the distance of a front node to its nearest nonfront neighboring node exceeds a given distance, a new node is inserted in the grid at a location that preserves a regular grid spacing. Findings: When applied to Stefan melting test problems, the proposed scheme provides smooth, accurate and conserved results. Practical implications: In addition to the solution of phase change problems, the results from the numerical testing in this work verify the conserved nature of the operation of the proposed adaptive scheme. This indicates that the wider application of the adaptive grid scheme to other conservation problems occurring in domains that evolve over time is valid. Social implications: The proposed scheme can be use​d to model hydrogeology problems in evolving landscapes; a problem with important consequences for coastal populations. Originality/value: The developed method offers a novel and useful approach for numerically solving problems in time dependent domains.