A study on the numerical performances of diffuse interface methods for simulation of melting and their practical consequences

Abstract

This work is the final one in a series of three papers devoted to shedding light on the performance of fixed grid methods, also known as enthalpy methods, for the modeling and the simulation of solid/liquid phase transition. After a detailed analysis of five of the most common enthalpy methods for conductive-dominated and conductive-convective problems and then a study concerning the formulation of the advective term in the energy balance equation, the aim of the present paper is to extend the above-mentioned studies by an investigation of the numerical performance. Such a goal is achieved by comparing the required iterations and, even if it is shown to be only a rough guide, the simulation time of each method, for a great variety of parameter variations. In terms of contribution, the main conclusions of this overall work are to demonstrate that almost all solvers give similar results when stable. However, there are still distinctive deviations with the experiments, highlighting the need for a proper validation experiment. The second important assessment concerns resilience: almost all solvers work well, with only the applied apparent heat capacity method being the major exception as it often leads to unrealistic results. As a rule of thumb, models are more resilient when only the sensible enthalpy is advected. As far as the average of the required iterations is concerned, the so-called optimum approach needs the least. The order of the other solvers depends on the advective formulation, whereas source-based methods perform averagely and the tested apparent heat capacity method poorly. Cases with only sensible enthalpy advected need fewer iterations for four of the five solvers and less computational time for all solvers.