Assessment of Basic Approaches to Numerical Modeling of Phase Change Problems—Accuracy, Efficiency, and Parallel Decomposition

Abstract

The fast and accurate modeling of phase change is of a significant importance in many processes from steel casting to latent heat thermal energy storage. The paper presents a numerical case study on the transient 3D heat diffusion problem with phase change. Three different approaches to modeling of the solid–liquid phase change in combination with four commonly used numerical schemes are compared for their efficiency, accuracy, applicability, simplicity of implementation, and robustness. The possibility of parallel decomposition of the approaches is also discussed. The results indicate that the best accuracy was achieved with the second-order implicit methods, and the best efficiency was reached with the simple explicit methods.

High Quality Steel Casting by Using Advanced Mathematical Methods

“…where ∆H is the latent heat (J/kg) and f s is the solid fraction (-). The Enthalpy method was used for modelling the solidification process, see Mauder et al [10]. The Enthalpy method is robust method because it ensures energy conservation and there is no discontinuity at either the liquidus or the solidus temperatures because the solidification/melting path is characterized strictly by decreasing/increasing enthalpy.…”

“…There are several discretization schemes how to solve the Equations (1)- (7). After large-scale numerical studies two numerical schemes proved to be good candidates for solving the case of 3-D transient heat transfer problem with solidification phenomena, Simple Explicit (SE) and Alternating Direction Implicit (ADI), see Mauder et al [10]. The ADI scheme proposed by Douglas and Gunn is unconditionally stable and retains the second-order accuracy when applied to 3-D problems.…”

“…In Table 1 there are computation times for ADI and SE schemes tested on three different types of meshes (coarse-mesh with 10 000 nodes, fine-mesh with 125,000 nodes and the very-fine mesh with 1,000,000 nodes) on Intel(R) Core(TM) i7-3770 CPU @ 3.4GHz 16GB RAM. More information about efficiency, robustness and accuracy of the examined numerical schemes can be found in Mauder et al [10]. This is the reason why the numerical core in presented solidification model is created by SE scheme.…”

“…The boundary conditions and initial condition are set on CPU. Further, numerical regions are separately send to the GPU units where Equations (10) and (11) are calculated. After the temperatures in future time step are calculated, the values in separated regions are send back to CPU where boundary conditions are recalculated and again send to the GPU.…”

Comparison of Corrected and Uncorrected Enthalpy Methods for Solving Conduction-Driven Solid/Liquid Phase Change Problems

“…Which solver performed best depended on the time step and mesh resoluti Tamma and Namburu [13] analyzed explicit and implicit enthalpy methods for the fin element method; they found that the explicit methods are faster since no update of mass matrix is necessary. Mauder et al [14] compared different methods in MATLAB accuracy, simulation time, and the applicability of parallelization. They stated that effectiveness of the methods depends on the problem under study.…”