期刊
COMPUTERS & MATHEMATICS WITH APPLICATIONS
卷 84, 期 -, 页码 77-96出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2020.11.008
关键词
Computational fluid dynamics; Phase-change; Mixed finite elements; Nonlinear; Regularization; Firedrake
资金
- Excellence Initiative of the German Federal and State Governments [GSC 111]
- Federal Ministry of Economic Affairs and Energy, Germany [50 NA 1502]
The enthalpy method accurately solves the multi-physics problem involving natural convection and phase change by separating mesh refinement from nonlinearity regularization and providing effective numerical solutions. Sensitivity analysis on key parameters effectively reduces numerical errors.
Melting and solidification processes are often affected by natural convection of the liquid, posing a multi-physics problem involving fluid flow, convective and diffusive heat transfer, and phase-change reactions. Enthalpy methods formulate this convection-coupled phase-change problem on a single computational domain. The governing equations can be solved accurately with a monolithic approach using mixed finite elements and Newton's method. Previously, the monolithic approach has relied on adaptive mesh refinement to regularize local nonlinearities at phase interfaces. This contribution instead separates mesh refinement from nonlinear problem regularization and provides a continuation procedure which robustly obtains accurate solutions on the tested 2D uniform meshes. A flexible and extensible open source implementation is provided. The code is formally verified to accurately solve the governing equations in time and in 2D space, and convergence rates are shown. Two benchmark simulations are presented in detail with comparison to experimental data sets and corresponding results from the literature, one for the melting of octadecane and another for the freezing of water. Sensitivities to key numerical parameters are presented. For the case of freezing water, effective reduction of numerical errors from these key parameters is successfully demonstrated. Two more simulations are briefly presented, one for melting at a higher Rayleigh number and one for melting gallium. (C) 2020 Elsevier Ltd. All rights reserved.
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