A new adaptive algorithm for phase change heat transfer problems based on quadtree SBFEM and smoothed effective heat capacity method

References

• R. W. Lewis, and K. Ravindran, “Finite element simulation of metal casting,” Int. J. Numer. Methods Eng., vol. 47, no. 1–3, pp. 29–59, 2000.DOI:10.1002/(SICI)1097-0207(20000110/30)47:1/3<29::AID-NME760>3.0.CO;2-X.
   Web of Science ®Google Scholar
• Y. Dutil, D. R. Rousse, N. B. Salah, S. Lassue, and L. Zalewski, “A review on phase-change materials: mathematical modeling and simulations,” Energy Rev., vol. 15, pp. 112–130, 2011.DOI:10.1016/j.rser.2010.06.011.
   Google Scholar
• P. Verma, Varun, and S. K. Singal, “Review of mathematical modeling on latent heat thermal energy storage systems using phase-change material,” Renew. Sust. Energy Rev., vol. 12, pp. 999–1031, 2008.
   Web of Science ®Google Scholar
• M. Augspurger, and H. S. Udaykumar, “A Cartesian grid solver for simulation of a phase-change material (PCM) solar thermal storage device,” Numer. Heat Tr. B-Fund., vol. 69, no. 3, pp. 179–196, 2016. DOI:10.1080/10407790.2015.1097106.
   Web of Science ®Google Scholar
• M. D. Muhammad, O. Badr, and H. Yeung, “CFD modeling of the charging and discharging of a shell-and-tube latent heat storage system for high-temperature applications,” Numer. Heat Tr. A-Appl., vol. 68, no. 8, pp. 813–826, 2015. DOI:10.1080/10407782.2015.1023094.
   Web of Science ®Google Scholar
• B. S. Yilbas, S. Z. Shuja, and M. M. Shaukat, “Thermal characteristics of latent heat thermal storage: comparison of aluminum foam and mesh configurations,” Numer. Heat Tr. A-Appl., vol. 68, no. 1, pp. 99–116, 2015. DOI:10.1080/10407782.2014.977116.
   Web of Science ®Google Scholar
• Q. Ren, Y.-L. He, K.-Z. Su, and C. L. Chan, “Investigation of the effect of metal foam characteristics on the PCM melting performance in a latent heat thermal energy storage unit by pore-scale lattice Boltzmann modeling,” Numer. Heat Tr. A-Appl., vol. 72, no. 10, pp. 745–764, 2017. DOI:10.1080/10407782.2017.1412224.
   Web of Science ®Google Scholar
• J. Crank, Free and Moving Boundary Problems. Oxford, UK: Calverdon Press, 1984.
   Google Scholar
• H. T. Yang, and Y. Q. He, “Solving heat transfer problems with phase change via smoothed effective heat capacity and element-free Galerkin methods,” Int. Commun. Heat Mass Tr., vol. 37, no. 4, pp. 385–392, 2010. DOI:10.1016/j.icheatmasstransfer.2009.12.002.
   Web of Science ®Google Scholar
• G. Beckett, J. A. Mackenzie, and M. L. Robertson, “A moving mesh finite element method for the solution of two-dimensional Stefan problems,” J. Comput. Phys., vol. 168, no. 2, pp. 500–518, 2001.DOI:10.1006/jcph.2001.6721.
   Web of Science ®Google Scholar
• W. M. Cao, W. Z. Huang, and R. Dr, “An r-adaptive finite element method based upon moving mesh PDEs,” J. Comput. Phys., vol. 149, no. 2, pp. 221–244, 1999.DOI:10.1006/jcph.1998.6151.
   Web of Science ®Google Scholar
• R. H. Nochetto, M. Paolini, and C. Verdi, “An adaptive finite element method for two-phase Stefan problems in two space dimensions. Part I: stability and error estimates,” Math. Comput., vol. 57, no. 195, pp. 73–108, 1991.DOI:10.2307/2938664.
   Web of Science ®Google Scholar
• B. Youssef, F. Andre, and C. Eric, “Anisotropic mesh adaptation for the solution of the Stefan problem,” J. Comput. Phys., vol. 194, pp. 233–255, 2004.DOI:10.1016/j.jcp.2003.09.008.
   Web of Science ®Google Scholar
• B. T. Helenbrook, and J. Hrdina, “High-order adaptive arbitrary-Lagrangian–Eulerian (ALE) simulations of solidification,” Comput. Fluids, vol. 167, pp. 40–50, 2018.DOI:10.1016/j.compfluid.2018.02.028.
   Web of Science ®Google Scholar
• M. Yerry, and M. Shephard, “Automatic three-dimensional mesh generation by the modified-octree technique,” Int. J. Numer. Methods Eng., vol. 20, no. 11, pp. 1965–1990, 1984. DOI:10.1002/nme.1620201103.
   Web of Science ®Google Scholar
• A. Tabarraei, and N. Sukumar, “Adaptive computations on conforming quadtree meshes,” Finite Elem. Anal. Des., vol. 41, no. 7–8, pp. 686–702, 2005.DOI:10.1016/j.finel.2004.08.002.
   Web of Science ®Google Scholar
• N. Provatas, N. Goldenfeld, and J. Dantzigy, “Adaptive mesh refinement computation of solidification microstructures using dynamic data structures,” J. Comput. Phys., vol. 148, no. 1, pp. 265–290, 1999.DOI:10.1006/jcph.1998.6122.
   Web of Science ®Google Scholar
• A. Saputra, H. Talebi, D. Tran, C. Birk, and C. Song, “Automatic image-based stress analysis by the scaled boundary finite element method,” Int. J. Numer. Methods Eng., vol. 109, no. 5, pp. 697–738, 2017.DOI:10.1002/nme.5304.
   Web of Science ®Google Scholar
• X. Chen, T. Luo, E. T. Ooi, E. H. Ooi, and C. Song, “A quadtree-polygon-based scaled boundary finite element method for crack propagation modeling in functionally graded materials,” Theor. Appl. Fract. Mech., vol. 94, pp. 120–133, 2018.DOI:10.1016/j.tafmec.2018.01.008.
   Web of Science ®Google Scholar
• E. T. Ooi, S. Natarajan, C. Song, and E. H. Ooi, “Crack propagation modelling in concrete using the scaled boundary finite element method with hybrid polygon–quadtree meshes,” Int. J. Fract., vol. 203, no. 1–2, pp. 135–157, 2017.DOI:10.1007/s10704-016-0136-4.
   Web of Science ®Google Scholar
• A. A. Saputra, V. Sladek, J. Sladek, and C. Song, “Micromechanics determination of effective material coefficients of cement-based piezoelectric ceramic composites,” J. Intell. Mater. Syst. Struct., vol. 29, no. 5, pp. 845–862, 2018.DOI:10.1177/1045389X17721047.
   Web of Science ®Google Scholar
• S. Chen, B. Merriman, S. Osher, and P. Smereka, “A simple level set method for solving Stefan problems,” J. Comput. Phys., vol. 135, no. 1, pp. 8–29, 1997.DOI:10.1006/jcph.1997.5721.
   Web of Science ®Google Scholar
• R. W. Lewis, K. Morgan, H. R. Thomas, and K. N. Seetharamu, The Finite Element Method in Heat Transfer Analysis. Chichester, UK: John Wiley & Sons, vol. 5, no. 28, 1996.
   Google Scholar
• Y. Q. He, J. Guo, and H. T. Yang, “Image-based numerical prediction for effective thermal conductivity of heterogeneous materials: A quadtree based scaled boundary finite element method,” Int. J. Heat Mass Tr., vol. 128, pp. 335–343, 2019.DOI:10.1016/j.ijheatmasstransfer.2018.08.099.
   Web of Science ®Google Scholar
• A. J. Deeks, and J. P. Wolf, “A virtual work derivation of the scaled boundary finite-element method for elastostatics,” Comput. Mech., vol. 28, no. 6, pp. 489–504, 2002. DOI:10.1007/s00466-002-0314-2.
   Web of Science ®Google Scholar
• C. W. Lan, Y. C. Chang, and C. J. Shih, “Adaptive phase field simulation of non-isothermal free dendritic growth of a binary alloy,” Acta Mater., vol. 51, no. 7, pp. 1857–1869, 2003.DOI:10.1016/S1359-6454(02)00582-7.
   Web of Science ®Google Scholar
• A. J. Dalhuijsen, and A. Segal, “Comparison of finite element techniques for solidification problems,” Int. J. Numer. Methods Eng., vol. 23, no. 10, pp. 1807–1829, 1986. DOI:10.1002/nme.1620231003.
   Web of Science ®Google Scholar
• G. R. Liu, and N. T. Trung, Smoothed Finite Element Methods. Boca Raton, FL: CRC Press 2010, 584.
   Google Scholar
• K. A. Rathjen, and L. A. Jiji, “Heat conduction with melting or freezing in a corner.” J. Heat Tr., vol. 93, pp. 101–109, 1971. DOI:10.1115/1.3449740.
   Google Scholar
• Y. B. Tao, and Y. L. He, “A review of phase change material and performance enhancement method for latent heat storage system,” Renew. Sust. Energy Rev., vol. 93, pp. 245–259, 2018. DOI:10.1016/j.rser.2018.05.028.
   Web of Science ®Google Scholar
• D. Zhao, and G. Tan, “Numerical analysis of a shell-and-tube latent heat storage unit with fins for air-conditioning application,” Appl. Energy, vol. 138, pp. 381–392, 2015.DOI:10.1016/j.apenergy.2014.10.051.
   Web of Science ®Google Scholar