Abstract
An algebraic multigrid method is developed to solve fully coupled multiphase problem involving heat and mass transfer in deforming porous media. The mathematical model consists of balance equations of mass, linear momentum and energy and of the appropriate constitutive equations. The chosen macroscopic field variables are temperature, capillary pressure, gas pressure and displacement. The gas phase is considered to be an ideal gas composed of dry air and vapour, which are regarded as two miscible species. The model makes further use of a modified effective stress concept together with the capillary pressure relationship. Phase change is taken into account as well as heat transfer though conduction and convection and latent heat transfer (evaporation-condensation). Numerical examples are given to demonstrate the computing efficiency of this method.
Similar content being viewed by others
References
Lewis R W, Schrefler B A.The Finite Element Methods in the Static and Dynamic Deformation and Consolidation of Porous Media [M]. New York: Wiley, 1998.
Gawin D, Baggio P, Schrefler B A. Coupled heat, water and gas flow in deformable porous media [J].Internet J Numer Methods Fluids, 1995,20(8): 969–987.
Webster R. An algebraic multigrid solver for Navier-Stokes problems [J].Internat J Numer Methods Fluids, 1994,18(6): 761–780.
Liakopoulos A C. Transient flow though unsaturated porous media [D]. Ph D Thesis. Berkeley, C A: University of California, 1965.
ZHANG Gen-de. Continum theories of sold-fluid mixtures and their applications in engineering [J].Advances in Mechanics, 1993,23(1): 58–67. (in Chinese)
LIU Chao-qun.Multigrid Method and Its Applications in Fluid Mechanics [M]. Beijing: Tsinghua University Press, 1995. (in Chinese)
Author information
Authors and Affiliations
Additional information
Communicated by CHENG Geng-dong
Foundation items: the National Natural Science Foundation of China (59778044); the High Performance Computing Foundation of China (99101); the Special Funds for Major State Basic Research Project (G1999032805)
Biography: WANG Xi-cheng (1946-)
Rights and permissions
About this article
Cite this article
Xi-cheng, W., Zeng-jie, G. & Hong-yu, W. An algebraic multigrid method for coupled thermo-hydro-mechanical problems. Appl Math Mech 23, 1464–1471 (2002). https://doi.org/10.1007/BF02438387
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02438387