| Abstract: | The conceptual framework of a least squares rate variational approach to the formulation of continuously deforming mixed-variable finite element computational scheme for a single evolution equation was presented in Part I.1 In this paper (Part II), we extend these concepts and present an adaptively deforming mixed variable finite element method for solving general two-dimensional transport problems governed by a system of coupled non-linear partial differential evolution equations. In particular, we consider porous media problems that involve coupled heat and mass transport processes that yield steep continuous moving fronts, and abrupt, discontinuous, moving phase-change interfaces. In this method, the potentials, such as the temperature, pressure and species concentration, and the corresponding fluxes, are permitted to jump in value across the phase-change interfaces. The equations, and the jump conditions, governing the physical phenomena, which were specialized from a general multiphase, multiconstituent mixture theory, provided the basis for the development and implementation of a two-dimensional numerical simulator. This simulator can effectively resolve steep continuous fronts (i.e. shock capturing) without oscillations or numerical dispersion, and can accurately represent and track discontinuous fronts (i.e. shock fitting) through adaptive grid deformation and redistribution. The numerical implementation of this simulator and numerical examples that demonstrate the performance of the computational method are presented in Part III2 of this paper. |
