Numerical simulation of thermal recovery processes like steam injection often involves localized phenomena such as saturation and temperature fronts due to hyperbolic features of governing conservation laws, Treating more efficiently convective terms could help to diminish spurious oscillation and/or numerical dispersion and better tracking of discontinuity shocks. But in regions near the shock numerical dispersion can only be removed by the use of very fine uniform grids with many grid blocks. To avoid expensive solution of such a finely girded domain, we develop a moving mesh approach combined with higher order up-winding schemes.

Numerical solver here have been employed is Finite volume method. A MMPDE(moving mesh PDE) is solved associated with physical PDE's of steam injection process in order to relocates the mesh nodes to concentrate them in regions of sharp discontinuity and Equi-distribute a measure of error-estimate (monitor function) over the meshes. Solution will advance more rapidly on course meshes and fluxes at the coarse-fine grid interfaces are refined to guarantee mass conservation.. Since the region surrounding the sharp discontinuity and requiring high resolution consists of only a small fraction of the entire domain, prescribed locally time stepping results in a great saving in computational time. Specific features of moving mesh methods like monitor-function smoothing, control of mesh widths and readjustment of solutions further to mesh movement are addressed. Numerical experiments are carried out to demonstrate the efficiency and robustness of the proposed method in 1-D and 2-D. However numerical results for moving coordinates are compared with those obtained from simulation on non-adapted mesh framework. Preferences of higher-order solvers over lower-order ones in terms of shock capturing is being investigated.. Although we have limited our modeling to steam flooding process, but simulation demonstrates main features of our approach, applicable to other EOR processes such as VAPEX, SAGD, and In Situ Combustion Process.

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