Selective Time-stepping adaptivity for Non-Linear Reactive Transport Problems
Numerical simulation of reactive, flow and transport in porous media requires that the increasingly non-linear models be solved in an accurate and computationally efficient manner. However, the time step sizes associated with each of these processes differ greatly. For example, kinetic reaction rates varying over order of magnitudes or layered reservoirs with fast and slow concentration changes in high and low permeability layers, respectively. A few texts can be found in literature to address this area: Mortar element technique in both space and time domain , Two-ways methods (Offline/Online) ,Optimized
Schwarz waveform relaxation (OSWR) method. We present an adaptive time-stepping approach with different time-step sizes in different spatial domains. In summary, we proposed a mass conservative, adaptive time-stepping scheme with different time step sizes in different spatial domains, a fully implicit solution algorithm was developed for coupled flow and transport problems, using block Jacobi for improved convergence rates, numerical results using DG0 in time and RT0 Mixed FEM in space (finite difference), and preliminary results are in good agreement with reduced error in the fine time domain.