4 - Temporal numerical discretization schemes

Abstract

This chapter is concerned with the numerical methods frequently used for temporal discretization in the problems of nanoparticles transport in porous media. The forward and backward Euler difference schemes are presented in the following section. Then, the Courant–Friedrichs–Lewy (CFL) stability condition was introduced. After that, we discussed the possibility of using a multiscale time-splitting scheme. Also, we defined the relaxation factor and how it can be used with the CFL condition. Then, we presented the Implicit Pressure Implicit Concentration scheme as well as the Implicit Pressure Explicit Saturation Implicit Concentration scheme. Finally, a stability analysis for the Implicit Pressure Explicit Saturation scheme has been provided.