  We develop a partially explicit time discretization based on the framework of
constraint energy minimizing generalized multiscale finite element method
(CEM-GMsFEM) for the problem of linear poroelasticity with high contrast.
Firstly, dominant basis functions generated by the CEM-GMsFEM approach are used
to capture important degrees of freedom and it is known to give
contrast-independent convergence that scales with the mesh size. In typical
situation, one has very few degrees of freedom in dominant basis functions.
This part is treated implicitly. Secondly, we design and introduce an
additional space in the complement space and these degrees are treated
explicitly. We also investigate the CFL-type stability restriction for this
problem, and the restriction for the time step is contrast independent.
