  In order to resolve the pressure checkerboard field problem with collocated
grid, it is essential to employ the momentum interpolation method when
formulating the pressure equation, and the flux reconstruction method when
updating the cell-centered velocity fields. In this study, we first derive a
momentum interpolation method for Euler-Euler simulation of gas-solid flows,
which is independent of the time step, the transient term discretization
scheme, the under-relaxation factor and the shape of grid; a complete
first-order flux reconstruction method is then proposed to update the
cell-centered velocities. Their effectiveness are proved by simulating the
hydrodynamics of solids settlement, gas-solid fixed bed, bubbling fluidized bed
and circulating fluidized bed riser, and then comparing the simulation results
to the theoretically known solutions. Their superiority over the standard
solver of OpenFOAM in suppressing the high-frequency oscillations and enhancing
the smoothness and accuracy is also proved. Finally, the difficulty in fully
eliminating the high-frequency oscillations is attributed to the insufficiency
of current methods in handling the situations where the independent variables
undergo abrupt change.
