Question

The most popular solution algorithms for pressure and velocity calculations with the finite volume method is SIMPLE method. Explain in detail, why are the staggered grids are used for velocities instead of checkerboard grids?

Answer 1

The most popular solution algorithms for pressure and velocity calculations with the finite volume method is SIMPLE method.

The Simple algorithm uses a relationship between velocity and pressure corrections to enforce mass conservation and to obtain the pressure field .

It is essentially a guess and correct procedure for the calculation of the staggered grid pressure field.

A Staggered grid is the setting for the spatial discretisation, in which the variables are not defined at the same position as in case of a Collocated grid.

the staggered grids are used for velocities instead of checkerboard grids as it does not results in the decoupling of the pressure and velocity, leading to the checkerboard problem.

The staggered grid is used when there are multiple functions being solved.It has the benefits of defining the functions at different points of the grid.For finite difference equations this make the finite difference approximation simpler.