# Changing lattice size from 100x100 to 200x200, what changes to apply?

Hi all,
My question in simple, when i’m running a simulation on for example 100x100 grid and i want to change to 200x200 or 256x256 what changes should i apply? does deltax change? what value should i assign to deltax ?
thanks.

Hi there,

It depends on whether or not you wish to keep the physical size of the system (and the physical properties of the fluid) the same.

If your 100x100 box represents a specific size and you want to keep this the same for the 200x200 simulation, then deltax will be halved. To preserve the speed of sound for the fluid, this would also halve the time step size (deltat): the speed of sound is equal to deltax/(sqrt(3) * deltat).

However, changing the grid spacing and time step would mean that the value of the relaxation time would need to change if you wish to keep the same kinematic viscosity (nu) for the fluid. The kinematic viscosity is given as (tau - 0.5)/3 * (deltax)^2 / deltat … this means the value of (tau - 0.5) would need to double if the grid spacing is halved. For instance, if you ran your 100x100 simulation with tau = 0.75, the same kinematic viscosity would be given in the 200x200 simulation if you set tau = 1.0.

If you go to a 256x256 box but preserving the same physical size and fluid properties, the values of deltax and deltat would decrease by a factor of 2.56, but the value of (tau - 0.5) would increase by that same factor, i.e. from tau = 0,75 to tau = 1.14.