  We study the numerical behaviour of a particle method for gradient flows
involving linear and nonlinear diffusion. This method relies on the
discretisation of the energy via non-overlapping balls centred at the
particles. The resulting scheme preserves the gradient flow structure at the
particle level, and enables us to obtain a gradient descent formulation after
time discretisation. We give several simulations to illustrate the validity of
this method, as well as a detailed study of one-dimensional
aggregation-diffusion equations.
