Large low shear velocity provinces have been observed beneath Africa and the Pacific. These large-scale structures are considered to have been stable the last hundred million years with their origin and nature still being an open question. In our 2D Cartesian study, we numerically investigate the temporal and spatial stability of thermochemical piles. We consider two different scenarios, in which the piles either arise from a primordial layer above the core-mantle boundary (CMB) or from an influx of iron-rich material through the CMB. The investigated mantle flow depends on viscosity varying with composition, depth, and stress. The rheological parameters affect the strength of convection and consequently the stability of piles. An increased top or bottom viscosity reduces the convective vigor yielding longer-lived and more stable piles. Likewise, a thermal expansivity decreasing with depth exhibits longer pile lifetimes and less pile movement. Furthermore, piles and plumes are two closely linked structures. While thermochemical plumes are anchored by piles, thermal plumes attract piles and deform them. Long-lived plumes tend to be located in the center of piles, but during dynamical processes, such as merging of piles, plumes also occur at the edges remaining there for several million years. In summary, we suggest that the LLSVPs might have formed early after the magma ocean, probably as several initially thin structures due to strong convection in the hot Archean mantle. With the cooling of the mantle, the structures would have broadened and stabilized in space and time, yielding the present-day state.