AbstractIn this paper we deal with the numerical simulation of time dependent three‐dimensional thermal convection on the array processor DAP 510. Applying finite differences in combination with a pressure correction method to the underlying non‐linear system of partial differential equations, we reduce the numerical solution of the problem to the solution of a sequence of sparse linear systems. Using polynomial preconditioned conjugate gradient methods for the solution of these systems results in a highly parallel algorithm for the simulation of the considered flows on the DAP 510. Using this parallel algorithm, data can be mapped in different ways onto the processor array. Depending on the number of grid points, several methods are shown. Numerical experiments illustrate the capabilities of the proposed algori