Application of parallel computing technologies for modeling the flow separation process behind the backward facing step in the channel with the buoyancy forces

Abstract

The paper presents numerical solutions of the two-dimensional laminar flow behind the backward
facing step in the channel with the buoyancy forces. A two-dimensional incompressible Navier-
Stokes equation is used to describe this process. This system is solved numerically by the projection
method, which is approximated by the control volume method. The resulting Poisson equation
satisfying the discrete equation of continuity is solved by the Jacobi iterative method at each time
step. The numerical solutions of the laminar flow behind the backward facing step are compared
with the numerical results of other authors. This numerical algorithm is completely parallelized
using various geometric decompositions (1D, 2D and 3D). Preliminary theoretical analysis of the
various decomposition methods effectiveness of the computational domain and real computational
experiments for this problem were made and the best method of domain decomposition was
determined. In the future, a proven mathematical model and numerical algorithm with the best
decomposition method can be applied for various complex flows with the buoyancy forces.