Computational complexity of the algorithm for a 2D adaptive mesh refinement method using lid-driven cavity flows

After successful accuracy and reliability verifications of the algorithm for a 2D adaptive mesh refinement method using exact and numerical benchmark results, we consider the computational complexity of this algorithm using 2D steady incompressible lid-driven cavity flows. The algorithm for the 2D adaptive mesh refinement method is proposed based on the qualitative theory of differential equations. The adaptive mesh refinement method performs mesh refinement based on the numerical solutions of Navier-Stokes equations solved by Navier2D, an open source vertex-centered finite volume code that uses the median dual mesh to form the control volumes about each vertex. We show the comparisons of the computational complexities between the algorithm of the adaptive mesh refinement method twice and the algorithm that uses uniform mesh with the same size of twice refined cells for Reynolds numbers 100, 1000, 2500. The adaptive mesh refinement method can be applied to find the accurate numerical solutions of any mathematical models containing continuity equations for incompressible fluid or steady-state fluid flows.