Grid sensitivity and role of error in computing a lid-driven cavity problem

The investigation on grid sensitivity for the bifurcation problem of the canonical lid-driven cavity (LDC) flow results is reported here with very fine grids. This is motivated by different researchers presenting different first bifurcation critical Reynolds number (Re_{cr1}), which appears to depend on the formulation, numerical method, and choice of grid. By using a very-high-accuracy parallel algorithm, and the same method with which sequential results were presented by Lestandi et al. [Comput. Fluids 166, 86 (2018)CPFLBI0045-793010.1016/j.compfluid.2018.01.038] [for (257 × 257) and (513 × 513) uniformly spaced grid], we present results using (1025×1025) and (2049×2049) grid points. Detailed results presented using these grids help us understand the computational physics of the numerical receptivity of the LDC flow, with and without explicit excitation. The mathematical physics of the investigated problem will become apparent when we identify the roles of numerical errors with the ambient omnipresent disturbances in real physical flows as interchangeable. In physical or in numerical setups, presence of disturbances cannot be ignored. In this context, the need for explicit excitation for the used compact scheme arises for a definitive threshold amplitude, below which the flow relaxes back to quiescent state after the excitation is removed in computations. We also implement the present parallel method to show the physical aspects of primary and secondary instabilities to be maintained for other numerical schemes, and we show the results to reflect the complex physics during multiple subcritical Hopf bifurcation. Also, we relate the various sources of errors during computations that is typical of such shear-driven flow. These results, with near spectral accuracy, constitute universal benchmark results for the solution of Navier-Stokes equation for LDC.