Regularized four-sided Cavity Flows: A spectral Bifurcation Benchmark implemented in Julia
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This work presents a regularized version of the four-sided lid-driven cavity for incompressible fluids. The four-sided driven cavity is an extension of the simple lid-driven case where all lids move with the same velocity profile and parallel lids move in opposite directions. Lid-driven cavity flows are used to validate Navier-Stokes solvers. This study focuses on the regularized version to overcome corner singularities. The proposed method recovers near exponential convergence in spectral discretization schemes. The flow presents a variety of bifurcation scenarios and can make up for an amenable Navier-Stokes bifurcation benchmark. The algorithms are implemented in Julia, a high-performance language for scientific computing. A developed Julia module provides a reproducible example of spectral discretization for the proposed benchmark.