2023/06/16 by Matthew Blomquist, Scott R. West, Blomquist, Matthew +5 · 4 citations
Earth and Planetary Sciences · Engineering · #Meteorological Phenomena and Simulations #Computational Fluid Dynamics and Aerodynamics #Advanced Numerical Methods in Computational Mathematics
paper · pdf · doi:10.48550/arxiv.2306.09957
We propose a novel collocated projection method for solving the incompressible Navier-Stokes equations with arbitrary boundaries. Our approach employs non-graded octree grids, where all variables are stored at the nodes. To discretize the viscosity and projection steps, we utilize supra-convergent finite difference approximations with sharp boundary treatments. We demonstrate the stability of our projection on uniform grids, identify a sufficient stability condition on adaptive grids, and validate these findings numerically. We further demonstrate the accuracy and capabilities of our solver with several canonical two- and three-dimensional simulations of incompressible fluid flows. Overall, our method is second-order accurate, allows for dynamic grid adaptivity with arbitrary geometries, and reduces the overhead in code development through data collocation.