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Scientific Computing and Data Science Seminar

November 3, 2022 - 3:00pm

Date and time: Thursday, November 3, 3pm-4pm

Room: ACS 362B

Speaker: Scott West

Title: A Stable Nodal Projection Method on Octree Grids


Abstract: We present a novel projection solver for the incompressible Navier-Stokes equations with arbitrary boundaries, where all variables are collocated at the nodes of non-graded octree grids. Both the viscosity and projection steps are discretized using supra-convergent finite difference approximations with sharp boundary treatments. The resulting projection operator is stable, as our analysis demonstrates. We verify the stability of our method on uniform Cartesian grids both analytically and numerically, as well as provide a framework for proving the stability on adaptive grids. On adaptive grids, we verify that the operator is stable for highly non-graded grids and arbitrary boundary conditions. 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.