A New class of higher order schemes for Navier-Stokes equations and application in rotating flows

  • Wu, Ke (Purdue University-Main Campus)

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A new class of time discretization schemes \cite{Ke22} for the Navier-Stokes equations with no-slip boundary conditions in rotating reference frame is constructed by combining the scalar auxiliary variable) SAV approach for general dissipative systems and the consistent splitting schemes. The time derivative is approximated by BDFk schemes and can be up to six-order accurate. The viscous force term, Coriolis force term and Euler force term are all treated implicitly. Then the governing equations are discretized in space using a Legendre-Galerkin spectral approach, which leads to a symmetric positive definite banded system with variable coefficients that can be solved efficiently by diagonalization procedures. A particular finding of these simulations is that, for flows with highly complex temporal and spatial structures, the third-order scheme is the most efficient choice for achieving a desired accuracy, as it is not only more accurate but also allows larger time steps than traditionally used second-order schemes. Delicate numerical simulations for highly complex rotating flows \cite{LSWW22,WWL22} are presented to validate the new schemes.