A numerical method for the two-dimensional, incompressible Navier–Stokes equations in vorticity-streamfunction form is proposed, which employs semi-Lagrangian discretizations for both the advection and diffusion terms, thus achieving unconditional stability without the need to solve linear systems beyond that required by the Poisson solver for the recon- struction of the streamfunction. A description of the discretization of Dirichlet boundary conditions for the semi-Lagrangian approach to diffusion terms is also presented. Numeri- cal experiments on classical benchmarks for incompressible flow in simple geometries val- idate the proposed method.

A fully semi-Lagrangian discretization for the 2D incompressible Navier–Stokes equations in the vorticity-streamfunction formulation

L. Bonaventura;
2018-01-01

Abstract

A numerical method for the two-dimensional, incompressible Navier–Stokes equations in vorticity-streamfunction form is proposed, which employs semi-Lagrangian discretizations for both the advection and diffusion terms, thus achieving unconditional stability without the need to solve linear systems beyond that required by the Poisson solver for the recon- struction of the streamfunction. A description of the discretization of Dirichlet boundary conditions for the semi-Lagrangian approach to diffusion terms is also presented. Numeri- cal experiments on classical benchmarks for incompressible flow in simple geometries val- idate the proposed method.
2018
Semi-Lagrangian methods Advection–diffusion equations Navier–Stokes equations Vorticity-streamfunction formulation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1041090
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