Second-Order Convergence of a Projection Scheme for the Incompressible Navier–Stokes Equations with Boundaries
Copyright policy )Second-Order Convergence of a Projection Scheme for the Incompressible Navier–Stokes Equations with Boundaries
Summary: A rigorous convergence result is given for a projection scheme for the Navier-Stokes equations in the presence of boundaries. The numerical scheme is based on a finite-difference approximation, and the pressure is chosen so that the computed velocity satisfies a discrete divergence-free condition. This choice for the pressure and the particular way that the discrete divergence is calculated near the boundary permit the error in the pressure to be controlled and the second-order convergence in the velocity and the pressure to the exact solution to be shown. Some simplifications in the calculation of the pressure in the case without boundaries are also discussed.
- University of British Columbia Canada
- California Institute of Technology United States
pressure, projection method, energy estimates, Navier-Stokes equations for incompressible viscous fluids, discrete divergence-free condition, Stability and convergence of numerical methods for boundary value problems involving PDEs, Finite difference methods applied to problems in fluid mechanics, 510
pressure, projection method, energy estimates, Navier-Stokes equations for incompressible viscous fluids, discrete divergence-free condition, Stability and convergence of numerical methods for boundary value problems involving PDEs, Finite difference methods applied to problems in fluid mechanics, 510
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