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On the solution of the Navier-Stokes equations using Chebyshev projection schemes with third-order accuracy in time. (English) Zbl 0898.76077
Summary: A third-order time-accurate projection method for approximating the Navier-Stokes equations for incompressible flow is presented. In order to compute a pressure unpolluted by spurious modes, two Chebyshev collocation spatial discretizations, where the pressure is approximated by lower-order polynomials than the velocity, are compared. One only collocation grid is used, and no pressure boundary condition is needed. The Navier-Stokes problem is reduced to the successive solution of Helmholtz problems for the velocity and pseudo-Poisson problems for the pressure. These problems are solved by direct methods. Using an exact solution, spectral spatial accuracy, and third-order time accuracy, for both the velocity and the pressure, are checked. The stability properties are discussed by considering the regularized cavity flow at different Reynolds numbers.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
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