A second-order projection method for the incompressible Navier-Stokes equations. (English) Zbl 0681.76030

Bell, John B.; Colella, Phillip; Glaz, Harland M.

J. Comput. Phys. 85, No. 2, 257-283 (1989).

We describe a second-order projection method for the time-dependent, incompressible Navier-Stokes equations. We first solve diffusion- convection equations to predict intermediate velocities which are then projected onto the space of divergence-free vector fields. By introducing more coupling between the diffusion-convection step and the projection step we obtain a temporal discretization that is second-order accurate. Our treatment of the diffusion-convection step uses a specialized higher order Godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high Reynolds number. The Godunov procedure is second-order accurate for smooth flow and remains stable for discontinuous initial data, even in the zero-viscosity limit. We approximate the projection directly using a Galerkin procedure that uses a local basis for discretely divergence-free vector fields. Numerical results are presented validating the convergence properties of the method. We also apply the method to doubly periodic shear-layers to assess the performance of the method on more difficult applications.

MSC:

76D05	Navier-Stokes equations for incompressible viscous fluids
65N99	Numerical methods for partial differential equations, boundary value problems

Keywords:

second-order projection method; time-dependent, incompressible Navier- Stokes equations; divergence-free vector fields; diffusion-convection step; specialized higher order Godunov method; doubly periodic shear- layers

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