Pressure and projection methods for viscous incompressible flows
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Mon, 11/05/2009 17:00 |
Jian-Guo Liu (College Park, Maryland) |
Partial Differential Equations Seminar  |
Gibson 1st Floor SR |
| For incompressible Navier-Stokes equations in a bounded domain, I will first present a formula for the pressure that involves the commutator of the Laplacian and Leray-Helmholtz projection operators. This commutator and hence the pressure is strictly dominated by the viscous term at leading order. This leads to a well-posed and computationally congenial unconstrained formulation for the Navier-Stokes equations. Based on this pressure formulation, we will present a new understanding and design principle for third-order stable projection methods. Finally, we will discuss the delicate inf-sup stability issue for these classes of methods. This is joint work with Bob Pego and Jie Liu. | |||