Title | ||
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A Numerical Method for the Incompressible Navier--Stokes Equations Based on an Approximate Projection |
Abstract | ||
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In this method we present a fractional step discretization of the time-dependent incompressible Navier--Stokes equations. The method is based on a projection formulation in which we first solve diffusion--convection equations to predict intermediate velocities, which are then projected onto the space of divergence-free vector fields. Our treatment of the diffusion--convection step uses a specialized second-order upwind method for differencing the nonlinear convective terms that provides a robust treatment of these terms at a high Reynolds number. In contrast to conventional projection-type discretizations that impose a discrete form of the divergence-free constraint, we only approximately impose the constraint; i.e., the velocity field we compute is not exactly divergence-free. The approximate projection is computed using a conventional discretization of the Laplacian and the resulting linear system is solved using conventional multigrid methods. Numerical examples are presented to validate the second-order convergence of the method for Euler, finite Reynolds number, and Stokes flow. A second example illustrating the behavior of the algorithm on an unstable shear layer is also presented. |
Year | DOI | Venue |
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1996 | 10.1137/S1064827593244213 | SIAM J. Scientific Computing |
Keywords | Field | DocType |
incompressible flow,projection methods | Discretization,Mathematical optimization,Nonlinear system,Reynolds number,Mathematical analysis,Projection method,Numerical analysis,Mathematics,Stokes flow,Multigrid method,Navier–Stokes equations | Journal |
Volume | Issue | ISSN |
17 | 2 | 1064-8275 |
Citations | PageRank | References |
19 | 11.97 | 0 |
Authors | ||
3 |
Name | Order | Citations | PageRank |
---|---|---|---|
Ann S. Almgren | 1 | 82 | 22.33 |
John B. Bell | 2 | 154 | 29.57 |
William G. Szymczak | 3 | 19 | 11.97 |