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Performance of under-resolved two-dimensional incompressible flow simulations. II. (English) Zbl 0914.76063
Summary: This paper presents a study of the behavior of several difference approximations for the incompressible Navier-Stokes equations as a function of the computational mesh resolution. In particular, the under-resolved case is considered. The methods considered include a Godunov projection method, a primitive variable ENO method, an upwind vorticity stream-function method, centered difference methods of both a pressure-Poisson and vorticity stream-function formulation, and a pseudospectral method. It is demonstrated that all these methods produce spurious, nonphysical vortices of the type described by the authors in part I [ibid. 122, No. 1, 165-183 (1995; Zbl 0849.76043)] when the flow is sufficiently under-resolved. The occurrence of these artifacts appears to be due to a nonlinear effect in which the truncation error of the difference method initiates a vortex instability in the computed flow. The implications of this study for adaptive mesh refinement strategies are also discussed. $$\copyright$$ Academic Press.

##### MSC:
 76M20 Finite difference methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids
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##### References:
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