Math @ Duke

Publications [#246924] of JianGuo Liu
Papers Published
 Weinan, E; Liu, JG, Finite difference schemes for incompressible flows in the velocity  impulse density formulation,
Journal of Computational Physics, vol. 130 no. 1
(January, 1997),
pp. 6776, Elsevier BV [doi]
(last updated on 2019/06/25)
Abstract: We consider finite difference schemes based on the impulse density variable. We show that the original velocity  impulse density formulation of Oseledets is marginally illposed for the inviscid flow, and this has the consequence that some ordinarily stable numerical methods in other formulations become unstable in the velocity  impulse density formulation. We present numerical evidence of this instability. We then discuss the construction of stable finite difference schemes by requiring that at the numerical level the nonlinear terms be convertible to similar terms in the primitive variable formulation. Finally we give a simplified velocity  impulse density formulation which is free of these complications and yet retains the nice features of the original velocity  impulse density formulation with regard to the treatment of boundary. We present numerical results on this simplified formulation for the driven cavity flow on both the staggered and nonstaggered grids. © 1997 Academic Press.


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