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Int. J. Numer. Anal. Mod., 8 (2011), pp. 118-136. |
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Stable computing with an enhanced physics based scheme for the 3D Navier-Stokes equations M. Case 1, V. Ervin 1, A. Linke 2, L. Rebholz 1, N. Wilson 1 1 Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, USA.2 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany. Received by the editors December 1, 2009 and, in revised form, May 5, 2010. Abstract
We study extensions of the energy and helicity preserving scheme for the 3D Navier-Stokes equations, developed in [23], to a more general class of problems. The scheme is studied together with stabilizations of grad-div type in order to mitigate the effect of the Bernoulli pressure error on the velocity error. We prove stability, convergence, discuss conservation properties, and present numerical experiments that demonstrate the advantages of the scheme. Key words: Finite element method, discrete helicity conservation, grad-div stabilization.Email: mcase@clemson.edu, vjervin@clemson.edu, linke@wias-berlin.de, rebholz@clemson.edu, newilso@clemson.edu |