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Vorticity errors in multidimensional Lagrangian codes. (English) Zbl 0743.76058
Summary: We investigate the apparent paradox, as exemplified by the well-known Saltzman test problem, of multidimensional Lagrangian codes experiencing mesh tangling when computing one-dimensional irrotational flows. We demonstrate that the cause is the generation of spurious vorticity, or vorticity error, by a nonuniform mesh. Based on this, we investigate two methods of constructing improved Lagrangian vertex velocities by removing, or filtering out, this spurious vorticity, rather than by the more common practice of introducing artificial viscosity. The first method reconstructs the velocity from the known flow divergence and from the true vorticity computed by means of a transport equation. The second method, which is much simpler and more efficient, subtracts a divergence- free correction from the velocity, such that the resulting velocity possesses the correct vorticity. We then successfully apply this method to solve a two-dimensional shock refraction problem, a problem which exhibits nonzero intrinsic vorticity.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76B99 Incompressible inviscid fluids
Software:
LINPACK
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References:
[1] Saltzman, J.; Colella, P., (), (unpublished)
[2] Wilkins, M.L., J. comput. phys., 36, 281, (1980)
[3] Margolin, L.G., (), (unpublished)
[4] O’Rourke, P.J., J. comput. phys., 53, 359, (1984)
[5] Addessio, F.L.; Carroll, D.E.; Dukowicz, J.K.; Harlow, F.H.; Johnson, J.N.; Kashiwa, B.A.; Maltrud, M.E.; Ruppel, H.M., (), (unpublished)
[6] Abraham, R.; Marsden, J.E., Foundations of mechanics, (), 154
[7] Morse, P.M.; Feshbach, H., Methods of theoretical physics, (), 52, Part. 1
[8] Arfken, G., Mathematical methods for physicists, (), 66 · Zbl 0135.42304
[9] Brackbill, J.U., Comput. phys. commun., 47, 1, (1987)
[10] Fritts, M.J.; Boris, J.P., J. comput. phys., 31, 173, (1979)
[11] Aris, R., Vectors, tensors, and the basic equations of fluid mechanics, (), 63
[12] Dongarra, J.J.; Moler, C.B.; Bunch, J.R.; Stewart, G.W., ()
[13] Henderson, L.F., J. fluid mech., 26, 607, (1966)
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