Elimination of artificial grid distortion and hourglass-type motions by means of Lagrangian subzonal masses and pressures.

*(English)*Zbl 0932.76068We show how the title grid distortions and motions can be eliminated by the proper use of subzonal Lagrangian masses and associated densities and pressures. These subzonal pressures give rise to forces that resist these spurious motions. The pressure is no longer a constant in a zone; it now accurately reflects the density gradients that can occur within a zone due to its differential distortion. Subzonal Lagrangian masses can be choosen in more than one manner to obtain subzonal density and pressure variation. However, these masses arise in a natural way from the intersection of the Lagrangian contours, through which no mass flows, that are associated with both the Lagrangian zonal and nodal masses in a staggered spatial grid hydrodynamics formulation. This is an extension of the usual Lagrangian assumption that is often applied to only the zonal mass. We show that with a proper discretization of the subzonal forces resulting from subzonal pressures, hourglass motion and spurious vorticity can be eliminated for a very large range of problems. \(\copyright\) Academic Press.

##### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

76N15 | Gas dynamics (general theory) |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |

##### Keywords:

compatible discretizations; beam bending problem; Saltzman piston problem; subtriangles; subquadrilaterals##### Software:

TENSOR
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\textit{E. J. Caramana} and \textit{M. J. Shashkov}, J. Comput. Phys. 142, No. 2, 521--561 (1998; Zbl 0932.76068)

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