ELIMINATION OF ARTIFICIAL GRID DISTORTION AND HOURGLASS-TYPE MOTIONS BY MEANS OF LAGRANGIAN SUBZONAL MASSES AND PRESSURES

The bane of Lagrangian hydrodynamics calculations is the premature bre akdown of grid topology that results in severe degradation of accuracy and run termination often long before the assumption of a Lagrangian zonal mass has ceased to be valid. At short spatial grid scales this i s usually referred to by the terms ''hourglass'' mode or ''keystone'' motion associated, in particular, with underconstrained grids such as quadrilaterals and hexahedrons in two and three dimensions, respective ly. At longer spatial lengths relative to the grid spacing there is wh at is referred to ubiquitously as ''spurious vorticity,'' or the long- thin zone problem. In both cases the result is anomalous grid distorti on and tangling that has nothing to do with the actual solution, as wo uld be the case for turbulent flow. In this work we show how such moti ons 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 g radients that can occur within a zone due to its differential distorti on. Subzonal Lagrangian masses can be choosen in more than one manner to obtain subzonal density and pressure variation. However, these mass es arise in a natural way from the intersection of the Lagrangian cont ours, through which no mass flows, that are associated with both the L agrangian zonal and nodal masses in a staggered spatial grid hydrodyna mics formulation. This is an extension of the usual Lagrangian assumpt ion that is often applied to only the zonal mass. We show that with a proper discretization of the subzonal forces resulting from subzonal p ressures, hourglass motion and spurious vorticity can be eliminated fo r a very large range of problems. (C) 1998 Academic Press.