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Exploration of new limiter schemes for stress tensors in Lagrangian and ALE hydrocodes. (English) Zbl 1290.76107
Summary: Limiter schemes are chiefly responsible for making high-resolution computations realizable in Lagrangian, Eulerian and ALE hydrocodes. Robust limiter schemes that are frame invariant and preserve symmetry have been established for scalars and to an extent, for vectors. However such limiter schemes have not been formulated and reported in the literature for tensor variables. In this work, new designs for limiter schemes for stress tensors are explored. Novel design principles are introduced and several limiter schemes are constructed based on these guiding principles. A scaling technique based on invariants and two new designs for slope limiter are proposed. In contrast to conventional slope limiters, the scaling technique designed by constraining the second invariant of stress tensor ensures monotonicity compliance by scaling the eigenvalues of the reconstructed stress tensors. Scalar slope limiter constructed based on constraining the second invariant is a formulation to extract a slope limiter from the scaling procedure. The tensor slope limiter scheme proposed for limiting velocity gradients is also extended for constraining stress tensor and the results from the same are considered as the basis for comparing and establishing the various limiter schemes formulated in this work. These limiter formulations are compared and contrasted in a cell-centered Lagrangian framework augmented with hypo-elastic model, by virtue of several one- and two-dimensional example problems.

76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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