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Volume consistency in a staggered grid Lagrangian hydrodynamics scheme. (English) Zbl 1147.76044
Summary: Staggered grid Lagrangian schemes for compressible hydrodynamics involve a choice of how internal energy is advanced in time. The options depend on two ways of defining cell volumes: an indirect one, that guarantees total energy conservation, and a direct one that computes the volume from its definition as a function of cell vertices. It is shown that the motion of vertices can be defined so that the two volume definitions are identical. A so modified total energy conserving staggered scheme is applied to Coggeshall adiabatic compression problem, and now also entropy is basically exactly conserved for each Lagrangian cell, and there is increased accuracy for internal energy. The overall improvement as the grid is refined is less than what might be expected.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
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[1] Caramana, E.J.; Whalen, P.P., Numerical preservation of symmetry properties of continuum problems, J. comput. phys., 141, 174, (1998) · Zbl 0933.76066
[2] Caramana, E.J.; Burton, D.E.; Shashkov, M.J.; Whalen, P.P., The construction of compatible hydrodynamics algorithms utilizing conservation of total energy, J. comput. phys., 146, 227, (1998) · Zbl 0931.76080
[3] R. Loubère, First steps into ALE INC(ubator) - Version 2.0.0, Los Alamos National Laboratory Report LA-UR-04-8840, 2004.
[4] Bauer, A.L.; Burton, D.E.; Caramana, E.J.; Loubère, R.; Shashkov, M.J.; Whalen, P.P., The internal consistency, stability, and accuracy of the discrete, compatible formulation of Lagrangian hydrodynamics, J. comput. phys., 218, 572, (2006) · Zbl 1161.76538
[5] Caramana, E.J.; Shashkov, M.J.; Whalen, P.P., Formulations of artificial viscosity for multi-dimensional shock wave computations, J. comput. phys., 144, 70, (1998) · Zbl 1392.76041
[6] Margolin, L.G.; Shashkov, M.J.; Taylor, M.A., Symmetry-preserving discretizations for Lagrangian gas dynamics, (), 725-732 · Zbl 0998.76068
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