Journal of Computational Physics
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This paper investigates the theoretical stability bound of a Lagrangian staggered scheme used to solve hydrodynamics equations. We present the two-dimensional (2D) wave equation as a possible model for this study and, by using the numerical radius of the amplification matrix, we prove that the family of schemes defined with two time-centering parameters is limited by a nonclassical stability bound limit defined with an analytical curve. We further show that 2D numerical experiments agree with this theoretical result.