Abstract: We present in this short note a simple construction of the convection operator in the variable density Navier-Stokes equations for MAC discretizations, which ensures the control of the kinetic energy. We thereby extend a similar construction performed in previous works for staggered finite element non-conforming discretizations, and, consequently, the stability results which were obtained for implicit or pressure correction schemes for compressible barotropic flows.
Key words : Compressible Navier-Stokes equations, staggered discretizations, MAC scheme.
Paper presented by: Jean-Marc Hérard
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