Modular grad-div stabilization for multiphysics flow problems

01/27/2020

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by   Mine Akbas, et al.

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This paper considers a modular grad-div stabilization method for approximating solutions of two multiphysics flow problems: incompressible non-isothermal flows governed by the Boussinesq equations, and magnetohydrodynamics (MHD). The proposed methods add a minimally intrusive step to an existing Boussinesq/MHD code, with the key idea being that the penalization of the divergence errors, is only in the extra step (i.e. nothing is added to the original equations). The paper provides a full mathematical analysis by proving unconditional stability and optimal convergence of the methods considered. Numerical experiments confirm theoretical findings, and show that the algorithms have a similar positive effect as the usual grad-div stabilization.