A second-order GSAV consistent-splitting scheme for the 2D perturbed Boussinesq system is proposed with unconditional weak stability and optimal second-order error estimates, though error constants grow exponentially with inverse viscosity and diffusivity.
Global regularity for the two-dimensional anisotropic Boussinesq equations with vertical dissipation.Archive for Rational Mechanics and Analysis, 208(3):985–1004, 2013
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A consistent-splitting generalized scalar auxiliary variable scheme for the perturbed Boussinesq system
A second-order GSAV consistent-splitting scheme for the 2D perturbed Boussinesq system is proposed with unconditional weak stability and optimal second-order error estimates, though error constants grow exponentially with inverse viscosity and diffusivity.