On the conservation properties of the two-level linearized methods for Navier-Stokes equations
CoRR(2023)
Abstract
This manuscript is devoted to investigating the conservation laws of
incompressible Navier-Stokes equations(NSEs), written in the
energy-momentum-angular momentum conserving(EMAC) formulation, after being
linearized by the two-level methods. With appropriate correction steps(e.g.,
Stoke/Newton corrections), we show that the two-level methods, discretized from
EMAC NSEs, could preserve momentum, angular momentum, and asymptotically
preserve energy. Error estimates and (asymptotic) conservative properties are
analyzed and obtained, and numerical experiments are conducted to validate the
theoretical results, mainly confirming that the two-level linearized methods
indeed possess the property of (almost) retainability on conservation laws.
Moreover, experimental error estimates and optimal convergence rates of two
newly defined types of pressure approximation in EMAC NSEs are also obtained.
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