GAUGE METHOD FOR VISCOUS INCOMPRESSIBLE FLOWS

By W. E, Jianguo Liu. 2003

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Stability and convergence of efficient Navier‐Stokes solvers via a commutator estimate (2007, methodology): “The method in [ EL , WL] diers only in that un in (42) is replaced by Pun.”
An overview of projection methods for incompressible flows (2006, methodology): “We review in this section the consistent splitting scheme introduced in Guermond and Shen [26] and we show that, up to an appropriate change of variables and when the space is continuous, this algorithm is equivalent to the so-called gauge method introduced in E and Liu [11] (see also Wang and Liu [”
A new class of truly consistent splitting schemes for incompressible flows (2003, unknown): “AMS: 76D05; 65M12; 65M60 Keywords: Navier–Stokes equations; Projection methods; Fractional step methods; Incompressibility; Finite elements; Spectral approximations”
A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities (2010, methodology): “schemes based on a gauge-Uzawa formulation [16] which is a modified version of the original gauge method [5].”
Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term (2004, unknown): “However, the main advantage of implicit treatment of the viscous term in the projection method is for low Reynolds number flow, and in this regime the effects of the numerical boundary layers are quite severe [10].”