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Several finite element methods for simulating incompressible flows rely onthe streamline upwind Petrov-Galerkin stabilization (SUPG) term, which isweighted by tau_SUPG. The conventional formulation of tau_SUPG includes aconstant that depends on the time step size, producing an overall method thatbecomes exceedingly less accurate as the time step size approaches zero. Inpractice, such method inconsistency introduces significant error in thesolution, especially in cardiovascular simulations, where small time step sizesmay be required. To overcome this issue, we propose a consistent method that isbased on a new definition of tau_SUPG. This method, which can be easilyimplemented on top of an existing streamline upwind Petrov-Galerkin andpressure stabilizing Petrov-Galerkin method, involves the replacement of thetime step size in tau_SUPG with a physical time scale. This time scale iscalculated in a simple operation once every time step for the entirecomputational domain from the ratio of the L2-norm of the acceleration and thevelocity. The proposed method is compared against the conventional method usingfour cases: a steady pipe flow, a blood flow through vascular anatomy, anexternal flow over a square obstacle, and a fluid-structure interaction case.These numerical experiments show that the proposed formulation eliminates theinconsistency issue associated with the conventional formulation in all cases.While the proposed method is slightly more costly than the conventional method,it significantly reduces the error, particularly at small time step sizes. Forthe pipe flow where an exact solution is available, we show the conventionalmethod can over-predict the pressure drop by a factor of three. This largeerror is almost completely eliminated by the proposed formulation, dropping toapproximately 1% for all time step sizes and Reynolds numbers considered.

A time-consistent stabilized finite element method for fluids with applications to hemodynamics