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- W4309129130 abstract "Several finite element methods for fluid rely on the streamline upwind Petrov-Galerkin stabilization (SUPG) term, which is weighted by $tau_{mathrm{SUPG}}$. The conventional formulation of $tau_{mathrm{SUPG}}$ includes a constant that depends on the time-step size, thus prohibiting consistent solutions from these methods as the time-step size is reduced. To overcome this issue, we propose a consistent method that is based on a new definition of $tau_{mathrm{SUPG}}$. The new method that is implemented on top of SUPG/PSPG stabilized formulation involves the replacement of the time-step size in $tau_{mathrm{SUPG}}$ with a physical quantity that is obtained from the ratio of the $L$textsuperscript{2}-norm of the acceleration and the velocity. The proposed method is compared against the conventional method using three cases: a steady pipe flow, an external flow over a square obstacle, and a blood flow through a patient-specific anatomy. These numerical experiments show that, in contrast to the conventional method, our proposed formulation remains consistent with regard to the time-step size. On the other hand, the proposed method produces a stiffer linear system that degrades the convergence of the linear solver by up to one order of magnitude. For the steady pipe flow case where the analytical solution is available, the proposed method reduces the error by up to 99.8% at smaller time-step sizes at high Reynolds numbers." @default.
- W4309129130 created "2022-11-23" @default.
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- W4309129130 date "2022-11-11" @default.
- W4309129130 modified "2023-10-14" @default.
- W4309129130 title "A consistent formulation for the stabilization terms in solving the Navier-Stokes equation using the finite element method" @default.
- W4309129130 doi "https://doi.org/10.48550/arxiv.2211.06505" @default.
- W4309129130 hasPublicationYear "2022" @default.
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