منابع مشابه
Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation
We present a second-order finite-difference scheme for viscoelastic flows based on a recent reformulation of the constitutive laws as equations for the matrix logarithm of the conformation tensor. We present a simple analysis that clarifies how the passage to logarithmic variables remedies the high-Weissenberg numerical instability. As a stringent test, we simulate an Oldroyd-B fluid in a lid-d...
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We study a defect correction method for the approximation of viscoelastic fluid flow. In the defect step, the constitutive equation is computed with an artificially reduced Weissenberg parameter for stability, and the resulting residual is corrected in the correction step. We prove the convergence of the defect correction method and derive an error estimate for the Oseen-viscoelastic model prob...
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The log conformation representation proposed in [1] has been implemented in a fem context using the DEVSS/DG formulation for viscoelastic fluid flow. We present a stability analysis in 1D and attribute the high Weissenberg problem to the failure of the numerical scheme to balance exponential growth. A slightly different derivation of the log based evolution equation than in [1] is also presente...
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The numerical simulation of viscoelastic fluid flow becomes more difficult as a physical parameter, the Weissenberg number, increases. Specifically, at a Weissenberg number larger than a critical value, the iterative nonlinear solver fails to converge, a phenomenon known as the High Weissenberg Number Problem. In this work we describe the application and implementation of continuation methods t...
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While much of the hemodynamics in a healthy human body has low Reynolds number, resulting in laminar flow, relatively high Reynolds number flow is observed at some specific locations, which can cause transition to turbulence. (The term “turbulence” refers to the motion of a fluid having local velocities and pressures that fluctuate randomly.) For example, the peak Reynolds number in the human a...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2007
ISSN: 0893-9659
DOI: 10.1016/j.aml.2006.12.003