The Variational Multiscale Formulation for the Fully-Implicit Log-Morphology Equation as a Tensor-Based Blood Damage Model

Abstract

We derive a variational multiscale (VMS) finite element formulation for a viscoelastic, tensor-based blood damage model. The tensor equation is numerically stabilized by a logarithmic shape tensor description that prevents unphysical, negative eigenvalues. The resulting VMS stabilization terms for this so-called log-morph equation are presented together with their special numerical treatment. Results for a 2D rotating stirrer test case obtained from log-morph simulations with both SUPG and VMS stabilization show significantly improved numerical behavior if compared with Galerkin/least squares (GLS) stabilized untransformed morphology simulation results. The newly proposed method is also successfully applied to a state-of-the-art centrifugal ventricular assist device (VAD), and clear advantages of the VMS stabilization compared to the SUPG stabilized formulation are presented.

23 pages, 7 figures

Cited by in corpus (4)

• Hemodynamics of the heart's left atrium based on a Variational Multiscale-LES numerical method
• Eulerian Formulation of the Tensor-Based Morphology Equations for Strain-Based Blood Damage Modeling
• Finite-Element Formulation for Advection-Reaction Equations with Change of Variable and Discontinuity Capturing
• In-silico Analysis of Hemodynamic Indicators in Idealized Stented Coronary Arteries for Varying Stent Indentation