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Numerical considerations for advection-diffusion problems in cardiovascular hemodynamics.

Sabrina R Lynch1, Nitesh Nama2, Zelu Xu3

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|June 24, 2020
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This study introduces novel numerical methods for cardiovascular mass transport simulations, improving accuracy in complex flow scenarios. These techniques enhance computational models for better understanding blood flow and drug delivery.

Keywords:
Neumann inflow boundary conditionbackflow stabilizationcardiovascular simulationconsistent flux boundary conditiondiscontinuity-capturing operatorscalar advection diffusion

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Area of Science:

  • Computational fluid dynamics
  • Biomedical engineering
  • Numerical analysis

Background:

  • Cardiovascular mass transport simulations face challenges with high Péclet numbers and Neumann boundary backflow.
  • Existing numerical methods can lead to instabilities and oscillations in advection-dominated flows.

Purpose of the Study:

  • To present and discuss numerical tools for stabilized finite element simulations of cardiovascular mass transport.
  • To address numerical instabilities arising from backflow at Neumann boundaries.
  • To improve the accuracy and stability of computational fluid dynamics models in cardiovascular research.

Main Methods:

  • Developed an approach based on total flux prescription to handle Neumann boundary backflow.
  • Introduced a "consistent flux" outflow boundary condition, comparing it to the traditional zero diffusive flux condition.
  • Applied discontinuity capturing (DC) stabilization techniques for advection-dominated flows.

Main Results:

  • The proposed total flux prescription effectively overcomes numerical instabilities at Neumann boundaries.
  • The "consistent flux" boundary condition demonstrated superior performance compared to the zero diffusive flux condition.
  • Discontinuity capturing techniques successfully mitigated solution oscillations near concentration fronts.

Conclusions:

  • The presented numerical tools effectively address common challenges in cardiovascular mass transport simulations.
  • These advancements enhance the reliability of computational models for studying physiological and pathological processes.
  • The study provides robust methods for simulating complex fluid dynamics and mass transport in the cardiovascular system.