Error analysis of pressure reconstruction from discrete velocities
Résumé
Magnetic Resonance Imaging allows to measure the three-dimensional velocity field in blood flows. There- fore, several methods have been proposed to reconstruct the pressure field from such measurements using the incompressible Navier-Stokes equations. However, those measurements are obtained at limited spatial resolution given by the voxel dimensions in the image. Therefore, the velocity entering to the right-hand-side corresponds to a piecewise linear interpolation of the exact velocity.
In this work we propose a strategy for convergence analysis of state-of-the-art pressure reconstruction meth- ods. The methods analyzed are the the so called Pressure Poisson Estimator (PPE) and Stokes Estimator (STE). In the theoretical error analysis, we show that many terms of different convergence order appear. However, numerical results, show in academic examples that only the PPE may profit of increasing the polynomial order, and that the STE presents a higher accuracy than the PPE.
Additionally, we compare the pressure estimation methods on real MRI data, assessing the impact of different spatial resolutions and polynomial degree on each of the methods. Here, the results are aligned with the academic test cases in terms of sensitivity to polynomial order and that the STE shows to be potentially more accurate when compared to reference pressure measurements.
Domaines
Analyse numérique [math.NA]Origine | Fichiers produits par l'(les) auteur(s) |
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