Bug report: reference geometry inconsistency (area-based vs radius-based linear interpolation)

Description

The reference geometry $A_0(z)$ used in the 1D solver is defined as a linear interpolation of the inlet and outlet areas (line 1341 in cvOneDBFSolver.cxx).
However, in the material model classes (e.g. cvOneDMaterialOlufsen.cxx), the reference radius $r_0(z)$ is computed as a linear interpolation of the inlet and outlet radii (line 158).

These two approaches are clearly mathematically inconsistent, since interpolating areas and then taking a square root $\quad r_0(z) = \sqrt{A_0(z) / \pi}$ is not equivalent to interpolating radii.

This inconsistency leads to a mismatch in the initial geometry and becomes visible when looking at the pressure at $t = 0$. The attached plot ( $p(z,0)$ along the centerline of a coronary artery) highlights the problem.

Proposed fix:

• Either update line 1341 in cvOneDBFSolver.cxx to interpolate radii instead of areas (and compute $A_0$ from them),
• or update the material classes to interpolate areas instead of radii.

bug_RCA-A18-B17_pressure_along_centerline.pdf

Reproduction

Run a 1D simulation over any vessel geometry, selecting for the material model $p_0 = 0$ and look at the pressure at time $t=0$ along the geometry itself. This will not be zero, but rather follow a parabolic profile over each segment.

Environment info

OS: Ubuntu 22.04
Skyline solver
commit: https://github.com/SimVascular/svOneDSolver/commit/66b31b4221b8dc9c04a767ed48e6a5367f63a499

Expected behavior

The pressure at the initial time, when imposing e.g. $p_0 = 0$, must be equal to $p_0$ (0 in this example).

Additional context

When the parameters of the material model are changed to make the vessel quasi-rigid, the effect of this bug becomes more evident.

Code of Conduct

• I agree to follow this project's Code of Conduct and Contributing Guidelines

Start by comparing the reference-geometry interpolation at line 1341 in cvOneDBFSolver.cxx with the radius interpolation at line 158 in cvOneDMaterialOlufsen.cxx and the other material classes. Run a 1D simulation on a vessel geometry with p₀ = 0 and inspect pressure at t = 0. Done means the geometry is handled consistently and the initial pressure remains equal to p₀ along the vessel.