Tutorial 01: area-to-wall kinematics

This case isolates the nonlinear geometric map used by the vessel-wall interaction:

\[ R_0=\sqrt{A_0/\pi},\qquad \delta R(A)=\sqrt{A/\pi}-R_0, \qquad P(A)=\delta R(A)n. \]

A0 is read from MetricFlowX vessel metadata. It is not replaced by a_d or r_d. At A=A0, the displacement is exactly zero. The selected TensorProduct cross-section modes are 3 and 7, with the same scalar coefficient, so their reconstructed field is delta R n.

The derivative gate checks

\[ \frac{d\delta R}{dA}=\frac{1}{2\sqrt{\pi A}}, \]

against a centered finite difference. The pressure-work factor is evaluated as 2*pi*R*dR/dA = 1; this is the circumference normalization that gives the multiplier pressure units.

The executable runs with MMS case = kinematics in the MetricFlowX elastodynamics tutorial subsection. It initializes a constant perturbed area and zero wall state, then evaluates the assembled two-way residual so that the A -> delta R n representation is exercised.

build-metric-flow-x-debug/metric_flow_x_elastodynamics_debug \
  build-metric-flow-x-debug/tutorials/metric_flow_x_elastodynamics/01_wall_kinematics.prm

Run the independent mathematical and two-way residual gate with:

ctest --test-dir build-metric-flow-x-debug -V \
  -R '^metric_flow_x_elastodynamics_mms_verification$'

The configured input is build-metric-flow-x-debug/tutorials/metric_flow_x_elastodynamics/01_wall_kinematics.prm. Output is under build-metric-flow-x-debug/test_output/tutorial-output/metric-flow-x-elastodynamics-01.