Idealised Ventricle Inflation: idealisedVentricle

Tutorial Aims

  • Demonstrate the simulation of large-strain incompressible hyperelastic inflation of an idealised left ventricle.
  • Show two solution approaches available in solids4foam:
    • PETSc SNES (default), as used in [1].
    • Block-coupled pressure-displacement (foam-extend), as used in [2].

Case Overview

The case models the quasi-static inflation of an idealised, axisymmetric left ventricle under an internal endocardial pressure that ramps linearly from 0 to 10 kPa over a unit pseudo-time. The myocardium is described with a nearly-incompressible Guccione passive law; for the pressure-displacement approach, an isotropic Guccione form is used (cf = ct = cfs = 1).

Two solution approaches are provided:

  • petsc (default): solved with the nonLinearGeometryTotalLagrangianTotalDisplacement solid model and the PETSc SNES nonlinear solver. The mesh is generated with blockMesh and rotationally extruded with extrudeMesh to produce a full-revolution ventricle.
  • pressureDisplacement: solved with the foam-extend coupledPressureDisplacementSolid block-coupled solid model on a symmetric (one-quarter) tetrahedral mesh imported from a Fluent .msh file.

Running the Case

The tutorial case is located at solids4foam/tutorials/solids/hyperelasticity/idealisedVentricle. The case can be run using the included Allrun script:

./Allrun

The default option uses the PETSc SNES approach. The script also supports the pressure-displacement solution option:

./Allrun petsc
./Allrun pressureDisplacement

The default petsc case requires OpenFOAM.com with PETSc enabled. The pressureDisplacement option is foam-extend-only.

The default approach can also be run in parallel using:

./Allrun parallel

Verification and Convergence Study

The opt-in verification/ directory holds a mesh convergence study. It refines the blockMesh divisions and the rotational extrusion layers together, samples the deformed mid-wall line of Problem 2 of Land et al. [3], and checks self-convergence of that line:

cd verification
./Allverify

The default sweep runs the 1 620-, 12 960-, and 103 680-cell levels; an 829 440-cell level is available explicitly. Over all four levels the mid-wall line converges at a net order of 1.99, and the finest apex position differs from an independent block-coupled mixed pressure-displacement solution by 0.99%. The study is separate from regressionTest.sh and is not run by the normal tutorial test suites. See the verification README for the mesh levels, options, and acceptance criteria.

References

[1] P. Cardiff, D. Armfield, Ž. Tuković, and I. Batistić, "A Jacobian-Free Newton-Krylov Method for Cell-Centred Finite Volume Solid Mechanics", International Journal for Numerical Methods in Engineering, 127(3), e70268, 2026.

[2] A. Horvat, P. Milović, I. Karšaj, and Ž. Tuković, "A Block-Coupled Finite Volume Method for Incompressible Hyperelastic Solids", Applied Sciences, 15(23), 12660, 2025.

[3] S. Land, V. Gurev, S. Arens, et al., "Verification of cardiac mechanics software: benchmark problems and solutions for testing active and passive material behaviour", Proceedings of the Royal Society A, 471(2184), 20150641, 2015.