Efficient solvers for coupled models in respiratory mechanics.

Area of Science:

• Computational fluid dynamics
• Biomedical engineering
• Numerical analysis

Background:

• Physiologically relevant pulmonary models are crucial for understanding lung mechanics.
• Simulating these models efficiently on high-performance computing platforms is challenging.
• Existing fluid-structure interaction (FSI) preconditioners are inadequate for lung models with algebraic constraints.

Purpose of the Study:

• To develop efficient preconditioners for simulating complex pulmonary models.
• To enable the assessment of mechanical ventilation strategies.
• To contribute to designing patient-specific ventilation treatments.

Main Methods:

• The study addresses a monolithic system from FSI with additional algebraic constraints, forming a saddle point problem.
• The semi-implicit method for pressure-linked equations (SIMPLE) is employed to transform the saddle point problem into a standard FSI problem.
• The proposed preconditioners are evaluated numerically on complex, patient-specific lung geometries.

Main Results:

• The developed preconditioners demonstrate performance comparable to optimal multigrid methods.
• The method effectively handles the multiphysics nature of the lung model.
• The preconditioners are robust for physiologically relevant simulations with complex geometries.

Conclusions:

• Efficient preconditioners have been developed for complex pulmonary models.
• The SIMPLE-based approach successfully overcomes limitations of standard FSI preconditioners.
• This methodology is applicable to other biomedical applications involving coupled flow and tissue deformation.