Advanced Computational Modelling of Cerebrovascular Hemodynamics Using Navier-Stokes Equations

Overview:
We are seeking an experienced computational modeling expert to assist with a cutting-edge research project focused on the advanced computational modeling of cerebrovascular hemodynamics using Navier-Stokes equations. This project involves developing and validating numerical methods, generating meshes, and conducting simulations using both the Finite Element Method (FEM) and Smooth Particle Hydrodynamics (SPH).


1. Algorithm Development:
- Develop an algorithm to convert discrete vascular segments into a continuous mesh.
- Implement the Navier-Stokes equations using FEM on the generated mesh.
- Explore and implement SPH to compare its accuracy with FEM.

2. Mesh Generation:
- Create and refine continuous meshes from segmented vascular data.
- Ensure accurate approximation of complex geometries and application of boundary conditions.

3. Simulation Setup and Execution:
- Define boundary conditions necessary for solving Navier-Stokes equations.
- Configure solver settings and run simulations using FEM and SPH.
- Analyze flow patterns, pressure distribution, and hemodynamic parameters from simulation results.

Deliverables:
Validated Computational Model:
A validated computational model for simulating cerebrovascular hemodynamics.
Algorithm for Mesh Generation:
An algorithm that converts discrete vascular segments into a continuous mesh. The mesh should be generated at four levels (Level 0, Level 1, Level 2 and unified level) .
Numerical Solutions:
Numerical solutions to the Navier-Stokes equations on the generated mesh using both FEM and SPH.
Comprehensive Documentation:
Detailed guidelines and documentation on how to apply the model.
Documentation of methodologies and validation results.
Sensitivity Analysis Report:
A report detailing the sensitivity analysis and the impact of varying parameters on the simulation outcomes.
Mesh generation should be done in python and for FEM Fenics should be used.