Related Experiment Video
Updated: May 23, 2025
13:07
Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression
Published on: January 15, 2022
3.8K
A Posteriori Error Analysis for a Coupled Stokes-Poroelastic System with Multiple Compartments.
Ivan Fumagalli1, Nicola Parolini1, Marco Verani1
1MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy.
Journal of Scientific Computing
|March 11, 2025
Summary
This study develops a posteriori error estimates for complex brain fluid-poromechanics models. This work aims to reduce computational demands for multiphysics flow simulations in the brain.
Area of Science:
- Computational fluid dynamics
- Biomedical engineering
- Mathematical modeling
Background:
- Fluid-poromechanics systems, especially for brain multiphysics flows, require significant computational resources due to complex anatomy and numerous variables.
- Modeling these systems involves coupled Stokes equations for cerebrospinal fluid and Multiple-network Poro-Elasticity (MPE) equations for brain tissue and vascular networks.
Purpose of the Study:
- To derive rigorous a posteriori error estimates for the coupled Stokes-MPE problem.
- To lay the groundwork for adaptive mesh refinement and reduced-order modeling strategies.
- To decrease the computational burden of simulating brain fluid dynamics.
Main Methods:
- Derivation of a posteriori error estimators for the coupled Stokes-MPE system.
- Numerical experiments to validate the proposed estimators.
- Analysis of the contribution of different solution variables to the error estimation.
Main Results:
- Reliability and optimal efficiency of the developed a posteriori error estimator were confirmed through numerical experiments.
- The influence of various solution variables on the estimator's composition was identified.
Conclusions:
- The derived a posteriori error estimates are reliable and efficient for coupled Stokes-MPE problems.
- This work provides a foundation for developing more computationally efficient models for brain fluid-poromechanics.
- Understanding variable contributions aids in optimizing simulation strategies.
Related Concept Videos
01:28Navier–Stokes Equations
365
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
365
01:18Newtonian Fluid: Problem Solving
169
Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
169
01:15Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity
236
Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
236
01:06Divergence and Stokes' Theorems
1.5K
The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...
1.5K
01:30Bernoulli's Equation for Flow Along a Streamline
586
Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
586
01:11Pressure Variation in a Fluid at Rest
201
In a fluid at rest, the pressure at any point beneath the fluid surface depends solely on the depth, not on the container's shape or size. This principle, known as hydrostatic pressure, arises because, in stationary fluids, there is no acceleration, meaning the forces within the fluid balance out. Only vertical forces, caused by the weight of the fluid above, contribute to pressure changes with depth.
When measuring pressure at two different levels within the fluid, the difference in...
When measuring pressure at two different levels within the fluid, the difference in...
201