Hybrid ALE-Lagrange Fluid-Structure Simulation for Heart Valves
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Solution Overview
Problem
Current methods for fluid-structure interaction simulations, such as those involving heart pulsation and blood flow, face challenges in accurately tracking large deformations of structures like heart valves, particularly when using the ALE method, while the Lagrange multiplier method lacks stability and accuracy for such interactions.
Innovation Solution
A biological simulation apparatus that employs a combination of Lagrange description for structural domains and ALE fluid mesh models to deform and track interfaces, allowing for accurate fluid-structure interaction simulations by generating deformed ALE fluid mesh models that maintain mesh integrity and capture complex valve motions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the ALE method is used to track the interface between blood and myocardial wall, then the accuracy of fluid-structure interaction simulation is improved, but the mesh deformation capability is limited and cannot handle very large deformations
Solution Approach 1:
The patent combines the ALE method and Lagrange multiplier method into a hybrid approach. The ALE method is used for general fluid-structure interaction where high accuracy is needed, while the Lagrange multiplier method is applied specifically at the interface to handle large deformations and maintain mesh integrity, thus merging the advantages of both methods.
Solution Approach 2:
The patent applies different numerical methods to different regions: the ALE method is used in the bulk fluid domain for accurate interface tracking, while the Lagrange multiplier method is applied locally at the structural interface where large deformations occur. This local differentiation allows each method to operate in its optimal performance zone.
2Adaptability or versatility
If the Lagrange multiplier method is used for fluid-structure interaction, then the mesh does not need to be matched with the structural interface and large deformations can be handled, but the accuracy of the simulation is reduced
Solution Approach 1:
The patent merges the ALE method for accurate bulk fluid simulation with the Lagrange multiplier method for flexible interface handling. By combining these methods, the system achieves both the accuracy of ALE in the fluid domain and the large deformation capability of Lagrange multiplier at the interface.
Solution Approach 2:
The patent introduces an intermediary approach where the Lagrange multiplier method acts as a mediator between the fluid domain (modeled with ALE) and the structure domain. This intermediary layer enables large deformations and complex motions while maintaining coupling accuracy through the hybrid formulation.
3Measurement precision
If the ALE fluid mesh model is deformed to track the interface, then the interface tracking accuracy is improved, but mesh failure may occur under very large deformations
Solution Approach 1:
The Lagrange multiplier method serves as an intermediary that decouples the fluid mesh from direct deformation requirements. By using Lagrange multipliers to enforce interface conditions, the ALE fluid mesh can track the interface accurately without undergoing extreme deformations that would cause mesh failure.
Solution Approach 2:
The patent effectively creates a virtual copy of the interface conditions through the Lagrange multiplier formulation. Instead of deforming the ALE mesh to match the structural interface, the Lagrange multipliers enforce the interface conditions on a separate computational level, allowing the mesh to remain intact while still achieving accurate interface tracking.
Data Source
AI summary
In a biological simulation apparatus, an operation unit represents a structure domain where tissues of a biological organ exist by a structure mesh model based on a Lagrange description and a fluid domain where fluid inside the biological organ exists by an ALE fluid mesh model based on an ALE description method. In a fluid-structure interaction simulation, the operation unit deforms the structure mesh model, and then deforms the ALE fluid mesh model so as to form no gap on a first interface between a domain where a site other than a certain site of the biological organ in the structure domain exists and the fluid domain or no overlap with the structure domain. The operation unit captures a position of a second interface between a domain where the certain site exists and the fluid domain by using the ALE fluid mesh model as a reference.