Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present an efficient, accurate, and robust method for simulation of dense suspensions of deformable and rigid particles immersed in Stokesian fluid in two dimensions.  use a ll-established boundary integral formulation for the problem as the foundation of our approach. This type of formulations, with a high-order spatial discretization and an implicit and adaptive time discretization, have been shown to be able to handle complex interactions beten particles with high accuracy. Yet, for dense suspensions, very small time-steps or expensive implicit solves as ll as a large number of discretization points are required to avoid non-physical contact and intersections beten particles, leading to infinite forces and numerical instability. #R##N#Our method maintains the accuracy of previous methods at a significantly lor cost for dense suspensions. The key idea is to ensure interference-free configuration by introducing explicit contact constraints into the system. While such constraints are unnecessary in the formulation, in the discrete form of the problem, they make it possible to eliminate catastrophic loss of accuracy by preventing contact explicitly. #R##N#Introducing contact constraints results in a significant increase in stable time-step size for explicit time-stepping, and a reduction in the number of points adequate for stability.
['Libin Lu', 'Abtin Rahimian', 'Denis Zorin']
I am writing a research paper on a idea Contact-aware simulations of particulate Stokesian suspensions
[{"from": "human", "value": "I am writing a research paper on a idea Contact-aware simulations of particulate Stokesian suspensions"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present an efficient, accurate, and robust method for simulation of dense suspensions of deformable and rigid particles immersed in Stokesian fluid in two dimensions.  use a ll-established boundary integral formulation for the problem as the foundation of our approach. This type of formulations, with a high-order spatial discretization and an implicit and adaptive time discretization, have been shown to be able to handle complex interactions beten particles with high accuracy. Yet, for dense suspensions, very small time-steps or expensive implicit solves as ll as a large number of discretization points are required to avoid non-physical contact and intersections beten particles, leading to infinite forces and numerical instability. #R##N#Our method maintains the accuracy of previous methods at a significantly lor cost for dense suspensions. The key idea is to ensure interference-free configuration by introducing explicit contact constraints into the system. While such constraints are unnecessary in the formulation, in the discrete form of the problem, they make it possible to eliminate catastrophic loss of accuracy by preventing contact explicitly. #R##N#Introducing contact constraints results in a significant increase in stable time-step size for explicit time-stepping, and a reduction in the number of points adequate for stability."}]