Stability analysis of the 4th order Runge Kutta method in application to colloidal particle interactions

Colloidal Particles;Stability;4th Order Runge Kutta

Velagala, Sindhuja ; Higdon ; Jonathan J.L.

关键词: Colloidal Particles;    Stability;    4th Order Runge Kutta;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/72750/Sindhuja_Velagala.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Colloidal particles have a wide range of industrial applications. This study is focused on the application to microstructured materials and the impact of external compressive forces on particles. Currently, in the large throughput manufacturing of microstructured materials, problems such as cracking are caused by these external forces. Numerical methods can be used to generate particle positions and obtain a better understanding of particle interactions under different conditions. The aim of this study was to obtain a better understanding of the stability limits of using the 4th order Runge Kutta method. By introducing the external forces as auxiliary functions, we were able to generate exact analytic solutions satisfying arbitrary hydrodynamic and interaction forces. This allowed rigorous comparison of the theoretical stability limits and the observed stability limits on time step. We found excellent agreement with the predicted and observed results.