Stochastic Analysis of electro-osmotic flow dynamics in porous media with energy dissipation

A novel stochastic computational scheme is proposed to handle stochastic time-dependent partial differential equations. The scheme is second-order accurate and constructed at two-time levels. In order to discretize, a compact scheme is proposed. The compact scheme refers to the spatial discretization method used for solving the governing equations with high accuracy and efficiency. The consistency and stability of the proposed scheme are provided. The consistency and stability of the scheme are theoretically proven using truncation error analysis and von Neumann stability criteria. In addition to this, the scheme is applied to a mathematical model in the form of partial differential equations. The model is established by applying transformations on governing equations of electro-osmosis fluid flow over the stationary plate. Results show that the velocity profile rises by growing Helmholtz–Smoluchowski velocity and the velocity profile has dual behaviour (both increasing and decreasing behaviour) by growing electro-osmotic parameter. Compared to existing methods, our approach enhances accuracy by minimizing numerical dispersion through a second-order compact scheme, ensuring a precise representation of electrokinetic effects. The two-level formulation improves stability by effectively controlling numerical errors in stochastic simulations. Compact discretization achieves higher accuracy with fewer grid points, enhancing computational efficiency and reducing costs. This study provides a comprehensive framework for analyzing electro-osmotic flow dynamics under deterministic and stochastic conditions, offering valuable insights for optimizing electrokinetic and heat transfer systems.