A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion

TL;DR

This paper introduces a fast semi-discrete Kansa method for efficiently solving two-dimensional spatiotemporal fractional diffusion equations, improving computational speed and accuracy over traditional methods in modeling anomalous diffusion.

Contribution

It proposes a novel algorithm combining the Kansa method for fractional derivatives with an analytical approach for time discretization, enhancing efficiency for complex domains.

Findings

Accurate simulation of solute plumes in heterogeneous media

Improved computational efficiency over Monte-Carlo methods

Effective handling of large irregular domains

Abstract

Anomalous diffusion is a common phenomenon observed in underground solute transport, soil water infiltration and sediment movement, etc. Time and space fractional derivative advection-dispersion equation (FADE) has been widely employed as the governing equation to characterize above mentioned anomalous diffusion related processes. However, a main problem in application of time and space FADE model to describe the real-world mass transport processes, is its low computation efficiency for long-time range and large irregular domain cases. This study offers a new algorithm in which the Kansa method is used for vector space fractional derivative term discretization and then analytical approach for resulted time fractional ordinary system. The influence of node distribution mode and node numbers on accuracy and convergence rate are analysed through the numerical examples in one and two dimensional cases. To test the application potentials of present methods, we offer the numerical results of two dimensional time and space FADE models in continuous and discrete cases. It shows that the solute plumes in heterogeneous and anisotropic media, can be well simulated by using present method compared with the previous time-consumed particle Monte-Carlo methods.