Mathematical modeling study demonstrates an accurate fractional framework for variable diffusion in disordered media, highlighting improved simulation of complex transport processes.
Key Points
To develop and validate a generalised fractional diffusion model combining temporal distributed-order operators, spatial Riesz fractional derivatives, and variable diffusion coefficients for disordered media.
Formulated a time-distributed-order and space-fractional diffusion equation incorporating spatially dependent diffusion coefficients.
Discretised the continuous spatial domain using the finite element method.
Approximated the temporal distributed-order operator using Simpson's numerical integration rule coupled with the L2-1σ difference formula.
Confirmed the stability and computational effectiveness of the numerical discretization using a test simulation example.
Demonstrated accurate representation of anomalous diffusion processes in heterogeneous media without relying on constant-coefficient simplifications.