Error analyses on block-centered finite difference schemes for distributed-order non-Fickian flow

In this article, two numerical schemes are designed and analyzed for the distributed-order non-Fickian flow. Two different processing techniques are applied to deal with the time distributed-order derivative for the constructed two schemes, while the classical block-centered finite difference method is used in spatial discretization. To be precise, one adopts the standard numerical scheme called SD scheme in the temporal direction, and the other utilizes an efficient method called EF scheme. We derive the stabilities of the two schemes rigorously. The convergence result of the SD scheme for pressure and velocity is O(Δt^2+𝜎 + 𝜎⁴ + h⁴ + k⁴). However, to get a faster computing speed, the super parameter 𝜀 is needed for the EF scheme, which leads to the accuracy is O(Δt^2+𝜎 + 𝜎⁴ + 𝜀² + h⁴ + k⁴)). Finally, some numerical experiments are carried out to verify the theoretical analysis. © 2023 Wiley Periodicals LLC.