Solution of two-dimensional time-fractional Burgers equation with high and low Reynolds numbers

Burgers' equation frequently appears in the study of turbulence theory, as well as some other scientific fields. High and low Reynolds numbers play important roles in both modeling and numerical simulation. In this paper, we apply a numerical scheme to solve a two-dimensional time-fractional Burgers equation. The key feature of the proposed method is formed by combining the discontinuous Galerkin method to spatial variables and a finite difference scheme to temporal variables. The corresponding numerical analysis is also presented. Several numerical tests are carried out to demonstrate the theoretical analysis and we present a shock wave phenomenon of the new Burgers model.