Numerical solution of 2-d advection equation using the modified finite element method and directional splitting technique

A method of the numerical solution of a 2-D linear advection equation is proposed. In the solution, the modified finite element method and directional splitting technique is used. For the time integration the two-step differential scheme is used. Two weighting parameters introduced into the schemes determine the accuracy and stability of the solution. Numerical diffusion and dispersion tensors are derived for the pure advection equation solved using the proposed method. They enable the explanation of numerical properties and applicability of this scheme. The proposed scheme is of third-order accuracy and is adaptive, allowing for simultaneous elimination of numerical diffusion and dispersion from the solution of a 2-D advection equation.