The characteristic variational multiscale method for convection-dominated convection-diffusion-reaction problems

In this paper, the characteristic variational multiscale (C-VMS) method is proposed for solving two-dimensional (2D) convection-dominated convection-diffusion-reaction problems. The scheme is combined the method of characteristics with the variational multiscale (VMS) method to create the C-VMS procedures. The stability analysis and error estimate of the C-VMS method are obtained. The scheme not only realizes the purpose of lowering the time-truncation error, using larger time step for solving the convection-dominated convection-diffusion-reaction problems, but also keeps the favorable stability and high precision. Finally, numerical experiments in 2D and 3D cases are presented to illustrate the availability and efficiency of the scheme.