Explicit characteristic finite volume method for convection–diffusion equation on rectangular grids

A Comparative Study of Characteristic Finite Element and Characteristic Finite Volume Methods for Convection-Diffusion-Reaction Problems on Triangular Grids

“…(27), but using the values from the neighboring cells according to the upwinding direction. Moreover, in this paper, the gradient term, , is approximated by the weighted residuals method, which is commonly used in the finite element technique [6].…”

“…By applying a characteristic approximation to trace advection in time, as explained in Ref. [5][6][7] to Eq. ( 1) yields (5) where all terms are to be evaluated at .…”

“…The fully explicit characteristic convectiondiffusion-reaction equation is given by (6) Together with the use of the divergence-free assumption , Equation ( 6) could be written finally in the conservation form as (7)…”

“…The rotating velocity field with the angular velocity of 4 rad/s is imposed as . This example has been used widely for testing the numerical artifacts that occur on different schemes [11,6]. The initial condition is given by…”

“…Recently, the author proposed an explicit characteristic finite volume method that can provide stabilized numerical solutions for pure advection and advectiondominated diffusion problems [5][6][7]. The idea of the characteristic-based scheme is used to discrete the Lagrangian derivative as the function of time.…”