About the Impact the Difference Schemes Produce on a Fictive Particle on the Grid

Abstract

Fictive Forces Factor (3F) is introduced as the measure of an impact of the fictive forces always arising and producing non-physical effects when a boundary-value (or Cauchy) problem is being solved with the use of a difference scheme. 3F is a mean derivative of total energy of the fictive particle travelling along the function codomain grid, on coordinate. To demonstrate the approach, a well-known one-dimensional pseudo-curl transfer problem is considered with the employment of two difference schemes, the central and the upwind scheme. Should the problem be solved analytically, the total energy is an invariant, whereas a numerical solution produces some quadratic deviation. In particular, it is demonstrated with the use of 3F that (and in which extent) the upwind scheme brings out a smaller impact of the fictive forces than the central does. The fictive particle total energy serves also as an indicator if the non-physical effects arose, resulting in the loss of the difference scheme stability.