Factors influencing the need for upwinding in two-dimensional field calculation

Numerical simulations have been conducted in an attempt to clarify some of the findings of previous work on the necessity of upwinding in the finite element analysis of electromagnetic problems that involve relative motion. The results presented demonstrate that, besides the Peclet number, the stability of the finite element solution also depends on the boundary conditions of the problem and the magnetic characteristics of the moving conductor. When the moving conductor is nonferromagnetic and a periodic boundary condition is imposed, a Galerkin method can model the problem successfully. Whenever numerical oscillation is exhibited, the upwind finite element scheme can be used to solve the problem. In a 3-D model where the biconjugate gradient solver is the most economical, and often the only, choice of solver to use, upwinding may be necessary to ensure convergence