The Constant-Flow Patch Test -- A Unique Guideline for the Evaluation of Discretization Schemes for the Current Continuity Equations

The first patch test applicable to equations of the form of the advection-diffusion equation is presented. In contrast to the traditional constant-strain patch test scheme, a constant-flow condition is proposed in the present test. Numerical experiments indicate that for an algorithm, such constant-flow patch test reproduces its numerical characteristics which have been observed in actual device applications. Hence, this new patch test permits a handy legitimacy check for an algorithm without the uncertainties and complexities involved in the solution of a device problem. Evaluation of some of the existing algorithms based on this test is discussed. Among the algorithms examined, only Algorithm OM passes the patch test on an irregular mesh.