Numerical Reliability of MHD Flow Calculations at High Hartmann Numbers

In this paper, a new numerical investigation is performed for the two-dimensional MHD flow in a rectangular duct and an error analysis of the traditional calculation of solution is given.Arbitrary values of the flow parameters: Hartmann number and wall conduction ratio can now be chosen, and the singular perturbation problem solved and analysed using the interval mathematics and verified inclusion methods (Ε-Methods). Furthermore, the error analysis of the traditional calculation applied to this MHD flow shows that there is a lack of reliability of the known numerical result of this physical problem, even for Hartmann numbers M ≤ 1000. These results indicate that the reliability of numerical data should, at least, be proved for any calculation with the control of rounding errors using an accurate floating-point arithmetic and inclusion methods of interval mathematics.