Benchmark solutions for MHD solver development

A benchmark solution is of great importance in validating algorithms and codes for magnetohydrodynamic （MHD） flows. Hunt and Shercliff＇s solutions are usually employed as benchmarks for MHD flows in a duct with insulated walls or with thin conductive walls, in which wall effects on MHD are represented by the wall conductance ratio. With wall thickness resolved, it is stressed that the solution of Sloan and Smith＇s and the solution of Butler＇s can be used to check the error of the thin wall ap- proximation condition used for Hunt＇s solutions. It is noted that Tao and Ni＇s solutions can be used as a benchmark for MHD flows in a duct with wall symmetrical or unsymmetrical, thick or thin. When the walls are symmetrical, Tao and Ni＇s solutions are reduced to Sloan and Smith＇s solution and Butler＇s solution, respectively.