Discontinuity-capturing finite element computation of unsteady flow with adaptive unstructured mesh

A discontinuity-capturing scheme of finite element method (FEM) is proposed. The unstructured-grid technique combined with a new type of adaptive mesh approach is developed for both compressible and incompressible unsteady flows, which exhibits the capability of capturing the shock waves and/or thin shear layers accurately in an unsteady viscous flow at high Reynolds number. In particular, a new testing variable, i.e., the disturbed kinetic energyE, is suggested and used in the adaptive mesh computation, which is universally applicable to the capturing of both shock waves and shear layers in the inviscid flow and viscous flow at high Reynolds number. Based on several calculated examples, this approach has been proved to be effective and efficient for the calculations of compressible and incompressible flows. The project supported by the National Natural Science Foundation of China (10125210), the Hundred-Talent Programme of the Chinese Academy of Sciences and the Innovation Project of the Chinese Academy of Sciences (KJCX-SW-L04, KJCX2-SW-L2)