Adaptive differential quadrature element refinement analyses of fluid mechanics problems Original Research Article

The differential quadrature element method (DQEM) has been proposed. The element weighting coefficient matrices are generated by the differential quadrature (DQ) or generic differential quadrature (GDQ). By using the DQ or GDQ technique and the mapping procedure the governing differential or partial differential equations, the transition conditions of two adjacent elements and the boundary conditions can be discretized. The overall algebraic equation system can be obtained by assembling all of the discretized equations. This method can convert a generic engineering or scientific problem having an arbitrary domain configuration into a computer algorithm. The DQEM analysis can be carried out by the adaptive refinement procedure. The development of adaptive DQEM refinement analysis procedure for fluid mechanics problems is carried out. Numerical results are presented.