A variable-order spectral element method for incompressible viscous flow simulation

A new variable-order spectral element scheme is proposed in this work for the numerical solution of the steady incompressible Navier-Stokes equations in primitive variables. The spectral orders of polynomial expansion in each spatial direction for each element are specified by the user in advance. Next, an interface-nodes-replacement procedure is initialized to recover the conformity of the mesh. The interpolation functions are modified to accommodate the new sets of nodes. The present formulation does not require any interface iteration scheme; in addition, any complicated data structure is also avoided. Implementation of this strategy toward the existing spectral element framework is direct and simple. Additionally, the performance of the method is examined by many numerical experiments. Improved flexibility and efficiency of the accurate spectral element method make it a highly promising candidate for solving practical fluid dynamics problems.