Nonconforming formulations with spectral element methods

Abstract

A spectral element algorithm for solution of the incompressible Navier-Stokes and heat transfer equations is developed, with an emphasis on extending the classical conforming Galerkin formulations to nonconforming spectral elements. The new algorithm employs both the Constrained Approximation Method (CAM), and the Mortar Element Method (MEM) for p-and h-type nonconforming elements. Detailed descriptions, and formulation steps for both methods, as well as the performance comparisons between CAM and MEM, are presented. This study fills an important gap in the literature by providing a detailed explanation for treatment of p-and h-type nonconforming interfaces. A comparative eigenvalue spectrum analysis of diffusion and convection operators is provided for CAM and MEM. Effects of consistency errors due to the nonconforming formulations on the convergence of steady and time dependent problems are studied in detail. Incompressible flow solvers that can utilize these nonconforming formulations on both p- and h-type nonconforming grids are developed and validated. Engineering use of the developed solvers are demonstrated by detailed parametric analyses of oscillatory flow forced convection heat transfer in two-dimensional channels.