A new multiblock pressure-based finite element algorithm has been developed. This methodology implements quadratic interpolation for both the elemental velocity and pressure fields. A direct streamline upwinding scheme previously developed by the authors is used to model the non-linear inertia effects. Details of the algorithm and its multiblock foundation are provided along with validating test cases. The results presented clearly demonstrate the accuracy of this new approach and the differences in the pressure field for an element using quadratic versus the traditional bi linear approximation of the pressure field.
KEY WORDS Finite elements Multiblock Quadratic elements Equal-order
1. Introduction
Computational fluid dynamics (CFD) algorithms often challenge the CPU/memory limitations of even the most capable supercomputers existing today. The large problem size commonly associated with this type of analysis is principally attributed to the accuracy of the algorithm, the physics of the flow being modelled and the complexity of the flow path geometry. For the same problem a first-order algorithm requires a comparatively more dense computational grid than, say, a third-order scheme to capture the same characteristics of the flow field. Complex flows involving shock waves, multiple shear layers a n d or turbulence require a finer grid to resolve the steep gradients in the flow variables. The size of the computational model in terms of element and node counts will also increase with increasing complexity of the flow field. For general flow domains with complex surface geometry more points are needed to accurately represent the shape of the domain boundary segments. All these situations give rise to the need for better CFD algorithms. These algorithms should attempt to reduce the use of computer resources such as in-core memory while increasing the accuracy of the algorithm and the capability to solve larger problems.
The primitive variable segregated approach is a conceptually attractive algorithm for subsonic flows. The basic idea of this algorithm is to sequentially solve for the velocity and pressure on either staggered or non-staggered grids. In this case the intermediate velocity (u*) is determined from the momentum equations, and the pressure (p) or pressure correction variable 07') is calculated from an * Formerly with Pratt & Whitney Aircraft, West Palm Beach, FL, U.S.A.