On the utility of finite element theory for computational fluid dynamicsAn implicit finite element numerical solution algorithm is derived for the compressible Navier-Stokes equations expressed in generalized coordinates. The theoretical basis utilizes a Galerkin-Weighted Residuals formulation, and extremization of approximation error within the context of a multipole expansion. A von Neumann analysis for a simplified form indicates the algorithm fourth- to sixth-order phase accurate, with third-order dissipation for the elementary linear element construction. Performance is improved for the algorithm constructed using quadratic interpolation. Numerical experiments for shocked duct flows are employed to optimize the several algorithm parameters. Additional numerical solutions validate algorithm accuracy and utility for aerodynamics applications.
Document ID
19810053154
Acquisition Source
Legacy CDMS
Document Type
Conference Proceedings
Authors
Baker, A. J. (Tennessee Univ. Knoxville, TN, United States)
Soliman, M. O. (Tennessee, University Knoxville, Tenn., United States)