A weak statement perturbation CFD algorithm with high-order phase accuracy for hyperbolic problems

• Published in: Computer methods in applied mechanics and engineering Vol. 131; no. 3; pp. 209 - 232
• Main Authors: Roy, Subrata, Baker, A.J.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 1996; Elsevier
• Subjects: Computational methods in fluid dynamics; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Physics; Finite element method; Perturbation method; Wave propagation; Modal analysis; Flow(fluid); Fluid-structure interactions; Fourier analysis; Taylor series; Galerkin method; Numerical method
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/0045-7825(95)00863-2

Achieving improved order of accuracy for any numerical method is a continuing quest. The discrete approximate solution error, in general, can be expressed as a truncation of a Taylor series expansion. Herein, we present a weak statement perturbation always yielding simple tridiagonal forms that can reduce, or annihilate in special cases, the Taylor series truncation error to high order. The procedure is analyzed via a von Neumann frequency analysis, and verification CFD solutions are reported in one and two dimensions. Finally, using the element specific (local) Courant number, a continuum (total) time integration procedure is derived that can directly produce a final time solution independent of mesh measure.