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

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.