Achieving improved CFD accuracy for hyperbolic problems via matrix perturbation

Improving the order of accuracy for any numerical method remains a continuing quest. For a large class of computational uid dynamics (CFD) problems, the discrete approximate solution error is viewed as truncation of a Taylor series expansion. In this paper, a weak statement Galerkin matrix perturbation (GMP) method is utilized yielding simple tridiagonal forms that reduce, or annihilate in special cases, the Taylor series truncation error. The procedure is analyzed via a von Neumann frequency analysis and can be theoretically compared with a wide class of algorithms, e.g. Taylor Weak Statement (TWS) and compact nite diierence schemes on a term by term basis. Veriication hyperbolic solution is given for a smooth and non-smooth wave cluster propagation using a combination algorithm of GMP and TWS.