Summary: A fifth order polynomic piecewise harmonic
method for hyperbolic conservation laws
In this paper a local Þfth order polynomic shock capturing method for hyper-
bolic conservation laws is presented. A comparation with the classical high order
methods is discussed also.
Essential Non-Oscillatory (ENO) methods, constructed by Harten, Osher, En-
gquist, and Chakravarthy are a class of high accuracy shock capturing numerical
methods for hyperbolic systems of conservation laws. These methods have been
applied in a great variety of compressible ßow problems.
Marquina introduced a new local third order accurate shock capturing method
(PHM), the main adventage of this method lies on the property that it is localer
than ENO and TVD upwind schemes of the same order, (and, thus, giving better
resolution of corners), because numerical ßuxes depend only on four variables.
In order to improve the accuracy of ENO methods, Shu and Osher developed
the WENO (weight ENO) methods.
Our methods are quiet similar to PHM method, but they are based on simpler
reconstructions (polynomic), thus they are local also. From the numerical exper-
iments, the method becomes efficient since it is low cost and it is not sensitive
to the Courant-Friedrichs-Lewy (CFL) number and the discretization parameter
unlike WENO and ENO methods. Moreover, it is stable and with lower viscosity