engleski

Polynomial weighted essentially non-oscillatory approximation

Weighted essentially non-oscillatory (WENO) approximation has been mainly used in numerical schemes for solving hyperbolic partial differential equations. The typical WENO procedure constructs a rational function for approximating values of the function v(x) on cell boundaries from its known cell averages. This approximation is essentially non-oscillatory and high order accurate for smooth enough functions v(x). However, the approximating rational function obtained by the classical WENO reconstruction contains poles. Therefore, if one needs to reconstruct the value of function v(x) in the interior of the numerical cell, the standard WENO procedure fails. In this paper we have developed a polynomial version of the WENO procedure that provides an elegant solution to this problem by constructing an approximating polynomial that is non-oscillatory and high order accurate not only at the cell boundaries but in the entire numerical cell. The proposed new algorithm is computationally comparable to the standard WENO procedure and gives the same reconstruction values on the the cell boundaries. The obtained numerical results show that the newly proposed procedure performs very well on the considered test examples.

WENO approximations; hyperbolic conservation laws; polynomial approximations

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