Data Bounded Polynomials and Preserving Positivity in High Order ENO and WENO Methods
نویسنده
چکیده
The positivity and accuracy properties of the widely used ENO and WENO methods are considered by undertaking an analysis based upon data-bounded polynomial methods. The positivity preserving approach of Berzins based upon data-bounded polynomial interpolants is generalized to arbitrary meshes. This makes it possible to prove positivity conditions for ENO Methods by using a derivation based on such bounded polynomial approximations. Numerical examples are used to show that although high order methods may be used in a way that preserves positivity, care must be taken in terms of resolving shock-like features with a fine enough mesh for high-order approximations to be effective. SCI Report UUSCI-2009-003 Data Bounded Polynomials and Preserving Positivity in High Order ENO and WENO Methods M. Berzins* July 24, 2009 Abstract The positivity and accuracy properties of the widely used ENO and WENO methods are considered by undertaking an analysis based upon data-bounded polynomial methods. The positivity preserving approach of Berzins based upon data-bounded polynomial interpolants is generalized to arbitrary meshes. This makes it possible to prove positivity conditions for ENO Methods by using a derivation based on such bounded polynomial approximations. Numerical examples are used to show that although high order methods may be used in a way that preserves positivity, care must be taken in terms of resolving shock-like features with a fine enough mesh for high-order approximations to be effective.The positivity and accuracy properties of the widely used ENO and WENO methods are considered by undertaking an analysis based upon data-bounded polynomial methods. The positivity preserving approach of Berzins based upon data-bounded polynomial interpolants is generalized to arbitrary meshes. This makes it possible to prove positivity conditions for ENO Methods by using a derivation based on such bounded polynomial approximations. Numerical examples are used to show that although high order methods may be used in a way that preserves positivity, care must be taken in terms of resolving shock-like features with a fine enough mesh for high-order approximations to be effective.
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