Afternotes on PHM: Harmonic ENO Methods

Antonio Marquina () and Susana Serna ()
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Antonio Marquina: Universitat de València, Departamento de Matemática Aplicada
Susana Serna: Universitat de València, Departamento de Matemática Aplicada

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2003, pp 717-725 from Springer

Abstract: Abstract PHM methods have been used successfully as reconstruction procedures to design high-order Riemann solvers for nonlinear scalar and systems of conservation laws, (see [8], [1], [4]). We introduce a new class of polynomial reconstruction procedures based on the harmonic mean of the absolute values of finite diferences used as difference-limiter, following the original idea used before to design the piecewise hyperbolic method, introduced in [8]. We call those methods ’harmonic ENO methods’, (HENO). Furthermore, we give analytical and numerical evidence of the good behavior of these methods used as reconstruction procedures for the numerical approximation by means of shock-capturing methods for scalar and systems of conservation laws in ID. We discuss, in particular, the behavior of a fourth order harmonic ENO method,(HEN04 in short), compared with PHM, EN03 and WEN05 methods, (see [2], [10], [3]).

Keywords: Reconstruction Procedure; Local Extremum; Smooth Region; Cell Interface; Total Variation Diminish (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55711-8_67

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DOI: 10.1007/978-3-642-55711-8_67

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