6533b856fe1ef96bd12b24a2

RESEARCH PRODUCT

Afternotes on PHM: Harmonic ENO Methods

Antonio MarquinaSusana Serna

subject

Riemann hypothesissymbols.namesakeNonlinear systemConservation lawFourth orderHarmonic meanScalar (mathematics)symbolsPiecewiseApplied mathematicsReconstruction procedureMathematics

description

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]).

yearjournalcountryeditionlanguage
2003-01-01
https://doi.org/10.1007/978-3-642-55711-8_67