A Geometric Approach to High Resolution TVD Schemes | Zendy

Jonathan Goodman | Zendy; Randall J. LeVeque | Zendy

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A Geometric Approach to High Resolution TVD Schemes

Author(s) -

Jonathan Goodman,

Randall J. LeVeque

Publication year - 1988

Publication title -

siam journal on numerical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.78

H-Index - 134

eISSN - 1095-7170

pISSN - 0036-1429

DOI - 10.1137/0725019

Subject(s) - conservation law , godunov's scheme , mathematics , rarefaction (ecology) , total variation diminishing , scalar (mathematics) , entropy (arrow of time) , mathematical analysis , numerical analysis , geometry , physics , ecology , quantum mechanics , species diversity , biology

We use a geometric approach, similar to van Leer's MUSCL schemes, to construct a second- order accurate generalization of Godunov's method for solving scalar conservation laws. By making suitable approximations we obtain a scheme which is easy to implement and total variation diminishing. We also investigate the entropy condition from the standpoint of the spreading of rarefaction waves. For Godunov's method we obtain quantitative information on the rate of spreading which explains the kinks in rarefaction waves often observed at the sonic point.

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