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Improved non‐staggered central NT schemes for balance laws with geometrical source terms
Author(s) -
ČrnjarićŽic N.,
Vuković S.,
Sopta L.
Publication year - 2004
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.790
Subject(s) - discretization , pointwise , mathematics , term (time) , scheme (mathematics) , mathematical analysis , law , physics , quantum mechanics , political science
In this paper we extend the non‐staggered version of the central NT (Nessyahu–Tadmor) scheme to the balance laws with geometrical source term. This extension is based on the source term evaluation that includes balancing between the flux gradient and the source term with an additional reformulation that depends on the source term discretization. The main property of the scheme obtained by the proposed reformulation is preservation of the particular set of the steady‐state solutions. We verify the improved scheme on two types of balance laws with geometrical source term: the shallow water equations and the non‐homogeneous Burger's equation. The presented results show good behaviour of the considered scheme when compared with the analytical or numerical results obtained by using other numerical schemes. Furthermore, comparison with the numerical results obtained by the classical central NT scheme where the source term is simply pointwise evaluated shows that the proposed reformulations are essential. Copyright © 2004 John Wiley & Sons, Ltd.