Improved non-staggered central NT schemes for balance laws

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Abstract

In this paper we extend the nonstaggered version of the central NT(Nessyahu-Tadmor) scheme to the balanced 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 formulation that depends on the source term discretization. The main property of the scheme obtained by the proposed reformulation is preserving of the particular set of the steady-state solutions. We verify our scheme on two types of balanced laws with geometrical source term: shallow-water equations and nonhomogeneous Burger's equation. The presented results show good behaviour when compared with the analytical or numerical results obtained by using other numerical schemes in the considered problems. Furthermore, comparison with the numerical results obtained by the classical central NT scheme where the source term is pointwise

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