We study central-upwind schemes for systems of hyperbolic conservation laws, recently introduced in [13]. Similarly to staggered non-oscillatory central schemes, these schemes are central Godunov-type projection-evolution methods that enjoy the advantages of high resolution, simplicity, universality and robustness. At the same time, the central-upwind framework allows one to decrease a relative...

Direct numerical simulation of transitional and turbulent hypersonic boundary layers using the Navier-Stokes equations requires high-order accurate numerical methods to resolve a wide range of time and length scales. Compact or explicit nite di erence methods used for such simulation have mainly been central di erence schemes containing only phase errors without any numerical dissipation. Centr...

1 Abstract. This paper examines a class of explicit nite-diierence advection schemes derived along the method of lines. An important application eld is large-scale atmospheric transport. The paper therefore focuses on the demand of positivity. For the spatial discretization, attention is connned to conservative schemes using 5 points per direction. The 4-th order central scheme and the family o...

Finite-volume central-upwind schemes for shallow water equations were proposed in [A. Kurganov and G. Petrova, Commun. Math. Sci., 5 (2007), 133–160]. These schemes are capable of maintaining “lake-at-rest” steady states and preserving the positivity of the computed water depth. The well-balanced and positivity preserving features of the central-upwind schemes are achieved, in particular, by us...

We introduce new Godunov-type semidiscrete central schemes for hyperbolic systems of conservation laws and Hamilton–Jacobi equations. The schemes are based on the use of more precise information about the local speeds of propagation and can be viewed as a generalization of the schemes from [A. Kurganov and E. Tadmor, J. Comput. Phys., 160 (2000), pp. 241–282; A. Kurganov and D. Levy, SIAM J. Sc...

Modeling transient CO2 two-phase flow in a pipe is essential studying depressurization mechanisms resulting from liquified accidental release. Generated data such models predict the released characteristics and possible propagating fractures. Accordingly, they provide valuable input for risk prevention designing safely operating transport pipelines. simulation involves fluid-mechanical thermody...

The present paper describes the use of various high-order schemes in a finite volume formulation for use on structured grids. In particular, WENO and compact upwind schemes as well as central and upwind schemes are investigated. Their efficiency and accuracy are compared to the well-established secondand third-order MUSCL family of schemes. The different schemes are analyzed and tested numerica...

Abstract The previous chapter has shown that the necessary numerical dissipation can be introduced in 1D CESE schemes through either a central or upwind approach.