Upwind Difference Schemes for Hyperbolic Systems of Conservation Laws
نویسندگان
چکیده
منابع مشابه
Adaptive Semidiscrete Central-Upwind Schemes for Nonconvex Hyperbolic Conservation Laws
We discover that the choice of a piecewise polynomial reconstruction is crucial in computing solutions of nonconvex hyperbolic (systems of) conservation laws. Using semi-discrete central-upwind schemes we illustrate that the obtained numerical approximations may fail to converge to the unique entropy solution or the convergence may be so slow that achieving a proper resolution would require the...
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We study central-upwind schemes for systems of hyperbolic conservation laws, recently introduced in [A. Kurganov, S. Noelle and G. Petrova, SIAM J. Sci. Comput., 23 (2001), pp. 707–740]. Similarly to the staggered central schemes, these schemes are central Godunov-type projection-evolution methods that enjoy the advantages of high resolution, simplicity, universality, and robustness. At the sam...
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We present a class of second-order conservative finite difference algorithms for solving numerically time-dependent problems for hyperbolic conservation laws in several space variables. These methods are upwind and multidimensional, in that the numerical fluxes are obtained by solving the characteristic form of the full multidimensional equations at the zone edge, and that all fluxes are evalua...
متن کاملCentral-Upwind Schemes on Triangular Grids for Hyperbolic Systems of Conservation Laws
We present a family of central-upwind schemes on general triangular grids for solving two-dimensional systems of conservation laws. The new schemes enjoy the main advantages of the Godunov-type central schemes—simplicity, universality, and robustness and can be applied to problems with complicated geometries. The “triangular” central-upwind schemes are based on the use of the directional local ...
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A finite compact (FC) difference scheme requiring only bi-diagonal matrix inversion is proposed by using the known high-resolution flux. Introducing TVD or ENO limiters in the numerical flux, several high-resolution FC-schemes of hyperbolic conservation law are developed, including the FC-TVD, third-order FC-ENO and fifth-order FC-ENO schemes. Boundary conditions formulated need only one unknow...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1982
ISSN: 0025-5718
DOI: 10.2307/2007275