Finite Volume Methods for Nonconservative Hyperbolic Systems: Application to Shallow-Flows
Abstract
In this work, a theoretical framework allowing to extend some
general concepts related to the numerical approximation of 1d
conservation laws to the more general case of first order
quasi-linear hyperbolic systems is presented. This framework is
intended to be useful for the design and the analysis of
well-balanced numerical schemes for solving balance laws or
coupled systems of conservation laws. The concept of
path-conservative numerical scheme is introduced and some
examples of Approximate Riemann Solvers are provided as well as a
general form of a high order scheme. Finally, some numerical
simulations concerning shallow-flows
will be presented.
[DOI: 10.1685 / CSC06042] About DOI
general concepts related to the numerical approximation of 1d
conservation laws to the more general case of first order
quasi-linear hyperbolic systems is presented. This framework is
intended to be useful for the design and the analysis of
well-balanced numerical schemes for solving balance laws or
coupled systems of conservation laws. The concept of
path-conservative numerical scheme is introduced and some
examples of Approximate Riemann Solvers are provided as well as a
general form of a high order scheme. Finally, some numerical
simulations concerning shallow-flows
will be presented.
[DOI: 10.1685 / CSC06042] About DOI
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PDFDOI: https://doi.org/10.1685/
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