| Abstract: |
| We consider nonlinear hyperbolic systems of conservation laws endowed with a convex entropy pair and their
weak solutions depending upon small-scale parameters. We design numerical schemes for the approximation of these weak solutions, which may contain nonclassical shock waves driven by diffusive-dispersive effects. We
introduce a general class of schemes satisfying a discrete form of the system of diffusive-dispersive conservation laws, a discrete form of the associated entropy inequality, and which are consistent with a given system at
arbitrarily high-order accuracy. We investigate several hyperbolic models arising in continuum physics. We
perform numerical experiments
which demonstrate that the proposed schemes are robust and accurate and allow us to compute
entropy solutions containing nonclassical shock waves. |
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