Undercompressive shocks for nonstrictly hyperbolic conservation laws

Undercompressive Shocks for a System of Hyperbolic Conservation Laws with Cubic Nonlinearity

RIEMANN PROBLEMS FOR NONSTRICTLY HYPERBOLIC 2x2 SYSTEMS OF CONSERVATION LAWS

The Riemann problem is solved for 2 x 2 systems of hyperbolic conservation laws having quadratic flux functions. Equations with quadratic flux functions arise from neglecting higher order nonlinear terms in hyperbolic systems that fail to be strictly hyperbolic everywhere. Such equations divide into four classes, three of which are considered in this paper. The solution of the Riemann problem i...

Undercompressive Shocks and Riemann Problems for Scalar Conservation Laws with Nonconvex Fluxes

The Riemann initial value problem is studied for scalar conservation laws whose uxes have a single innection point. For a regularization consisting of balanced diiusive and dispersive terms, the traveling wave criterion is used to select admissible shocks. In some cases, the Riemann problem solution contains an undercompressive shock. The analysis is illustrated by exploring parameter space for...

The comparison of two high-order semi-discrete central schemes for solving hyperbolic conservation laws

This work presents two high-order, semi-discrete, central-upwind schemes for computing approximate solutions of 1D systems of conservation laws. We propose a central weighted essentially non-oscillatory (CWENO) reconstruction, also we apply a fourth-order reconstruction proposed by Peer et al., and afterwards, we combine these reconstructions with a semi-discrete central-upwind numerical flux ...

Hyperbolic Systems of Conservation Laws

Conservation laws are first order systems of quasilinear partial differential equations in divergence form; they express the balance laws of continuum physics for media with "elastic" response, in which internal dissipation is neglected. The absence of internal dissipation is manifested in the emergence of solutions with jump discontinuities across manifolds of codimension one, representing, in...