The paper describes the construction of entropy-stable discontinuous Galerkin difference (DGD) discretizations for hyperbolic conservation laws on unstructured grids. takes advantage existing theory (diagonal-norm) summation-by-parts (SBP) discretizations. In particular, shows how DGD — both linear and nonlinear can be constructed by defining SBP trial test functions in terms interpolated degre...

A new discretization method for hyperbolic systems with stiff relaxation source terms (hyperbolic-relaxation equations) is introduced. The method is based on Huynh’s “upwind moment scheme” for hyperbolic conservation laws with implicit treatment of the source term. A Von Neumann analysis shows superiority in both stability and accuracy of the resulting fully discrete scheme over the method-of-l...

Dafermos regularization is a viscous regularization of hyperbolic conservation laws that preserves solutions of the form u = û(X/T ). A RiemannDafermos solution is a solution of the Dafermos regularization that is close to a Riemann solution of the conservation law. Using self-similar coordinate x = X/T , Riemann-Dafermos solutions become stationary. In a suitable Banach space, we show that the...

A fourth-order accurate finite-volume method is presented for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Novel considerations for formulating the semi-discrete system of equations in computational space combined with detailed mechanisms for accommodating the adapting grids ensure that conservation is maintained a...

In this article we present a method to extend high order finite volume schemes to networks of hyperbolic conservation laws with algebraic coupling conditions. This method is based on an ADER approach in time to solve the generalized Riemann problem at the junction. Additionally to the high order accuracy, this approach maintains an exact conservation of quantities if stated by the coupling cond...

We consider an hyperbolic conservation law with discontinuous flux. Such partial differential equation arises in different applicative problems, in particular we are motivated by a model of traffic flow. We provide a new formulation in terms of Riemann Solvers. Moreover, we determine the class of Riemann Solvers which provide existence and uniqueness of the corresponding weak entropic solutions...