The Derivative Riemann Problem: The basis for high order ADER Schemes

The corner stone of arbitrary high order schemes (ADER schemes) is the solution of the derivative Riemann problem at the element interfaces, a generalization of the classical Riemann problem first used by Godunov in 1959 to construct a first-order upwind numerical method for hyperbolic systems. The derivative Riemann problem extends the possible...

Development and application of generalized MUSTA schemes

Numerical methods for solving non-linear systems of hyperbolic conservation laws via finite volume methods or discontinuous Galerkin finite element methods require, as the building block, a monotone numerical flux. The simplest approach for providing a monotone numerical utilizes a symmetric stencil and does not explicitly make use of wave...

Force scheme applied to flux reconstruction in the numerical simulation of nonlinear acoustic problems

Nonlinear acoustic waves have many applications in very different fields of industry. The problem considered in this work consists of predicting the behaviour of gas filling a one dimensional tube when suffering the action of very high frequency waves. The numerical technique applied to solve this problem is a third order finite volume method...

Godunov schemes for compressible multiphase flows

Compressible multiphase models have been studied for a long time inspired on different applications in diverse engineering areas. Solutions for these equations are not simple and researcher have spent much time trying to bring answers. The possibility to properly solve these equations and perform real simulations represent a very ambitious goal....

ADER schemes for hyperbolic conservation laws with reactive terms

In this paper we generalizew the semi-analytical method16 for solving the Derivative Riemann Problem to hyperbolic systems for which the Riemann problem solution is not available. As an application example we implement the new derivative Riemann solver in the high-order finite-volume ADER advection schemes. We provide numerical examples for two...

ADER scheme for the shallow water equations in channel with irregular bottom elevation

In this paper we develop one dimensional non-linear ADER schemes for the shallow water system with source terms. In contrast to conventional schemes we adopt a formulation given in terms of the free surface elevation and water discharge. Data reconstruction is performed using ENO polynomials both for the conservative variables and for the bottom...