## Explicit Finite Volume Schemes of Arbitrary High Order of Accuracy for Hyperbolic Systems with Stiff Source Terms (2007)

### BibTeX

@MISC{Dumbser07explicitfinite,

author = {Michael Dumbser and et al.},

title = {Explicit Finite Volume Schemes of Arbitrary High Order of Accuracy for Hyperbolic Systems with Stiff Source Terms},

year = {2007}

}

### OpenURL

### Abstract

In this article we propose a new class of finite volume schemes of arbitrary accuracy in space and time for systems of hyperbolic balance laws with stiff source terms. The new class of schemes is based on a three stage procedure. First, in order to achieve high order accuracy in space, a nonlinear weighted essentially non-oscillatory reconstruction procedure is applied to the cell averages at the current time level. Second, the temporal evolution of the resulting reconstruction polynomials is computed locally inside each cell exploiting directly the full system of governing equations. In previous ADER schemes, this was achieved via the Cauchy-Kovalewski procedure, where the governing equation is repeatedly differentiated with respect to space and time to construct a Taylor series expansion of the local solution. As the Cauchy-Kovalewski procedure is based on Taylor series expansions, it is not able to handle systems with stiff source terms since the Taylor series diverges for this case. Therefore, in this article, we present a new strategy that replaces the Cauchy-Kovalewski procedure for high order time interpolation: we present a special local space-time