Search results for "35L60"
showing 2 items of 2 documents
Partially implicit Runge-Kutta methods for wave-like equations
2012
In this work we present a new class of Runge-Kutta (RK) methods for solving systems of hyperbolic equations with a particular structure, generalization of a wave-equation. The new methods are {\it partially implicit} in the sense that a proper subset of the equations of the system contains some terms which are treated implicitly. These methods can be viewed as a particular case of the implicit-explicit (IMEX) RK methods for systems of equations with wave-like structure. For these systems, the optimal methods with the new structure are easier to derive than the IMEX ones, specially when aiming at higher-order (up to fourth-order in this work). The methods are constructed considering the clas…
On the convexity of relativistic ideal magnetohydrodynamics
2015
We analyze the influence of the magnetic field in the convexity properties of the relativistic magnetohydrodynamics system of equations. To this purpose we use the approach of Lax, based on the analysis of the linearly degenerate/genuinely non-linear nature of the characteristic fields. Degenerate and non-degenerate states are discussed separately and the non-relativistic, unmagnetized limits are properly recovered. The characteristic fields corresponding to the material and Alfv\'en waves are linearly degenerate and, then, not affected by the convexity issue. The analysis of the characteristic fields associated with the magnetosonic waves reveals, however, a dependence of the convexity con…