Search
Results
-
The method of transport for nonlinear systems of hyperbolic conservation laws in several space dimensions
(1997)SAM Research ReportThe idea of the method of transport is introduced by means of non-linear conservation laws. The systems are rewritten in an advection form accounting for the characteristic propagation directions. A straightforward linearization of this advection form leads to a genuinely multi-dimensional method. Approximations using infinitely many or a finite number of propagation directions are shown.Report -
Error Estimators for the Position of Discontinuities in Hyperbolic Conservation Laws with Source Terms which are solved using Operator Splitting
(1997)SAM Research ReportWhen computing numerical solutions of hyperbolic conservation laws with source terms, one may obtain spurious solutions --- these are unphysical solutions that only occur in numerics such as shock waves moving with wrong speeds, cf. [7], [2], [1], [10], [3]. Therefore it is important to know how errors of the location of a discontinuity can be controlled. To derive appropriate error-estimates and to use them to control such errors, is the ...Report -
An Accuracy Barrier for Stable Three-Time-Level DifferenceSchemes for Hyperbolic Equations
(1997)SAM Research ReportWe consider three-time-level difference schemes for the linear constant coefficient advection equation $u_t$ = $cu_x$. In 1985 it was conjectured that the varrier to the local order $p$ of schemes which are stable is giben by $p \le $2 min {$R$,$S$}. Here $R$ and $S$ denote the number of downwind and upwind points, respectively, in the difference stencil with respect to the characteristic of the differential equation through the update ...Report