Search
Results
-
The Method of Transport for solving the Euler-equations
(1995)SAM Research ReportIn many technical applications it is necessary to compute a numerical solution of complex flow problems in several space dimensions. Most available codes split the multi-dimensional problem into several one-dimension\-al ones. Those are aligned with the cell interfaces of the underlying grid. In some of the applications, e.g.high Mach number flow, this approach does not work very well, since the physical properties of the model equations ...Report -
Decomposition of the multidimensional Euler equations into advection equations
(1995)SAM Research ReportBased on a genuine multi-dimensional numerical scheme, called Method of Transport, we derive a form of the compressible Euler-equations, capable of a linearization for any space dimension. This form allows a rigorous error analysis of the linearization error without the knowledge of the numerical method. The generated error can be eliminated by special correction terms in the linear equations. Hence, existing scalar high order methods can ...Report -
Multidimensional schemes for nonlinear systems of hyperbolic conservation laws
(1995)SAM Research ReportMost commonly used schemes for unsteady multidimensional systems of hyperbolic conservation laws use dimensional splitting. In each coordinate direction a scheme for a one dimensional system is used. Such an approach does not take in account the infinitely many propagation directions which are present in a system in several space dimensions. In 1992 M. Fey introduced what he called the Method of Transport, MoT, for the Euler equations of ...Report -
Multidimensional method of transport for the shallow water equations
(1995)SAM Research ReportA truly two-dimensional scheme based on a finite volume discretization on structured meshes will be developed for solving the shallow water equations. The idea of the method of transport, developed by M. Fey for the compressible Euler equations [6], is modified for our case. In contrast to this, the flux of the shallow water equations is not homogeneous. Hence, the eigenvectors of the Jacobi matrix of the flux can not be used to decompose ...Report