Higher order upwind schemes on unstructured grids for the compressible Euler equations in time-dependent geometries in 3D

We present a numerical algorithm to solve the nonstationary three-dimensional compressible Euler equations in complex timedependent geometries. This algorithm is an upwind finite volume method working on an unstructured grid. Such kinds of grids allow a big flexibility in approximating complex three-dimensional geometries. Furthermore local adaption of the grid to nonstationary flow phenomena (shocks, steep gradients, vortices) and singularities can be used without additional effort in the numerical scheme. Another possibility to achieve high resolution of flow phenomena is to use a numerical scheme of higher order in space. I shall present a new cell-centered finite volume scheme of second order in space working on a grid of simplices. This approach is motivated by a theoretical result of convergence in the case of scalar conservation laws in two space dimensions. Tests with this approach show that this really is of higher order for problems with smooth solutions and the new limiter function avoid oscillations at discontinuities. For the local adaption of the grid a criterion is necessary which controlls the fineness of the grid according to the numerical error of the numerical scheme. In contrast to elliptic or parabolic problems no a-posteriori error estimator is available for the system of the Euler equations. An approach based on the residual is well motivated for scalar conservation laws in 1D with a result of Tadmor. Therefore an interpretation of the residual approach for the system of the Euler equation will be discussed. The combination of solving conservation laws and moving boundaries of the geometry demands a numerical scheme which guarantees the conservation. A new approach to fulfill that for a finite volume scheme working on simplices will be presented. The presented algorithm has been applied to calculate the flow in model cylinder of a two-stroke engine with a moving piston. (orig.)Available from TIB Hannover: RO 5389(393) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Objektorientierte Programmentwicklung mit einheitlicher Graphikschnittstelle

SIGLEAvailable from TIB Hannover: RO 7837(8) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman