Virtual Grid Deformation for Hyperbolic Problems.

Kurzfassung

Transformation of the hyperbolic conservation laws into a time- dependent boundary-fitted coordinate system enables in particular the calculation of flows around any body which has time-dependent surfaces. Of particular interest is the implementation of the grid motion in the numerical algorithm. Extracted from the grid motion are those values which express the temporal changes of the metric terms. The extracted values are represented analytically as a function of the spatial coordinates of the computational domain and of time with regard to the time-dependent boundary conditions and are taken into account in the numerical solution algorithm at every time step. In this new method only the information of the moving grid required for the numerical algorithm is used. Detailed information on the geometric positions is not necessary. This is quite understandable: The basic equations are those of differential equations and the metric terms always appear as differentials. Since the time-dependentpositions of the grid points are not taken into account in the numerical algorithm, the grid motion can be regarded as virtual mapping. For this reason, the method is advantageous since the basic grid is always the same boundary-fitted grid of the initial steady state solution and the numerical algorithm is computationally time efficient and does not limit the quality of the solution.