Simulation of one-dimensional Euler-flow by means of multidimensional wave digital filters

Multidimensional Wave Digital Filters (MDWDF) are used for the integration of partial differential equations (PDE). A new approach based on the integration of systems of conservation laws is presented. For each conservation law a separate lossless Kirchhoff network is used as reference circuit for the derivation of the MDWDF. In each network the energy stored in the network represents the property that is conserved by the corresponding conservation law. The networks do not exchange stored energy. Nevertheless, the networks are coupled because they all are described by the same variables. This approach is used for the integration of the one-dimensional Euler-equations, describing inviscid, non-heatconducting flow. Simulation results are presented, showing that this approach leads to correct shock speeds and shock intensities in the well known shock-tube problem