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Standard numerical methods for hyperbolic PDEs require for stability aCFL-condition which implies that the time step size depends on the size of theelements of the mesh. On cut-cell meshes, elements can become arbitrarily smalland thus the time step size cannot take the size of small cut-cells intoaccount but has to be chosen based on the background mesh elements. A remedyfor this is the so called DoD (domain of dependence) stabilization for whichseveral favorable theoretical and numerical properties have been shown in oneand two space dimensions. Up to now the method is restricted to stabilizationof cut-cells with exactly one inflow and one outflow face, i.e. triangularcut-cells with a no-flow face. We extend the DoD stabilization to cut-cellswith multiple in- and out-flow faces by properly considering the flowdistribution inside the cut-cell. We further prove L2-stability for thesemi-discrete formulation in space and present numerical results to validatethe proposed extension.

DoD Stabilization of linear hyperbolic PDEs on general cut-cell meshes