Linearly implicit peer methods for the compressible Euler equations

When cut cells are used for the representation of orography this leads to very small cells. For explicit methods this results in very harsh time step restrictions due to the CFL criterion. Therefore we consider linearly implicit peer methods for the integration of the compressible Euler equations. To be more efficient we use a simplified Jacobian. We present a linear stability theory which takes the effects of this simplified Jacobian in account. The developed second-order two-stage peer method is A-stable not only in the common sense but also when using the simplified Jacobian and retains the order independently of the Jacobian. In numerical tests the presented method produces good results even with time steps 100 times larger than explicit schemes could stably use.