DoD Stabilization for non-linear hyperbolic conservation laws on cut cell meshes in one dimension
Loading...
Date
2021-07
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Alternative Title(s)
Abstract
In this work, we present the Domain of Dependence (DoD) stabilization for sys tems of hyperbolic conservation laws in one space dimension. The base scheme uses a
method of lines approach consisting of a discontinuous Galerkin scheme in space and
an explicit strong stability preserving Runge-Kutta scheme in time. When applied
on a cut cell mesh with a time step length that is appropriate for the size of the
larger background cells, one encounters stability issues. The DoD stabilization con sists of penalty terms that are designed to address these problems by redistributing
mass between the inflow and outflow neighbors of small cut cells in a physical way.
For piecewise constant polynomials in space and explicit Euler in time, the stabi lized scheme is monotone for scalar problems. For higher polynomial degrees p, our
numerical experiments show convergence orders of p + 1 for smooth flow and robust
behavior in the presence of shocks.