Pressure-robust ALE space-time DG method for the Stokes equations on moving domains
Provides a theoretically sound and robust numerical method for incompressible flow simulations on moving domains, addressing the pressure-robustness issue in ALE formulations.
Proposed a pressure-robust space-time DG method for Stokes equations on moving domains, achieving pointwise divergence-free velocity and inf-sup stability with no mesh/time constraints. Numerical experiments confirm robustness at low viscosity for low-order time approximations.
We propose and analyze a space-time discontinuous Galerkin method for the incompressible Stokes equations on moving domains within the arbitrary Lagrangian-Eulerian setting. We use a contravariant Piola map in the definition of the discrete velocity space to preserve the pointwise divergence-free property on the discrete level. We show that the method is inf-sup stable, with no constraints on the spatial mesh or the time partition. We also establish a priori error estimates in the energy norm for arbitrary degrees of approximation in space and time. For piecewise-constant and piecewise-linear approximations in time, we show that the method is also robust at low viscosity regimes, and provide numerical evidence suggesting that this property extends to high-order cases as well. We present several numerical experiments to validate our theoretical findings.