On a linear stability issue of split form schemes for compressible flows
arXiv:2104.14941
Abstract
Split form schemes for Euler and Navier-Stokes equations are useful for computation of turbulent flows due to their better robustness. This is because they satisfy additional conservation properties of the governing equations like kinetic energy preservation leading to a reduction in aliasing errors at high orders. Recently, linear stability issues have been pointed out for these schemes for a density wave problem and we investigate this behaviour for some standard split forms. By deriving linearized equations of split form schemes, we show that most existing schemes do not satisfy a perturbation energy equation that holds at the continuous level. A simple modification to the energy flux of some existing schemes is shown to yield a scheme that is consistent with the energy perturbation equation. Numerical tests are given using a discontinuous Galerkin method to demonstrate these results.
References in corpus (8)
- Direct numerical simulation of turbulent channel flow up to
- Review of Summation-by-parts schemes for initial-boundary-value problems
- Split Form Nodal Discontinuous Galerkin Schemes with Summation-By-Parts Property for the Compressible Euler Equations
- Numerically stable formulations of convective terms for turbulent compressible flows
- A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations
- On the use of kinetic energy preserving DG-schemes for large eddy simulation
- On the robustness and performance of entropy stable discontinuous collocation methods for the compressible Navier-Stokes equations
- Impact of wall modeling on kinetic energy stability for the compressible Navier-Stokes equations