2021/04/30 by Vikram Singh, Praveen Chandrashekar, Singh, Vikram +1 · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA) #cs.NA #math.NA #physics.comp-ph #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.2104.14941
arxiv created 2021/04/30 · openalex publication_date 2021/04/30 · arxiv updated 2021/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.