Error analysis of a pressure correction method with explicit time stepping
<|reference_start|>Error analysis of a pressure correction method with explicit time stepping: The pressure-correction method is a well established approach for simulating unsteady, incompressible fluids. It is well-known that implicit discretization of the time derivative in the momentum equation e.g. using a backward differentiation formula with explicit handling of the nonlinear term results in a conditionally stable method. In certain scenarios, employing explicit time integration in the momentum equation can be advantageous, as it avoids the need to solve for a system matrix involving each differential operator. Additionally, we will demonstrate that the fully discrete method can be expressed in the form of simple matrix-vector multiplications allowing for efficient implementation on modern and highly parallel acceleration hardware.   Despite being a common practice in various commercial codes, there is currently no available literature on error analysis for this scenario. In this work, we conduct a theoretical analysis of both implicit and two explicit variants of the pressure-correction method in a fully discrete setting. We demonstrate to which extend the presented implicit and explicit methods exhibit conditional stability. Furthermore, we establish a Courant-Friedrichs-Lewy (CFL) type condition for the explicit scheme and show that the explicit variant demonstrate the same asymptotic behavior as the implicit variant when the CFL condition is satisfied.<|reference_end|>
@article{kaya2024error,
    title={Error analysis of a pressure correction method with explicit time
  stepping},
    author={Utku Kaya and Thomas Richter},
    journal={arXiv preprint arXiv:2407.11159},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.11159},
    primaryClass={math.NA cs.NA}
}