A new family of projection schemes for the incompressible Navier–Stokes equations with control of high-frequency damping

Lovri?, A.; Dettmer, Wulf G.; Kadapa, Chennakesava; Peri?, Djordje

Abstract

A simple spatially discrete model problem consisting of mass points and dash-pots is presented which allows for the assessment of the properties of different projection schemes for the solution of the incompressible Navier–Stokes equations. In particular, the temporal accuracy, the stability and the numerical damping are investigated. The present study suggests that it is not possible to formulate a second order accurate projection/pressure-correction scheme which possesses any high-frequency damping. Motivated by this observation two new families of projection schemes are proposed which are developed from the generalised midpoint rule and from the generalised-alpha method, respectively, and offer control over high-frequency damping. Both schemes are investigated in detail on the basis of the model problem and subsequently implemented in the context of a finite element formulation for the incompressible Navier–Stokes equations. Comprehensive numerical studies of the flow in a lid-driven cavity and the flow around a cylinder are presented. The observations made are in agreement with the conclusions drawn from the model problem.

Citation

Lovrić, A., Dettmer, W. G., Kadapa, C., & Perić, D. (2018). A new family of projection schemes for the incompressible Navier–Stokes equations with control of high-frequency damping. Computer Methods in Applied Mechanics and Engineering, 339, 160-183. https://doi.org/10.1016/j.cma.2018.05.006

• Journal Article Type: Article
• Acceptance Date: May 7, 2018
• Online Publication Date: May 26, 2018
• Publication Date: 2018-09
• Deposit Date: Aug 29, 2022
• Journal: Computer Methods in Applied Mechanics and Engineering
• Print ISSN: 0045-7825
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 339
• Pages: 160-183
• DOI: https://doi.org/10.1016/j.cma.2018.05.006
• Keywords: Incompressible Navier–Stokes equations, Fractional step method, Projection method, Finite element method, Generalised-alpha method
• Public URL: http://researchrepository.napier.ac.uk/Output/2893893