A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains

Yi Zhang*, Artur Palha, Marc Gerritsma, Leo G. Rebholz

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

We introduce a mimetic dual-field discretization which conserves mass, kinetic energy and helicity for three-dimensional incompressible Navier-Stokes equations. The discretization makes use of a conservative dual-field mixed weak formulation where two evolution equations of velocity are employed and dual representations of the solution are sought for each variable. A temporal discretization, which staggers the evolution equations and handles the nonlinearity such that the resulting discrete algebraic systems are linear and decoupled, is constructed. The spatial discretization is mimetic in the sense that the finite dimensional function spaces form a discrete de Rham complex. Conservation of mass, kinetic energy and helicity in the absence of dissipative terms is proven at the discrete level. Proper dissipation rates of kinetic energy and helicity in the viscous case are also proven. Numerical tests supporting the method are provided.

Original languageEnglish
Article number110868
Number of pages23
JournalJournal of Computational Physics
Volume451
DOIs
Publication statusPublished - 2022

Keywords

  • de Rham complex
  • Helicity conservation
  • Kinetic energy conservation
  • Mass conservation
  • Mimetic discretization
  • Navier-Stokes equations

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