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

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

Zhang, Y. (TU Delft Computational Design and Mechanics)
Palha da Silva Clérigo, A. (TU Delft Aerodynamics)
Gerritsma, M.I. (TU Delft Aerodynamics)
Rebholz, Leo G. (Clemson University)

2022

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.

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

http://resolver.tudelft.nl/uuid:365b262d-347d-4e0f-b786-0358f5f09763

https://doi.org/10.1016/j.jcp.2021.110868

0021-9991

Journal of Computational Physics, 451

Institutional Repository

journal article

© 2022 Y. Zhang, A. Palha da Silva Clérigo, M.I. Gerritsma, Leo G. Rebholz