TY - JOUR

T1 - A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I

T2 - Periodic domains

AU - Zhang, Yi

AU - Palha, Artur

AU - Gerritsma, Marc

AU - Rebholz, Leo G.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - de Rham complex

KW - Helicity conservation

KW - Kinetic energy conservation

KW - Mass conservation

KW - Mimetic discretization

KW - Navier-Stokes equations

UR - http://www.scopus.com/inward/record.url?scp=85121810949&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2021.110868

DO - 10.1016/j.jcp.2021.110868

M3 - Article

AN - SCOPUS:85121810949

VL - 451

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

M1 - 110868

ER -