On conservation laws of Navier–Stokes Galerkin discretizations
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It is aimed in this work to construct discrete formulations that conserve as many physical laws as possible without utilizing a strong enforcement of the divergence constraint, and doing so leads to a new formulation that conserves each of energy, momentum, angular momentum, enstrophy in 2D, helicity and vorticity.Citations
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On the Navier-Stokes equations
TL;DR: In this paper, a criterion for the convergence of numerical solutions of Navier-Stokes equations in two dimensions under steady conditions is given, which applies to all cases, of steady viscous flow in 2D.
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Finite elements for scalar convection-dominated equations and incompressible flow problems: a never ending story?
TL;DR: Important recent results concerning finite element methods for convection-dominated problems and incompressible flow problems are described and a number of important open problems in these fields are discussed.
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Divergence-Free H(div)-FEM for Time-Dependent Incompressible Flows with Applications to High Reynolds Number Vortex Dynamics
Philipp W. Schroeder,Gert Lube +1 more
TL;DR: Focussing on dynamic high Reynolds number examples with vortical structures, the proposed H(div)-FEM method proves to be capable of reliably handling the planar lattice flow problem, Kelvin–Helmholtz instabilities and freely decaying two-dimensional turbulence.
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A low-dissipation finite element scheme for scale resolving simulations of turbulent flows
TL;DR: The conservative convective scheme proposed by Charnyi et al. (2017) is extended, allowing the use of finite element pairs that do not satisfy the inf-sup conditions, such as equal order interpolation for the velocity and pressure used in this work.
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Energy balance and mass conservation in reduced order models of fluid flows
TL;DR: This paper investigates theoretically and computationally the conservation properties of reduced order models (ROMs) for fluid flows and proposes a new approach, in which the snapshot average is replaced with the Stokes extension, which produces an accurate energy balance and mass conservation.
References
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Book
Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms
TL;DR: This paper presents the results of an analysis of the "Stream Function-Vorticity-Pressure" Method for the Stokes Problem in Two Dimensions and its applications to Mixed Approximation and Homogeneous Stokes Equations.
Book
Navier-Stokes Equations
TL;DR: Schiff's base dichloroacetamides having the formula OR2 PARALLEL HCCl2-C-N ANGLE R1 in which R1 is selected from the group consisting of alkenyl, alkyl, alkynyl and alkoxyalkyl; and R2 is selected by selecting R2 from the groups consisting of lower alkylimino, cyclohexenyl-1 and lower alkynyl substituted cycloenenyl -1 as discussed by the authors.
On the Navier-Stokes equations
TL;DR: In this paper, a criterion for the convergence of numerical solutions of Navier-Stokes equations in two dimensions under steady conditions is given, which applies to all cases, of steady viscous flow in 2D.
Journal ArticleDOI
A flexible inner-outer preconditioned GMRES algorithm
TL;DR: A variant of the GMRES algorithm is presented that allows changes in the preconditioning at every step, resulting in a result of the flexibility of the new variant that any iterative method can be used as a preconditionser.
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Computational Design for Long-Term Numerical Integration of the Equations of Fluid Motion
TL;DR: In this article, it was shown that the derived form of the finite difference Jacobian can prevent nonlinear computational instability and thereby permit long-term numerical integrations, which is not the case in finite difference analogues of the equation of motion for two-dimensional incompressible flow.