Topic
Navier–Stokes equations
About: Navier–Stokes equations is a research topic. Over the lifetime, 18180 publications have been published within this topic receiving 552555 citations. The topic is also known as: Navier-Stokes equations.
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TL;DR: The newly developed unifying discontinuous formulation named the correction pro- cedure via reconstruction (CPR) for conservation laws is extended to solve the Navier-Stokes equations for 3D mixed grids to demonstrate its performance.
Abstract: The newly developed unifying discontinuous formulation named the correction pro- cedure via reconstruction (CPR) for conservation laws is extended to solve the Navier-Stokes equations for 3D mixed grids. In the current development, tetrahedrons and triangular prisms are considered. The CPR method can unify several popular high order methods including the dis- continuous Galerkin and the spectral volume methods into a more efficient differential form. By selecting the solution points to coincide with the flux points, solution reconstruction can be com- pletely avoided. Accuracy studies confirmed that the optimal order of accuracy can be achieved with the method. Several benchmark test cases are computed by solving the Euler and compress- ible Navier-Stokes equations to demonstrate its performance.
114 citations
TL;DR: In this article, two different models for the evolution of incompressible binary fluid mixtures in a three-dimensional bounded domain are considered and the existence of the trajectory attractor for both systems is proved.
Abstract: Two different models for the evolution of incompressible binary fluid mixtures in a three-dimensional bounded domain are considered. They consist of the 3D incompressible Navier-Stokes equations, subject to time-dependent external forces and coupled with either a convective Allen-Cahn or Cahn-Hilliard equation. Such systems can be viewed as generalizations of the Navier-Stokes equations to two-phase fluids. Using the trajectory approach, the authors prove the existence of the trajectory attractor for both systems.
114 citations
TL;DR: In this article, a two-and a three-level finite element method for numerical simulation of incompressible flow governed by the Navier-Stokes equations is presented, where the resolution of the large and small scales takes place on levels 1 and 2 with the aid of diverse approaches and the dynamic calculation of a subgrid viscosity representing the effect of the unresolved scales constitutes level 3 of the algorithm.
113 citations
TL;DR: 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.
113 citations
TL;DR: This paper considers the stability and convergence results for the Euler implicit/explicit scheme applied to the spatially discretized two-dimensional (2D) time-dependent Navier-Stokes equations and provides the H 2 -stability of the scheme under the stability condition.
Abstract: This paper considers the stability and convergence results for the Euler implicit/explicit scheme applied to the spatially discretized two-dimensional (2D) time-dependent Navier-Stokes equations. A Galerkin finite element spatial discretization is assumed, and the temporal treatment is implicit/explict scheme, which is implicit for the linear terms and explicit for the nonlinear term. Here the stability condition depends on the smoothness of the initial data u 0 ∈ H α , i.e., the time step condition is τ < C 0 in the case of a = 2, τ| log h| ≤ C 0 in the case of a = 1 and Th -2 ≤ C 0 in the case of a = 0 for mesh size h and some positive constant C 0 . We provide the H 2 -stability of the scheme under the stability condition with a = 0,1, 2 and obtain the optimal H 1 - L 2 error estimate of the numerical velocity and the optimal L 2 error estimate of the numerical pressure under the stability condition with a = 1, 2.
113 citations