This chapter discusses the spatially periodic case of the incompressible Navier-Stokes equations. All functions in the spatially periodic case in two dimensions are assumed to be real, C-smooth and 2蟺-periodic
In summary, the contributions of this paper are firstly, the introduction of two reduced stress–velocity least-squares formulations for the incompressible Navier–Stokes equations, which are based on the well-known SVP formulation. Secondly, a low- and a high-order discretization of the solution ...
In this paper the incompressible Navier-Stokes equations are discretized by the finite element method. After linearization large, sparse systems of linear equations have to be solved. A well known problem is the occurrence of zero elements on the main diagonal. We describe ordering techniques of ...
There have been several efforts to Physics-informed neural networks (PINNs) in the solution of the incompressible Navier-Stokes fluid. The loss function in PINNs is a weighted sum of multiple terms, including the mismatch in the observed velocity and pressure data, the boundary and initial constra...
1.1The free boundary problem of the Navier–Stokes system We consider the initial boundary value problem of the incompressible Navier–Stokes equations with free boundary condition. Letbe a domain that is occupied by the fluid in then-dimensional Euclidean spacewithand let the initial domain be desc...
北京大学 Peking University The incompressible Navier-Stokes equations with vacuum讲座论坛 02017-10-17 16:00 理科1号楼1114主讲人 Raphael Danchin 主讲人介绍 Universite Paris-Est0 条评论查看学校相关机会 北京大学 Peking University 查看专业相关机会 数学 想看更多 查看同类型机会 查看所有机会...
We present a hybridizable discontinuous Galerkin method for the numerical solution the incompressible Navier-Stokes equations. The method is devised by using the discontinuous Galerkin approximation with a special choice of the numerical traces and a fully implicit time-stepping method for temporal discre...
In the framework of the incompressible Navier-Stokes equations in dimension 2, we dealt in 3] with linear transport with values in Sobolev spaces. Since the proof of Theorem 4 involves the very same methods as those used in 3] and 2], we state it without proof. Theorem 4 Under the ...
Aortic blood flow simulations were performed using Sierra/Fuego. The incompressible Navier–Stokes equations were solved using a Newtonian constitutive model with dynamic viscosityμ = 0.003 kg ⋅ m−1 ⋅ s−1and blood densityρ = 1060 kg ⋅ m−3 63. No...
In this paper, an implicit fractional-step method for numerical solutions of the incompressible Navier–Stokes equations is studied. The time advancement is decomposed into a sequence of two steps, and the first step can be seen as a linear elliptic problem; on the other hand, the second step...