We aim to derive the incompressible Navier–Stokes equations from classical mechanics. We define Lagrange and Euler coordinates and the mass density within the framework of measure theory. This yields a mathematical statement that expresses the mass conservation principle, which allows to derive the ...
Navier-Stokes equationslock-invortex sheddingThe authors propose combination of the coupled method and the extrapolation method as a numerical technique suitable for calculation of an incompressible flow on a massively parallel computer. In the coupled method, the momentum equations and the continuity ...
Thanks to the underlying theory of Clebsch velocity decomposition, which divides the velocity vector as the sum of three velocity components due to the potential, rotational, and viscous contributions, the mixed-type Navier-Stokes equations cast in primitive variables can be fractionally split into ...
We first construct the global existence of the classical solutions near the absolute equilibrium to the Boltzmann equation with general collision kernels under the Navier-Stokes scaling in whole space. In particular, a global energy estimate uniform in the Knudsen number is derived. Then using the ...
A three-dimensional incompressible Navier-Stokes solver using primitive variables. AIAA Journal 1986; 24(3):390-396.Kwak, D., Chang, J. L. C., Shanks, S. P., and Chakravarthy, S. K., "A Three-Dimensional Incompressible Navier-Stokes Solver Using Primitive Variables," AIAA J., Vol. ...
This paper is concerned with the 3D incompressible Navier–Stokes equations with density-dependent viscosity in a smooth bounded domain. The global well-posedness of strong solutions is established for the case when the bound of density is suitably small, or when the total mass is small with larg...
We discretize the incompressible Navier–Stokes equations on a polytopal mesh by using mimetic reconstruction operators. The resulting method conserves discrete mass, momentum, and kinetic energy in the inviscid limit, and determines the vorticity such that the global vorticity is consistent with the bou...
The Maxwell–Stefan equations for the molar fluxes, supplemented by the incompressible Navier–Stokes equations governing the fluid velocity dynamics, are analyzed in bounded domains with no-flux boundary conditions. The system models the dynamics of a multicomponent gaseous mixture under isothermal conditi...
不可压 avier Stokes 方程基于误差估算的 网格自适应解法 周春华 ( 南京航空航天大学空气动力学系 南京 210016) 摘要 : 首先导出了广义方程 P -G 有限元数值解的当地事后误差估算公式 ; 以非连续二阶鼓 包 (b ) 函数空间为速度 ~ 压强误差的近似空间 该估算基于求解当地单元上的广义问题...
We are concerned with the existence and uniqueness issue for the inhomogeneous incompressible Navier‐Stokes equations supplemented with H 1 initial velocity and only bounded nonnegative density . In contrast to all the previous works on those topics, we do not require regularity or a positive lower...