Numerical solution of the Navier-Stokes equations [PDF]
, 1968 A finite-difference method for solving the time-dependent Navier- Stokes equations for an incompressible fluid is introduced. This method uses the primitive variables, i.e. the velocities and the pressure, and is equally applicable to problems in two and
A. Chorin
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Generalizations of incompressible and compressible Navier–Stokes equations to fractional time and multi-fractional space [PDF]
Scientific Reports, 2022 This study develops the governing equations of unsteady multi-dimensional incompressible and compressible flow in fractional time and multi-fractional space. When their fractional powers in time and in multi-fractional space are specified to unit integer
M. Levent Kavvas, Ali Ercan
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Uniform Finite Element Error Estimates with Power-Type Asymptotic Constants for Unsteady Navier–Stokes Equations [PDF]
Entropy, 2022 Uniform error estimates with power-type asymptotic constants of the finite element method for the unsteady Navier–Stokes equations are deduced in this paper.
Cong Xie, Kun Wang
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Hydrodynamics beyond Navier-Stokes: Exact solution to the lattice Boltzmann hierarchy [PDF]
Phys. Rev. Lett. 98, 124502 (2007), 2007 Exact solution to the hierarchy of nonlinear lattice Boltzmann (LB) kinetic equations in the stationary planar Couette flow is found at non-vanishing Knudsen numbers. A new method of solving LB kinetic equations which combines the method of moments with boundary conditions for populations enables to derive closed-form solutions for all higher-order ...
arxiv +1 more source
Splitting method and the existence of a strong solution of the Navier-Stokes equations
Қарағанды университетінің хабаршысы. Математика сериясы, 2019 In the author’s article from the previous issue of the journal from the properties of the ONS solutions the relation between pressure and module square of velocity vector is set.
A.Sh. Akysh (Akishev)
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Average Process of Fractional Navier–Stokes Equations with Singularly Oscillating Force
Fractal and Fractional, 2022 The averaging process between two-dimensional fractional Navier–Stokes equations driven by a singularly oscillating external force and the averaged equations corresponding to the limiting case are investigated.
Chunjiao Han +3 more
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Accurate iteration-free mixed-stabilised formulation for laminar incompressible Navier-Stokes: Applications to fluid-structure interaction [PDF]
, 2020 Stabilised mixed velocity-pressure formulations are one of the widely-used finite element schemes for computing the numerical solutions of laminar incompressible Navier-Stokes. In these formulations, the Newton-Raphson scheme is employed to solve the nonlinearity in the convection term. One fundamental issue with this approach is the computational cost
arxiv +1 more source
On the hydrostatic approximation of compressible anisotropic Navier–Stokes equations
Comptes Rendus. Mathématique, 2021 In this work, we obtain the hydrostatic approximation by taking the small aspect ratio limit to the Navier–Stokes equations. The aspect ratio (the ratio of the depth to horizontal width) is a geometrical constraint in general large scale motions meaning ...
Gao, Hongjun +2 more
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Lid-driven cavity flow using dual reciprocity [PDF]
MATEC Web of Conferences, 2020 The paper presents the use of the multi-domain dual reciprocity method of fundamental solutions (MD-MFSDR) for the analysis of the laminar viscous flow problem described by Navier-Stokes equations.
Mužík Juraj, Bulko Roman
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Conservation laws of some lattice equations [PDF]
Front. Math. China, 8(5) (2013) 1001-16, 2012 We derive infinitely many conservation laws for some multi-dimensionally consistent lattice equations from their Lax pairs. These lattice equations are the Nijhoff-Quispel-Capel equation, lattice Boussinesq equation, lattice nonlinear Schr\"{o}dinger equation, modified lattice Boussinesq equation, Hietarinta's Boussinesq-type equations, Schwarzian ...
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