36,790 research outputs found
Applications of the contravariant form of the Navier-Stokes equations
The contravariant Navier-Stokes equations in weak conservation form are well suited to certain fluid flow analysis problems. Three dimensional contravariant momentum equations may be used to obtain Navier-Stokes equations in weak conservation form on a nonplanar two dimensional surface with varying streamsheet thickness. Thus a three dimensional flow can be simulated with two dimensional equations to obtain a quasi-three dimensional solution for viscous flow. When the Navier-Stokes equations on the two dimensional nonplanar surface are transformed to a generalized body fitted mesh coordinate system, the resulting equations are similar to the equations for a body fitted mesh coordinate system on the Euclidean plane. Contravariant momentum components are also useful for analyzing compressible, three dimensional viscous flow through an internal duct by parabolic marching. This type of flow is efficiently analyzed by parabolic marching methods, where the streamwise momentum equation is uncoupled from the two crossflow momentum equations. This can be done, even for ducts with a large amount of turning, if the Navier-Stokes equations are written with contravariant components
On the Inviscid Limit of the 3D Navier-Stokes Equations with Generalized Navier-slip Boundary Conditions
In this paper, we investigate the vanishing viscosity limit problem for the
3-dimensional (3D) incompressible Navier-Stokes equations in a general bounded
smooth domain of with the generalized Navier-slip boundary conditions
(\ref{VSg}). Some uniform estimates on rates of convergence in
and of the solutions to the
corresponding solutions of the idea Euler equations with the standard slip
boundary condition are obtained
A dynamically adaptive multigrid algorithm for the incompressible Navier-Stokes equations: Validation and model problems
An algorithm is described for the solution of the laminar, incompressible Navier-Stokes equations. The basic algorithm is a multigrid based on a robust, box-based smoothing step. Its most important feature is the incorporation of automatic, dynamic mesh refinement. This algorithm supports generalized simple domains. The program is based on a standard staggered-grid formulation of the Navier-Stokes equations for robustness and efficiency. Special grid transfer operators were introduced at grid interfaces in the multigrid algorithm to ensure discrete mass conservation. Results are presented for three models: the driven-cavity, a backward-facing step, and a sudden expansion/contraction
On Meshfree GFDM Solvers for the Incompressible Navier-Stokes Equations
Meshfree solution schemes for the incompressible Navier--Stokes equations are
usually based on algorithms commonly used in finite volume methods, such as
projection methods, SIMPLE and PISO algorithms. However, drawbacks of these
algorithms that are specific to meshfree methods have often been overlooked. In
this paper, we study the drawbacks of conventionally used meshfree Generalized
Finite Difference Method~(GFDM) schemes for Lagrangian incompressible
Navier-Stokes equations, both operator splitting schemes and monolithic
schemes. The major drawback of most of these schemes is inaccurate local
approximations to the mass conservation condition. Further, we propose a new
modification of a commonly used monolithic scheme that overcomes these problems
and shows a better approximation for the velocity divergence condition. We then
perform a numerical comparison which shows the new monolithic scheme to be more
accurate than existing schemes
Convergence study and optimal weight functions of an explicit particle method for the incompressible Navier--Stokes equations
To increase the reliability of simulations by particle methods for
incompressible viscous flow problems, convergence studies and improvements of
accuracy are considered for a fully explicit particle method for incompressible
Navier--Stokes equations. The explicit particle method is based on a penalty
problem, which converges theoretically to the incompressible Navier--Stokes
equations, and is discretized in space by generalized approximate operators
defined as a wider class of approximate operators than those of the smoothed
particle hydrodynamics (SPH) and moving particle semi-implicit (MPS) methods.
By considering an analytical derivation of the explicit particle method and
truncation error estimates of the generalized approximate operators, sufficient
conditions of convergence are conjectured.Under these conditions, the
convergence of the explicit particle method is confirmed by numerically
comparing errors between exact and approximate solutions. Moreover, by focusing
on the truncation errors of the generalized approximate operators, an optimal
weight function is derived by reducing the truncation errors over general
particle distributions. The effectiveness of the generalized approximate
operators with the optimal weight functions is confirmed using numerical
results of truncation errors and driven cavity flow. As an application for flow
problems with free surface effects, the explicit particle method is applied to
a dam break flow.Comment: 27 pages, 13 figure
Viscous motion in an oceanic circulation model
The barotropic motion of a viscous fluid in a laboratory simulation of ocean circulation may be modelled by Beards ley's vorticity equations. It is established here that these equations have unique smooth solutions which depend continuously on initial conditions. To avoid a boundary condition which involves an integral operator, the vorticity equations are replaced by an equivalent system of momentum equations. The system resembles the two-dimensional incompressible Navier-Stokes equations in a rotating reference frame. The existence of unique generalized solutions of the system in a square domain is established by modifying arguments used by Ladyzhenskaya for the Navier-Stokes equations. Smoothness of the solutions is then established by modifying Golovkin's arguments, again originally for the Navier- Stokes equations. A numerical procedure for solving the vorticity equations is discussed, as are the effects of reentrant corners in the domain modelling islands and peninsulae
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