1,546 research outputs found
Discrete exterior calculus (DEC) for the surface Navier-Stokes equation
We consider a numerical approach for the incompressible surface Navier-Stokes
equation. The approach is based on the covariant form and uses discrete
exterior calculus (DEC) in space and a semi-implicit discretization in time.
The discretization is described in detail and related to finite difference
schemes on staggered grids in flat space for which we demonstrate second order
convergence. We compare computational results with a vorticity-stream function
approach for surfaces with genus 0 and demonstrate the interplay between
topology, geometry and flow properties. Our discretization also allows to
handle harmonic vector fields, which we demonstrate on a torus.Comment: 21 pages, 9 figure
A Two-Level Finite Element Discretization of the Streamfunction Formulation of the Stationary Quasi-Geostrophic Equations of the Ocean
In this paper we proposed a two-level finite element discretization of the
nonlinear stationary quasi-geostrophic equations, which model the wind driven
large scale ocean circulation. Optimal error estimates for the two-level finite
element discretization were derived. Numerical experiments for the two-level
algorithm with the Argyris finite element were also carried out. The numerical
results verified the theoretical error estimates and showed that, for the
appropriate scaling between the coarse and fine mesh sizes, the two-level
algorithm significantly decreases the computational time of the standard
one-level algorithm.Comment: Computers and Mathematics with Applications 66 201
Fine Grid Numerical Solutions of Triangular Cavity Flow
Numerical solutions of 2-D steady incompressible flow inside a triangular
cavity are presented. For the purpose of comparing our results with several
different triangular cavity studies with different triangle geometries, a
general triangle mapped onto a computational domain is considered. The
Navier-Stokes equations in general curvilinear coordinates in streamfunction
and vorticity formulation are numerically solved. Using a very fine grid mesh,
the triangular cavity flow is solved for high Reynolds numbers. The results are
compared with the numerical solutions found in the literature and also with
analytical solutions as well. Detailed results are presented
Navier-Stokes equations on the flat cylinder with vorticity production on the boundary
We study the two-dimensional Navier-Stokes system on a flat cylinder with the
usual Dirichlet boundary conditions for the velocity field u. We formulate the
problem as an infinite system of ODE's for the natural Fourier components of
the vorticity, and the boundary conditions are taken into account by adding a
vorticity production at the boundary. We prove equivalence to the original
Navier-Stokes system and show that the decay of the Fourier modes is
exponential for any positive time in the periodic direction, but it is only
power-like in the other direction.Comment: 25 page
Global existence and uniqueness for the Lake equations with vanishing topography : elliptic estimates for degenerate equations
This paper deals with global existence and uniqueness for the lake equations
with a bottom topography vanishing on the shore. Our result generalizes
previous studies that assumed the depth to be nondegenerate. Elliptic estimates
for degenerate equations has to be established studying the behavior of the
associated Green function
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