187 research outputs found
Comparison of Wide and Compact Fourth Order Formulations of the Navier-Stokes Equations
In this study the numerical performances of wide and compact fourth order
formulation of the steady 2-D incompressible Navier-Stokes equations will be
investigated and compared with each other. The benchmark driven cavity flow
problem will be solved using both wide and compact fourth order formulations
and the numerical performances of both formulations will be presented and also
the advantages and disadvantages of both formulations will be discussed
Numerical Performance of Compact Fourth Order Formulation of the Navier-Stokes Equations
In this study the numerical performance of the fourth order compact
formulation of the steady 2-D incompressible Navier-Stokes equations introduced
by Erturk et al. (Int. J. Numer. Methods Fluids, 50, 421-436) will be
presented. The benchmark driven cavity flow problem will be solved using the
introduced compact fourth order formulation of the Navier-Stokes equations with
two different line iterative semi-implicit methods for both second and fourth
order spatial accuracy. The extra CPU work needed for increasing the spatial
accuracy from second order (O(x2)) to fourth order (O(x4)) formulation will be
presented
A pseudospectral matrix method for time-dependent tensor fields on a spherical shell
We construct a pseudospectral method for the solution of time-dependent,
non-linear partial differential equations on a three-dimensional spherical
shell. The problem we address is the treatment of tensor fields on the sphere.
As a test case we consider the evolution of a single black hole in numerical
general relativity. A natural strategy would be the expansion in tensor
spherical harmonics in spherical coordinates. Instead, we consider the simpler
and potentially more efficient possibility of a double Fourier expansion on the
sphere for tensors in Cartesian coordinates. As usual for the double Fourier
method, we employ a filter to address time-step limitations and certain
stability issues. We find that a tensor filter based on spin-weighted spherical
harmonics is successful, while two simplified, non-spin-weighted filters do not
lead to stable evolutions. The derivatives and the filter are implemented by
matrix multiplication for efficiency. A key technical point is the construction
of a matrix multiplication method for the spin-weighted spherical harmonic
filter. As example for the efficient parallelization of the double Fourier,
spin-weighted filter method we discuss an implementation on a GPU, which
achieves a speed-up of up to a factor of 20 compared to a single core CPU
implementation.Comment: 33 pages, 9 figure
A low-cost parallel implementation of direct numerical simulation of wall turbulence
A numerical method for the direct numerical simulation of incompressible wall
turbulence in rectangular and cylindrical geometries is presented. The
distinctive feature resides in its design being targeted towards an efficient
distributed-memory parallel computing on commodity hardware. The adopted
discretization is spectral in the two homogeneous directions; fourth-order
accurate, compact finite-difference schemes over a variable-spacing mesh in the
wall-normal direction are key to our parallel implementation. The parallel
algorithm is designed in such a way as to minimize data exchange among the
computing machines, and in particular to avoid taking a global transpose of the
data during the pseudo-spectral evaluation of the non-linear terms. The
computing machines can then be connected to each other through low-cost network
devices. The code is optimized for memory requirements, which can moreover be
subdivided among the computing nodes. The layout of a simple, dedicated and
optimized computing system based on commodity hardware is described. The
performance of the numerical method on this computing system is evaluated and
compared with that of other codes described in the literature, as well as with
that of the same code implementing a commonly employed strategy for the
pseudo-spectral calculation.Comment: To be published in J. Comp. Physic
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
The remapped particle-mesh advection scheme
We describe the remapped particle-mesh method, a new mass-conserving method
for solving the density equation which is suitable for combining with
semi-Lagrangian methods for compressible flow applied to numerical weather
prediction. In addition to the conservation property, the remapped
particle-mesh method is computationally efficient and at least as accurate as
current semi-Lagrangian methods based on cubic interpolation. We provide
results of tests of the method in the plane, results from incorporating the
advection method into a semi-Lagrangian method for the rotating shallow-water
equations in planar geometry, and results from extending the method to the
surface of a sphere
Numerical Solutions of 2-D Steady Incompressible Flow in a Driven Skewed Cavity
The benchmark test case for non-orthogonal grid mesh, the "driven skewed
cavity flow", first introduced by Demirdzic et al. (1992, IJNMF, 15, 329) for
skew angles of alpha=30 and alpha=45, is reintroduced with a more variety of
skew angles. The benchmark problem has non-orthogonal, skewed grid mesh with
skew angle (alpha). The governing 2-D steady incompressible Navier-Stokes
equations in general curvilinear coordinates are solved for the solution of
driven skewed cavity flow with non-orthogonal grid mesh using a numerical
method which is efficient and stable even at extreme skew angles. Highly
accurate numerical solutions of the driven skewed cavity flow, solved using a
fine grid (512x512) mesh, are presented for Reynolds number of 100 and 1000 for
skew angles ranging between 15<alpha<165
Numerical Solutions of 2-D Steady Incompressible Driven Cavity Flow at High Reynolds Numbers
Numerical calculations of the 2-D steady incompressible driven cavity flow
are presented. The Navier-Stokes equations in streamfunction and vorticity
formulation are solved numerically using a fine uniform grid mesh of 601x601.
The steady driven cavity solutions are computed for Re<21,000 with a maximum
absolute residuals of the governing equations that were less than 10-10. A new
quaternary vortex at the bottom left corner and a new tertiary vortex at the
top left corner of the cavity are observed in the flow field as the Reynolds
number increases. Detailed results are presented and comparisons are made with
benchmark solutions found in the literature
Band Formation during Gaseous Diffusion in Aerogels
We study experimentally how gaseous HCl and NH_3 diffuse from opposite sides
of and react in silica aerogel rods with porosity of 92 % and average pore size
of about 50 nm. The reaction leads to solid NH_4Cl, which is deposited in thin
sheet-like structures. We present a numerical study of the phenomenon. Due to
the difference in boundary conditions between this system and those usually
studied, we find the sheet-like structures in the aerogel to differ
significantly from older studies. The influence of random nucleation centers
and inhomogeneities in the aerogel is studied numerically.Comment: 7 pages RevTex and 8 figures. Figs. 4-8 in Postscript, Figs. 1-3 on
request from author
On the fourth-order accurate compact ADI scheme for solving the unsteady Nonlinear Coupled Burgers' Equations
The two-dimensional unsteady coupled Burgers' equations with moderate to
severe gradients, are solved numerically using higher-order accurate finite
difference schemes; namely the fourth-order accurate compact ADI scheme, and
the fourth-order accurate Du Fort Frankel scheme. The question of numerical
stability and convergence are presented. Comparisons are made between the
present schemes in terms of accuracy and computational efficiency for solving
problems with severe internal and boundary gradients. The present study shows
that the fourth-order compact ADI scheme is stable and efficient
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