Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Consistency and Convergence of a High Order Accurate Meshless Method for
  Solution of Incompressible Fluid Flows   Computations of incompressible flows with velocity boundary conditions
require solution of a Poisson equation for pressure with all Neumann boundary
conditions. Discretization of such a Poisson equation results in a
rank-deficient matrix of coefficients. When a non-conservative discretization
method such as finite difference, finite element, or spectral scheme is used,
such a matrix also generates an inconsistency which makes the residuals in the
iterative solution to saturate at a threshold level that depends on the spatial
resolution and order of the discretization scheme. In this paper, we examine
inconsistency for a high-order meshless discretization scheme suitable for
solving the equations on a complex domain. The high order meshless method uses
polyharmonic spline radial basis functions (PHS-RBF) with appended polynomials
to interpolate scattered data and constructs the discrete equations by
collocation. The PHS-RBF provides the flexibility to vary the order of
discretization by increasing the degree of the appended polynomial. In this
study, we examine the convergence of the inconsistency for different spatial
resolutions and for different degrees of the appended polynomials by solving
the Poisson equation for a manufactured solution as well as the Navier-Stokes
equations for several fluid flows. We observe that the inconsistency decreases
faster than the error in the final solution, and eventually becomes vanishing
small at sufficient spatial resolution. The rate of convergence of the
inconsistency is observed to be similar or better than the rate of convergence
of the discretization errors. This beneficial observation makes it unnecessary
to regularize the Poisson equation by fixing either the mean pressure or
pressure at an arbitrary point. A simple point solver such as the SOR is seen
to be well-convergent, although it can be further accelerated using multilevel
methods.

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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga