3,227 research outputs found
Enhancing SPH using moving least-squares and radial basis functions
In this paper we consider two sources of enhancement for the meshfree
Lagrangian particle method smoothed particle hydrodynamics (SPH) by improving
the accuracy of the particle approximation. Namely, we will consider shape
functions constructed using: moving least-squares approximation (MLS); radial
basis functions (RBF). Using MLS approximation is appealing because polynomial
consistency of the particle approximation can be enforced. RBFs further appeal
as they allow one to dispense with the smoothing-length -- the parameter in the
SPH method which governs the number of particles within the support of the
shape function. Currently, only ad hoc methods for choosing the
smoothing-length exist. We ensure that any enhancement retains the conservative
and meshfree nature of SPH. In doing so, we derive a new set of
variationally-consistent hydrodynamic equations. Finally, we demonstrate the
performance of the new equations on the Sod shock tube problem.Comment: 10 pages, 3 figures, In Proc. A4A5, Chester UK, Jul. 18-22 200
Stabilisation of the lattice-Boltzmann method using the Ehrenfests' coarse-graining
The lattice-Boltzmann method (LBM) and its variants have emerged as
promising, computationally efficient and increasingly popular numerical methods
for modelling complex fluid flow. However, it is acknowledged that the method
can demonstrate numerical instabilities, e.g., in the vicinity of shocks. We
propose a simple and novel technique to stabilise the lattice-Boltzmann method
by monitoring the difference between microscopic and macroscopic entropy.
Populations are returned to their equilibrium states if a threshold value is
exceeded. We coin the name Ehrenfests' steps for this procedure in homage to
the vehicle that we use to introduce the procedure, namely, the Ehrenfests'
idea of coarse-graining. The one-dimensional shock tube for a compressible
isothermal fluid is a standard benchmark test for hydrodynamic codes. We
observe that, of all the LBMs considered in the numerical experiment with the
one-dimensional shock tube, only the method which includes Ehrenfests' steps is
capable of suppressing spurious post-shock oscillations.Comment: 4 pages, 9 figure
Extending the range of error estimates for radial approximation in Euclidean space and on spheres
We adapt Schaback's error doubling trick [R. Schaback. Improved error bounds
for scattered data interpolation by radial basis functions. Math. Comp.,
68(225):201--216, 1999.] to give error estimates for radial interpolation of
functions with smoothness lying (in some sense) between that of the usual
native space and the subspace with double the smoothness. We do this for both
bounded subsets of R^d and spheres. As a step on the way to our ultimate goal
we also show convergence of pseudoderivatives of the interpolation error.Comment: 10 page
Life, service and the cost of service of farm machines on 400 Iowa farms
That farmers of Iowa make an extensive use of farm machines is indicated by the 16th Census of the United States which gives the value of farm implements and machinery on Iowa farms, April 1, 1940, as 1,134 for each Iowa farm. Under these circumstances it is recognized that the use of farm machines occupies an important role in the agricultural practices of the state. Farm machines not only give the farm workers control over large units of power, thus making possible large individual productive capacity, but they also make farm labor less arduous. For these reasons the cost of farm-machine service or use as discussed in this bulletin should be of general interest
Improving Patient Decision-Making in Health Care
Outlines regional variations within Minnesota in rates of patients with similar conditions receiving elective surgery, the concept of shared decision making, treatment choices for eight conditions, and steps for ensuring patients make informed decisions
Enhancing SPH using moving least-squares and radial basis functions
In this paper we consider two sources of enhancement for the meshfree Lagrangian particle method smoothed particle hydrodynamics (SPH) by improving the accuracy of the particle approximation. Namely, we will consider shape functions constructed using: moving least-squares approximation (MLS); radial basis functions (RBF). Using MLS approximation is appealing because polynomial consistency of the particle approximation can be enforced. RBFs further appeal as they allow one to dispense with the smoothing-length - the parameter in the SPH method which governs the number of particles within the support of the shape function. Currently, only ad hoc methods for choosing the smoothing-length exist. We ensure that any enhancement retains the conservative and meshfree nature of SPH. In doing so, we derive a new set of variationally-consistent hydrodynamic equations. Finally, we demonstrate the performance of the new equations on the Sod shock tube problem
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