This paper compares two models predicting elastic and viscoelastic properties
of large arteries. Models compared include a Kelvin (standard linear) model
and an extended 2-term exponential linear viscoelastic model. Models were validated
against in-vitro data from the ovine thoracic descending aorta and the carotid
artery. Measurements of blood pressure data were used as an input to predict vessel
cross-sectional area. Material properties were predicted by estimating a set of
model parameters that minimize the difference between computed and measured
values of the cross-sectional area. The model comparison was carried out using
generalized analysis of variance type statistical tests. For the thoracic descending
aorta, results suggest that the extended 2-term exponential model does not improve
the ability to predict the observed cross-sectional area data, while for the carotid
artery the extended model does statistically provide an improved fit to the data.
This is in agreement with the fact that the aorta displays more complex nonlinear
viscoelastic dynamics, while the stiffer carotid artery mainly displays simpler linear
The purpose of this paper is to gain some insight into the characteristic
behavior of a general compressible two-fluid gas-liquid model in 2D by using numerical
computations. Main focus is on mass transport phenomena. Relatively few
numerical results in higher dimensions can be found in the literature for this two-fluid model, in particular, for cases where mass transport dynamics are essential.
We focus on natural extensions to 2D of known 1D benchmark test cases, like water
faucet and gas-liquid separation, previously employed by many researchers for the
purpose of testing various numerical schemes. For the numerical investigations,
the WIMF discretization method introduced in [SIAM J. Sci. Comput. 26 (2005),
1449] is applied, in combination with a standard dimensional splitting approach.
Highly complicated flow patterns are observed reflecting the balance between acceleration
forces, gravity, interfacial forces, and pressure gradients. An essential
ingredient in these results is the appearance of single-phase regions in combination
with mixture regions (dispersed flow). Solutions are calculated and shown from
early times until a steady state is reached. Grid refinement studies are included to
demonstrate that the obtained solutions are not grid-sensitive.
We present a proof of the discrete maximum principle (DMP) for the
1D Poisson equation $−u''=f$ equipped with mixed Dirichlet-Neumann boundary
conditions. The problem is discretized using finite elements of arbitrary lengths
and polynomial degrees ($hp$-FEM). We show that the DMP holds on all meshes
with no limitations to the sizes and polynomial degrees of the elements.
A meshless method based on the method of fundamental solutions (MFS)
is proposed to solve the time-dependent partial differential equations with variable
coefficients. The proposed method combines the time discretization and the one-stage
MFS for spatial discretization. In contrast to the traditional two-stage process,
the one-stage MFS approach is capable of solving a broad spectrum of partial differential
equations. The numerical implementation is simple since both closed-form
approximate particular solution and fundamental solution are easier to find than the
traditional approach. The numerical results show that the one-stage approach is
robust and stable.
Numerical simulation of heat transfer in a high aspect ratio rectangular
microchannel with heat sinks has been conducted, similar to an experimental study.
Three channel heights measuring 0.3 mm, 0.6 mm and 1 mm are considered and the
Reynolds number varies from 300 to 2360, based on the hydraulic diameter. Simulation
starts with the validation study on the Nusselt number and the Poiseuille
number variations along the channel streamwise direction. It is found that the predicted
Nusselt number has shown very good agreement with the theoretical estimation,
but some discrepancies are noted in the Poiseuille number comparison. This
observation however is in consistent with conclusions made by other researchers
for the same flow problem. Simulation continues on the evaluation of heat transfer
characteristics, namely the friction factor and the thermal resistance. It is found
that noticeable scaling effect happens at small channel height of 0.3 mm and the
predicted friction factor agrees fairly well with an experimental based correlation.
Present simulation further reveals that the thermal resistance is low at small channel
height, indicating that the heat transfer performance can be enhanced with the
decrease of the channel height.
In this paper, we present an a posteriori error estimates of semilinear
quadratic constrained optimal control problems using triangular mixed finite element
methods. The state and co-state are approximated by the order $k\leq 1$ Raviart-
Thomas mixed finite element spaces and the control is approximated by piecewise
constant element. We derive a posteriori error estimates for the coupled state and
control approximations. A numerical example is presented in confirmation of the
A general and easy-to-code numerical method based on radial basis functions
(RBFs) collocation is proposed for the solution of delay differential equations
(DDEs). It relies on the interpolation properties of infinitely smooth RBFs, which allow
for a large accuracy over a scattered and relatively small discretization support.
Hardy's multiquadric is chosen as RBF and combined with the Residual Subsampling
Algorithm of Driscoll and Heryudono for support adaptivity. The performance
of the method is very satisfactory, as demonstrated over a cross-section of
benchmark DDEs, and by comparison with existing general-purpose and specialized
numerical schemes for DDEs.
In the paper, an inf-sup stabilized finite element method by multiscale
functions for the Stokes equations is discussed. The key idea is to use a Petrov-Galerkin approach based on the enrichment of the standard polynomial space for
the velocity component with multiscale functions. The inf-sup condition for $P_1$-$P_0$ triangular element (or $Q_1$-$P_0$ quadrilateral element) is established. And the optimal
error estimates of the stabilized finite element method for the Stokes equations
In this paper, we present a finite difference method to track a network of
curves whose motion is determined by mean curvature. To study the effect of inhomogeneous
surface tension on the evolution of the network of curves, we include
surfactant which can diffuse along the curves. The governing equations consist of
one parabolic equation for the curve motion coupled with a convection-diffusion
equation for the surfactant concentration along each curve. Our numerical method
is based on a direct discretization of the governing equations which conserves the
total surfactant mass in the curve network. Numerical experiments are carried out
to examine the effects of inhomogeneous surface tension on the motion of the network,
including the von Neumann law for cell growth in two space dimensions.
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