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 viscoelastic dynamics.

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 theory.

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 are obtained.

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.