This paper presents a study of pressure and velocity relaxation in two-phase flow calculations. Several of the present observations have been made elsewhere, and the purpose of the paper is to strengthen these observations and draw some conclusions. It is numerically demonstrated how a single-pressure two-fluid model is recovered when applying instantaneous pressure relaxation to a two-pressure two-fluid model. Further, instantaneous velocity relaxation yields a drift-flux model. It is also shown that the pressure relaxation has the disadvantage of inducing a large amount of numerical smearing. The comparisons have been conducted by using nalogous numerical schemes, and a multi-stage centred (MUSTA) scheme for non-conservative two-fluid models has been applied to and tested on the two-pressure two-fluid model. As for others, previously tested two-phase flow models, the MUSTA schemes have been found to be robust, accurate and non-oscillatory. However, compared to their Roe reference schemes, they consistently have a lower computational efficiency for problems involving mass transport.

In this paper we study influenza viral membrane deformation related to the refolding of Hemagglutinin (HA) protein. The focus of the paper is to understand membrane deformation and budding due to experimentally observed linear HA-protein clusters, which have not been mathematically studied before. The viral membrane is modeled as a two dimensional incompressible lipid bilayer with bending rigidity. For tensionless membranes, we derive an analytical solution while for membrane under tension we solve the problem numerically. Our solution for tensionless membranes shows that the height of membrane deformation increases monotonically with the bending moment exerted by HA-proteins and attains its maximum when the size of the protein cluster reaches a critical value. Our results also show that the hypothesis of dimple formation proposed in the literature is valid in the two dimensional setting. Our comparative study of axisymmetric HA-clusters and linear HA-clusters reveals that the linear HA-clusters are not favorable to provide a sufficient energy required to overcome an energy barrier for a successful fusion, despite their capability to cause membrane deformation and budding.

In this paper we consider a geometric inverse problem which requires detecting an unknown obstacle such as a submarine or an aquatic mine immersed in a Stokes slow viscous stationary flow of an incompressible fluid, from a single set of Cauchy (fluid velocity and stress force) boundary measurements. The numerical reconstruction is based on the method of fundamental solutions (MFS) for the pressure and streamfunction in two dimensions combined with regularization. Numerical results are presented and discussed.

In this paper, a well-balanced kinetic scheme for the gas dynamic equations under gravitational field is developed. In order to construct such a scheme, the physical process of particles transport through a potential barrier at a cell interface is considered, where the amount of particle penetration and reflection is evaluated according to the incident particle velocity. This work extends the approach of Perthame and Simeoni for the shallow water equations [Calcolo, 38 (2001), pp. 201-231] to the Euler equations under gravitational field. For an isolated system, this scheme is probably the only well-balanced method which can precisely preserve an isothermal steady state solution under time-independent gravitational potential. A few numerical examples are used to validate the above approach.

The parabolic variational inequality for simulating the valuation of American option is used to analyze a continuous dependence of the solution with respect to the uncertain volatility parameter. Three kinds of the continuity are proved, enabling us to employ the maximum range method for the uncertain parameter, under the condition that the criterion-functional has the corresponding property.

Peristaltic motion of an incompressible micropolar fluid in a two-dimensional channel with wall effects is studied. Assuming that the wave length of the peristaltic wave is large in comparison to the mean half width of the channel, a perturbation method of solution is obtained in terms of wall slope parameter, under dynamic boundary conditions. Closed form expressions are derived for the stream function and average velocity and the effects of pertinent parameters on these flow variables have been studied. It has been observed that the time average velocity increases numerically with micropolar parameter. Further, the time average velocity also increases with stiffness in the wall.

The propagation characteristics of elasto-thermodiffusive Lamb waves in a homogenous isotropic, thermodiffusive, elastic plate have been investigated in the context of linear theory of generalized thermodiffusion. After developing the formal solution of the mathematical model consisting of partial differential equations, the secular equations have been derived by using relevant boundary conditions prevailing at the surfaces of the plate for symmetric and asymmetric wave modes in completely separate terms. The secular equations for long wavelength and short wavelength waves have also been deduced and discussed. The amplitudes of displacement components, temperature change and mass concentration under the Lamb wave propagation conditions have also been obtained. The complex transcendental secular equations have been solved by using a hybrid numerical technique consisting of irreducible Cardano method along with function iteration technique after splitting these in a system of real transcendental equations. The numerically simulated results in respect of phase velocity, attenuation coefficient, specific loss factor and relative frequency shift of thermoelastic diffusive waves have been presented graphically in the case of brass material.