On modelling of thermodynamic interaction of particles suspended in two-dimensional medium

Analytical description of temperature distribution in a medium with foreign inclusions is difficult due to the complicated geometry of the problem, so asymptotic and numerical methods are usually used to model thermodynamic processes in heterogeneous media. To be convinced in convergence of these methods the authors consider model problem about two identical round particles in infinite planar medium with temperature gradient which is constant at infinity. Authors refine multipole expansion of the solution obtained earlier by continuing it up to higher powers of small parameter, that is nondimensional radius of thermodynamically interacting particles. Numerical approach to the problem using ANSYS software is described; in particular, appropriate choice of approximate boundary conditions is discussed. Authors ascertain that replacement of infinite medium by finite-sized domain is important source of error in FEM. To find domain boundaries in multiple inclusions’ problem the authors develop “fictituous particle” method; according to it the cloud of particles far from the center of the cloud acts approximately as a single equivalent particle of greater size and so may be replaced by it. Basing on particular quantitative data the dependence of domain size that provides acceptable accuracy on thermal conductivities of medium and of particles is explored. Authors establish series of numerical experiments confirming convergence of multipole expansions method and FEM as well; proximity of their results is illustrated, too.

Exact Artificial Boundary Conditions for Quasi-Linear Problems in Semi-Infinite Strips

In this paper, the exact artificial boundary conditions for quasi-linear problems in semi-infinite strips are investigated. Based on the Kirchhoff transformation, the exact and approximate boundary conditions on a segment artificial boundary are derived. The error estimate for the finite element approximation with the artificial boundary condition is obtained. Some numerical examples show the efficiency of this method.

Predicting river channel pattern based on stream power, bed material and bank strength

Rivers exhibit a wide variety of channel patterns, and predicting changes in channel pattern is important in order to foresee river responses to climate change and river restoration. Many discriminators have been developed to define approximate boundary conditions for different channel patterns, based on channel-pattern-controlling parameters such as discharge and valley gradient. However, presently available discriminators have two main shortcomings. First, they perform poorly for rivers with cohesive, relatively erosion-resistant banks. For this subset, discriminators tend to indicate an actively meandering channel pattern, whereas the river morphology and dynamics show that many of these rivers should be classified as laterally stable. Second, channel pattern discriminators are often used to predict channel patterns, which is only valid when parameters are used that are independent of actual channel pattern. This condition is often not met, as many discriminators use the channel slope or width–depth ratio of the channel as input. To resolve both shortcomings, we first propose an additional class of rivers with scroll bars and tortuous channel patterns, which have an inhibited mobility due to their self-formed cohesive deposits. Second, we compare frequently used empirical and mechanistic channel pattern discriminators, taking into account the success in predicting channel pattern and the independence of causal factors used. Thirdly, we present a novel channel pattern discriminator and predictor that includes the effect of a cohesive floodplain, using the average silt-plus-clay fraction of the river banks as proxy. We show that this new predictor outperforms previously used empirical and mechanistic approaches, and successfully predicts channel pattern for 87% of the rivers from a dataset of 70. This new predictor is widely applicable, as it is relatively simple and based on easily obtainable, and mostly independent, parameters.

The Validity of Approximate Boundary Conditions for Natural Convection With Thermal Radiation in Open Cavities

The use of approximate boundary conditions at the opening of the cavities leads to restriction of the computational domain and, hence, the reduction in computational effort. However, the accuracy of the restricted domain approach (RDA) had been evaluated only for the natural convection inside open cavities and that too only for one aspect ratio (AR). The validity of the approach had not been evaluated for inclined, as well as, shallow cavities. This study focuses on the analysis of the accuracy of RDA against extended domain approach (EDA) in open cavities of different ARs, at different inclinations and different Rayleigh numbers (Ra). The results show that the difference between the approaches is only significant in very shallow cavities (AR is defined as the height of the hot wall divided by the depth of the cavity) at low Ra. For Ra higher than 106 and an AR greater than 0.2, the maximum difference between the two approaches is around 5% and hence RDA can be recommended in these ranges, resulting in increased computational efficiency without significant loss in the accuracy. Moreover, the maximum difference in the results for the two methods is for intermediate inclinations. Even there, an increase in the difference is more pronounced at lower Ra. Furthermore, distribution of the exit velocity and temperature at the opening as well as the distribution of the Nusselt number at the hot wall is compared for RDA and EDA to explain the behavior of error at different ARs and inclinations.

Приближенные граничные условия для задачи нахождения оптических коэффициентов ультратонких металлических пленок в СВЧ и ТГЦ диапазонах

Approximate boundary conditions for a problem of calculating the optical coefficients of a system composed of inhomogeneous ultrathin metallic film with an arbitrary thickness dependence of conductivity deposited on dielectric substrate are obtained. The derivation of the boundary conditions is based on the Picard method of successive approximations. Analytical expressions for the errors in calculating the optical coefficients with use of the proposed approximate boundary conditions are presented. It is shown that the error increases with the frequency and the film thickness increasing. The maximum error for films of 10 nm-thickness does not exceed 10.7% at 1 THz. As an example, the complex optical coefficients of a system similar to Fabry-Perot etalon and a metal film without a substrate with model thickness dependence of conductivity are calculated. The coincidence between the results of numerical simulation and calculations performed with approximate boundary conditions is shown. The possibility of direct calculating the average conductivity of a film from experimentally measured reflection and transmission coefficients is demonstrated.

Effect of Thermal Radiation on Accuracy of Restricted Domain Approach in a Square Open Cavity

To reduce computational time for simulation of natural convection in open cavities, it is quite common to use a domain restricted to the cavity with approximate boundary conditions at the cavity opening. It had been shown that such approach leads to quite accurate solutions for high Rayleigh number (Ra) flows. Such approach has been extended to flows involving radiative heat transfer as well. However, it is important to note that the effect of radiation on the accuracy of restricted domain approach has not been evaluated. In the present work, a comparison of Nusselt numbers is obtained by restricted domain approach with those obtained by using extended domain approach. The convective as well as radiative Nusselt numbers are considered for comparison for various values of Ra and radiation conduction parameter (Nr). It is observed that the accuracy of the restricted domain approach varies with the radiation conduction parameter as well and the approach is found to be quite accurate for high values of Nr.

Acoustic boundary conditions at an impedance lining in inviscid shear flow

The accuracy of existing impedance boundary conditions is investigated, and new impedance boundary conditions are derived, for lined ducts with inviscid shear flow. The accuracy of the Ingard–Myers boundary condition is found to be poor. Matched asymptotic expansions are used to derive a boundary condition accurate to second order in the boundary layer thickness, which shows substantially increased accuracy for thin boundary layers when compared with both the Ingard–Myers boundary condition and its recent first-order correction. Closed-form approximate boundary conditions are also derived using a single Runge–Kutta step to solve an impedance Ricatti equation, leading to a boundary condition that performs reasonably even for thicker boundary layers. Surface modes and temporal stability are also investigated.

On the Accuracy of Asymptotic Solutions for TM Waves Diffracting on an Impedance Wedge

The contribution focuses on the accuracy of two asymptotic solutions aimed at representing the electromagnetic field scattered by penetrable wedges. One is a heuristic manipulation of the solution for the perfect electrical conductor, and the other one is a more rigorous coefficient based on approximate boundary conditions. The results presented here extend those proposed by other authors by illustrating the accuracy of such solutions at the edge of validity of the uniform theory of diffraction. In particular, they show that the heuristic formulation can be freely applied in similar conditions, while the other might not always lead to accurate predictions.