On Radiation Boundary Conditions and Wave Transformation Across the Surf Zone

The purpose of this paper is to extend the validity of Li's parabolic model (1994) by incorporating a combined energy factor in the mild-slope equation and by improving the traditional radiation boundary conditions. With wave breaking and energy dissipation expressed in a direct form in the equation, the proposed model could provide an efficient numerical scheme and accurate predictions of wave transformation across the surf zone. The radiation boundary conditions are iterated in the model without use of approximations. The numerical predictions for wave height distributions across the surf zone are compared with experimental data over typical beach profiles. In addition, tests of waves scattering around a circular pile show that the proposed model could also provide reasonable improvement on the radiation boundary conditions for large incident angles of waves.

Statistical second-order two-scale analysis and computation for heat conduction problem with radiation boundary condition in porous materials

This paper discusses a statistical second-order two-scale（SSOTS） analysis and computation for a heat conduction problem with a radiation boundary condition in random porous materials.Firstly,the microscopic configuration for the structure with random distribution is briefly characterized.Secondly,the SSOTS formulae for computing the heat transfer problem are derived successively by means of the construction way for each cell.Then,the statistical prediction algorithm based on the proposed two-scale model is described in detail.Finally,some numerical experiments are proposed,which show that the SSOTS method developed in this paper is effective for predicting the heat transfer performance of porous materials and demonstrating its significant applications in actual engineering computation.

RADIATION BOUNDARY CONDITIONS FOR MAXWELL'S EQUATIONS:A REVIEW OF ACCURATE TIME-DOMAIN FORMULATIONS

We review time-domain formulations of radiation boundary conditions for Maxwell＇s equations, focusing on methods which can deliver arbitrary accuracy at acceptable compu-tational cost. Examples include fast evaluations of nonlocal conditions on symmetric and general boundaries, methods based on identifying and evaluating equivalent sources, and local approximations such as the perfectly matched layer and sequences of local boundary conditions. Complexity estimates are derived to assess work and storage requirements as a function of wavelength and simulation time.

Second-Order Two-Scale Analysis Method for the Heat Conductive Problem with Radiation Boundary Condition in Periodical Porous Domain

In this paper a second-order two-scale(SOTS)analysismethod is developed for a static heat conductive problem in a periodical porous domain with radiation boundary condition on the surfaces of cavities.By using asymptotic expansion for the temperature field and a proper regularity assumption on the macroscopic scale,the cell problem,effective material coefficients,homogenization problem,first-order correctors and second-order correctors are obtained successively.The characteristics of the asymptotic model is the coupling of the cell problems with the homogenization temperature field due to the nonlinearity and nonlocality of the radiation boundary condition.The error estimation is also obtained for the original solution and the SOTS’s approximation solution.Finally the corresponding finite element algorithms are developed and a simple numerical example is presented.

Complete Radiation Boundary Conditions for Convective Waves

Local approximate radiation boundary conditions of optimal efficiency for the convective wave equation and the linearized Euler equations in waveguide geometry are formulated,analyzed,and tested.The results extend and improve for the convective case the general formulation of high-order local radiation boundary condition sequences for anisotropic scalar equations developed in[4].

An application of radiation boundary condition to scattering problem of acoustic waves in fluids

A numerical method of solving acoustic wave scattering pnblem in fluids is described. Radiation boundary condition (RBC) obtained by factorization method of Helmholtz equation is applied to transforming the exterior boundary value problem in unbounded region into one in a finite region. Combined with RBC and scatterer surface boundary condition, Helmholtz equation is solved numerically by the finite difference method. Computational results for sphere and prolate spheroidal scatterers are in excellent agreement with eigenfunction solutions and much better than the results of OSRC method.

Radiation efects on MHD stagnation point flow of nano fluid towards a stretching surface with convective boundary condition

The aim of the present paper is to study the numerical solutions of the steady MHD two dimensional stagnation point flow of an incompressible nano fluid towards a stretching cylinder.The effects of radiation and convective boundary condition are also taken into account.The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis.The resulting nonlinear momentum,energy and nano particle equations are simplifed using similarity transformations.Numerical solutions have been obtained for the velocity,temperature and nanoparticle fraction profles.The influence of physical parameters on the velocity,temperature,nanoparticle fraction,rates of heat transfer and nanoparticle fraction are shown graphically.

Numerical manifold method for steady-state nonlinear heat conduction using Kirchhoff transformation

The numerical manifold method(NMM)introduces the mathematical and physical cover to solve both continuum and discontinuum problems in a unified manner.In this study,the NMM for solving steady-state nonlinear heat conduction problems is presented,and heat conduction problems consider both convection and radiation boundary conditions.First,the nonlinear governing equation of thermal conductivity,which is dependent on temperature,is transformed into the Laplace equation by introducing the Kirchhoff transformation.The transformation reserves linearity of both the Dirichlet and the Neumann boundary conditions,but the Robin and radiation boundary conditions remain nonlinear.Second,the NMM is employed to solve the Laplace equation using a simple iteration procedure because the nonlinearity focuses on parts of the problem domain boundaries.Finally,the temperature field is retrieved through the inverse Kirchhoff transformation.Typical examples are analyzed,demonstrating the advantages of the Kirchhoff transformation over the direct solution of nonlinear equations using the NewtonRaphson method.This study provides a new method for calculating nonlinear heat conduction.

A Multiscale Algorithm for Heat Conduction-Radiation Problems in Porous Materials with Quasi-Periodic Structures

This paper develops a second-order multiscale asymptotic analysis and numerical algorithms for predicting heat transfer performance of porous materials with quasi-periodic structures.In these porousmaterials,they have periodic configurations and associated coefficients are dependent on the macro-location.Also,radiation effect at microscale has an important influence on the macroscopic temperature fields,which is our particular interest in this study.The characteristic of the coupled multiscale model between macroscopic scale and microscopic scale owing to quasi-periodic structures is given at first.Then,the second-ordermultiscale formulas for solving temperature fields of the nonlinear problems are constructed,and associated explicit convergence rates are obtained on some regularity hypothesis.Finally,the corresponding finite element algorithms based on multiscale methods are brought forward and some numerical results are given in detail.Numerical examples including different coefficients are given to illustrate the efficiency and stability of the computational strategy.They show that the expansions to the second terms are necessary to obtain the thermal behavior precisely,and the local and global oscillations of the temperature fields are dependent on the microscopic and macroscopic part of the coefficients respectively.