Higher-order Boundary Conditions Research Articles

Higher-order boundary condition of the space–time diffusion equation

The higher-order boundary condition on the boundary of free space is investigated for the space–time diffusion equation, and the resulting additional term of the solution is shown explicitly in terms of the Green function. The higher-order term of the solution is generally negligible, however, in the region where the diffusion approximation is applicable.

PREDICTION OF NATURAL CONVECTION IN NONRECTANGULAR ENCLOSURES USING ORTHOGONAL CURVILINEAR COORDINATES

In order to predict natural convection in nonrectangular enclosures the equations of motion are written for orthogonal curvilinear coordinates, using stream function and vorticity as dependent variables. Special integration techniques are described that permit an accurate grid to be found. The solution of the finite-difference equations is obtained by using a novel iterative technique that solves simultaneously for vorticity and stream function along lines. This was found to be economical and stable despite the use of a high-order boundary condition on vorticity. These techniques were applied to the problem of laminar two-dimensional natural convection in an air layer bounded above by an isothermal flat plate and below by a higher-temperature vee-corrugated isothermal surface. The dependence of heat transfer on Rayleigh number, aspect ratio and inclination angle is presented. Where possible, comparisons are made with previous predictions and measurements.

Diffusion approximation for large absorption in radiative transfer

A new diffusion model is developed for radiative transfer in particulate media. It includes the effects of higher Legendre moments while avoiding the mathematical complexities of solving multiple coupled differential moment equations and satisfying higher-order boundary conditions. The method accurately extrapolates the conventional Eddington approximation to problems involving large absorption. Although the simplifying assumptions limit the model to nonbeam incidence and spatial homogeneity of the scattering material, they are nonrestrictive with regard to the size and shape of the medium, the character of background reflections, and the type of phase function.

High-order hydrodynamics and boundary conditions. Application to the thermal force

For higher-order constitutive laws boundary conditions are derived by a thermodynamic method due to Waldmann. The application to the thermal force yields an expression which can account for the experimental data over a wide range of Knudsen numbers and all ratios of the heat conductivities of the aerosol particle and the gas.

High-order Non-reflecting Boundary Conditions For Dispersive WaveProblems In Stratified Media

High-order Non-reflecting Boundary Conditions For Dispersive WaveProblems In Stratified Media

Hot Plasma in a Cylindrical Waveguide

An approximate theory for the propagation of waves in a hot plasma in a cylindrical waveguide with an arbitrary axial magnetic field is presented. The boundary value problem is treated by a perturbation expansion in the smallness of the Larmor radius compared to the transverse wavelength. In the limit of zero Larmor radius, only the electromagnetic boundary conditions are important, while acoustic and higher-order boundary conditions appear as corrections. The results to zero order in Larmor radius are found to be formally identical to the cold plasma equations. Mode orthogonality and some limiting cases are also discussed.

Elliptic Differential Problems with High Order Boundary Conditions.

Elliptic Differential Problems with High Order Boundary Conditions.