Finite difference method

Abstract: Domain decomposition procedures for solving parabolic equations are considered. The underlying discretization consists of block-centered finite differences. In these procedures, fluxes at subdomain interfaces are calculated from the solution at the previous time level. These fluxes serve as Neumann boundary data for implicit, block-centered discretizations in the subdomains. A priori error estimates are presented, and numerical results examining the stability, accuracy, and parallelism of the scheme are presented.

Abstract: A finite difference formulation is developed for computing the frequency domain electromagnetic fields due to a point source in the presence of two‐dimensional conductivity structures. Computing costs are minimized by reducing the full three‐dimensional problem to a series of two‐dimensional problems. This is accomplished by Fourier transforming the problem into the x-wavenumber (kx) domain; here the x-direction is parallel to the structural strike. In the kx domain, two coupled partial differential equations for H⁁x(kx,y,z) and E⁁x(kx,y,z) are obtained. These equations resemble those of two coupled transmission sheets. For a requisite number of kx values these equations are solved by the finite difference method on a rectangular grid on the y-z plane. Application of the inverse Fourier transform to the solutions thus obtained gives the electric and magnetic fields in the space domain. The formulation is general; complex two‐dimensional structures containing either magnetic or electric dipole sources can ...

Abstract: Natural convection in laminar boundary layers along slender vertical cylinders is analyzed for the situation in which the wall temperature T{sub w}(x) varies arbitrarily with the axial coordinate x. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form by a nonsimilar transformation and the resulting system of equations is then solved by a finite difference method in conjunction with the cubic spline interpolation technique. As an example, numerical results were obtained for the case of T{sub w}(x) = T{infinity} + ax{sup n}, a power-law wall temperature variation. They cover Prandtl numbers of 0.1, 0.7, 7, and 100 over a wide range of values of the surface curvature parameter. Representative local Nusselt number as well as velocity and temperature profiles are presented. Correlation equations for the local and average Nusselt numbers are also given.