A boundary element solution for the s-dimensional convective diffusion equation in a steady state is formulated by means of transforming its governing operator into symmetric or selfadjoint operator. The traveling material under consideration is assumed to be orthotropic. The velocity field is also assumed to be uniform or variable in spaces. Simple and two-dimensional examples (s2) are treated in numerical experiments in order to demonstrate the validity of the present formulation. A comparison with standard and upwind finite element solutions is also given. It is shown that the boundary element solution is stable and accurate with respect to the Peclet number and the ratio of orthotropy. Moreover, an example of the variable velocity field is treated using the boundary element model without internal cells. It is finally proved that the present method is an improvement over the usual boundary element method.

A boundary element method is presented for the analysis of shielded microstrip lines with dielectric layers. The formulation is based on (a) the Green's second identity, (b) the method of subdomains, (c) the constant boundary element discretization and (d) the discrete conservation law of total charge. In particular, the above (b) and (d) are originated for dealing with the dielectric layers. Numerical results for the balance-type and coplanar-type striplines are shown in order to examine the validity of the boundary element method. By user of the technique of subdivision into boundary element, it is also found that the calculated values for line characteristics are with the second-order accuracy.

Transient solution of convective diffusion equation in s dimension (s1, 2 or 3) is formulated by boundary integral equation. Fundamental solution to the convective diffusion operator is also presented in uniform velocity field. In particular, the one-dimensional case (s1) is treated because a discussion on the stability of transient solution is very important in practical applications. For discretization of the integral equation, constant and linear elements in time and constant elements in space (internal cells) are employed. A simple time-marching scheme is also developed. In numerical experiments, three model problems are considered. As the result, it is found out that the transient solution is stably calculated in time and space, and that its stability is independent upon the usual criteria that the Courant number C(vΔt/Δx)1 and the diffusion number D(kΔt/Δx2)1/2. In addition, a comparison with the exact solution is given, and the accuracy is discussed.

The stability of n-th order finite element (FE) solutions for steady-state convective diffusion equations (CDE) is studied. By eliminating intermediate nodal values of the FE, it is found that the odd-order FE solutions (n is odd) are stable under the criterion Lf (n) 2.01.4(n1) where L is the cell Peclet number, and that the even-order FE solutions (n is even) are unconditionally stable.

A boundary element solution is formulated for steady-state convective diffusion equation with the Dirichlet's boundary condition. A simple example is considered in three dimensions. It is shown that the boundary element solution is unconditionally stable. In order to demonstrate the usefulness of the boundary element solution, the comparison with finite element solutions is given.