On exponential variable transformation based boundary element formulation for advection–diffusion problems

Abstract

This paper presents an alternative boundary element formulation based on an exponential variable transformation for the steady state advection–diffusion problems. Use of this transformation converts the advection–diffusion equation into modified Helmholtz equation. Standard boundary element formulation is used to obtain the integral equation for the resulting modified Helmholtz equation. Three different strategies for the solution of this boundary integral equation are discussed. These include (a) the solution of the modified Helmholtz equation followed by transformation at post-processing stage, (b) use of inverse transformation before boundary element discretization, and (c) use of inverse transformation after the boundary element discretization to obtain the discretized equations for the advection–diffusion problem. Computational features of each of these strategies have been discussed. Numerical results are presented for a set of standard test problems. It is found that strategy (a) is the most accurate and efficient choice for diffusion-dominated ( Pe≪1) as well as low Peclét number ( Pe≤20) situations. Strategy (c) is as accurate as strategy (a), but is of little practical use owing to its computational inefficiency. Further, strategy (b), which is same as the boundary element formulation using the fundamental solution of the adjoint of the advection–diffusion equation, is the most accurate and efficient choice for advection-dominated problems.