Application of the trajectory image method to solve convection-diffusion equations

Abstract

The trajectory image method (TIM), a new modelling technique based on image theory, can be used to solve convection-diffusion equations without numerical dispersion. Whether finite difference or finite element methods are used, these approximations always introduce truncation errors that often can distort the accuracy and stability of the solution. Analytical solutions in an infinite domain, which are similar to the fundamental solution of the boundary element method must be solved. TIM offers the following advantages for this type of equations: (1) No numerical dispersion occurs. (2) No magnification errors occur near sources or sinks. (3) Only zones with differing conductivities have to be discretized. (4) TIM is simple in modelling flow through anisotropic media without requiring that principal directions be parallel to coordinate directions or be transformed into another coordinate system. (5) In contrast to the boundary element method, near-boundary computations are very accurate, and complicated integrations are avoided under unsteady-state conditions. (6) Problem setup is easier than in finite difference and finite element methods.