The computation of transport problems are especially troublesome when the solution field contains steep gradients such as those of temperature or concentration. When solving such problems associated with convection either wiggly or unstable, solutions generally result when the standard finite difference of finite element methods are applied. There are schemes that add artificial or numerical diffusion to the computation to dampen numerical instabilities. However, such non-physical diffusion often serves to confuse the real damping that exists in the problem. The objective of this Engineering Initiation project is to expand on the recent developments in higher order schemes which are non-diffusive. In particular, the fractional step method will be used to treat a class of convective dominated problems. The benefits of this procedure includes accuracy and a relative increase in computational scheme will be possible. The institutional support is adequate and the P.I. has extensive experience on the NSF-JVNC supercomputer. I strongly recommend support.