Some aspects of solving advection dominated flows

A new method for solving the fluid transport equation for advection dominated flows is introduced in this paper. A transform modifies the asymmetric fluid transport equation into a symmetric positive definite equation. Symmetry is achieved by imbedding the first order spatial derivative of the transport equation into the second order derivative term through functional transformation. A variational formulation for the finite element approximation preserves this desirable feature to generate a symmetric system of equations. For the steady state case, the proposed method has been validated against three methods: analytical solution, Galerkin finite element solution and upwind-weighted finite element solution. The results indicate that the proposed method gives the best approximation to the analytical solution. There is no constraint on the magnitude of Peclet number. For the transient case, validation shows that the proposed method is accurate but application is restricted to certain Peclet number magnitudes.