Objectives   

1.      Validate the provided m-file template for the FE implemtation of GWSh for 1-D steady scalar field transport.

2.      Determine the smallest uniform mesh M that supports generation of an oscillation-free GWSh steady solution for Pe = 100. Then determine the least geometric progression ratio for a non-uniform M = 20 mesh that will support generation of monotone solutions for Pe = 100 and Pe = 1000.

3.      Validate the provided m-file template for FE implemtation of the GWSh + theta TS algorithm for 1-D unsteady scalar field transport for Pe-1 = 0, i.e, pure advection.

4.      Evaluate the impact of mesh resolution M, implicit time factor theta and Courant Number C on the monotonicity/accuracy of the GWSh + theta TS algorithm solutions for the unsteady propagation of the gaussian wave IC. When altering C, adjust the solution time step and number of time steps to ensure the wave always travels the same distance.