HW #16 - Finite Difference Method

1) Write a spreadsheet to solve for the total head values for the problem shown below using the finite difference technique.

Use a 2.5 foot square grid. Extend the grid from the centerline of the cofferdam to 40 feet downstream from the outer edge of the cofferdam. This should give you 9 rows and 21 columns in your grid.  Don't forget to add an extra grid node at the location of the sheet pile for the first four rows of nodes.  The grid looks like this.

Lay out your spreadsheet so that you have a spreadsheet cell for each node of the grid (for each black dot).  Enter an equation for the head at each node. Using the default approach in Excel, you may get an error message about a circular reference. To avoid this and to properly iterate to a solution, do the following: Before entering the equations, go to the Tools/Options dialog and select the Calculate tab. Turn on the iteration option and the Manual calculate option. Once you have the equations entered, hit the F9 button repeatedly until you converge.

2) Add a section to your spreadsheet to compute the flow rate from your solution. To do this, compute the flux across the outgoing boundary. Using the head values at nodes on and adjacent to the nodes on the boundary to estimate the hydraulic gradient (dh/dx or dh/dy). Using this value, the appropriate contributing area, and Darcy's law, compute the flow rate.

When finished, log in to your student account to upload your spreadsheet.