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Test case, towed line (catenary)

Purpose

The purpose of this test case is to verify that the simulation model gives second order accuracy applied on a towed line (balance between normal fluid drag and axial line force).

Method

The towed line has been computed numerically and comparisons are made with the analytically calculated exact solution. With the normal fluid drag set proportional to the normal velocity squared and the axial fluid drag set to zero the exact solution becomes the catenary (which is also the solution for a static hanging chain).

The numerical and exact solutions are presented below. The fluid is flowing from right to left in the figure below.

The relative error norm versus no of spatial grid divisions is presented below verifying second order error decay.

Conclusion

· The comparisons demonstrate that the equations are solved correctly and that the numerical scheme is second order accurate (error decreases with the spacing between discrete points squared).