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Test case, travelling wave on a string

Purpose

The purpose of this test case is to verify that the simulation model is second order accurate for the time integration applied on a wave travelling on a string (balance between inertia and internal tensile line forces).

Method

A travelling wave has been computed numerically and comparisons are made with the analytically calculated exact solution. The calculations were done for a string with controlled/fixed vertical position at the left boundary and the right boundary free to move vertically.

Click on graph below to start animation.

The kinetic energy and work at boundary for the travelling wave

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).