Solving Highly Nonlinear Problems
When solving nonlinear problems the degree of nonlinearity, the number of harmonics generated and resolved, as well as the possibility of shock formation needs to be taken into account.
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For nonlinear problems where only a few harmonics are generated the default physics and solver settings will work well.
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For highly nonlinear problems (with no shock formation), where more than a few harmonics are generated, it is recommended to make some changes to the Time-Explicit Solver. Change the Update time step to Manual, this will ensure that the local speed of sound is reevaluated and the internal time step is updated to ensure numerical stability.
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For models that are highly nonlinear and exhibit shock formation, the use of the WENO limiter is necessary. This functionality is only available for linear discretization. Change the Element order to Linear in the Discretization section on the physics interface level. Then, in the Limiter section select WENO. When limiters are used and the problem is highly nonlinear changes in the Time-Explicit Solver are also necessary. The computation of discontinuous solutions requires that a Strong Stability Preserving (SSP) Runge–Kutta method be used. The third order SSP Runge–Kutta method is achievable by changing the Order of the Runge–Kutta method from the default 4 to 3. Moreover change the Update time step to Manual, this will ensure that the local speed of sound is reevaluated and the internal time step is update to ensure numerical stability.
For an example of a highly nonlinear problem with shocks see the Nonlinear Propagation of a Cylindrical Wave — Verification Model tutorial model. Application Library path Acoustics_Module/Nonlinear_Acoustics/nonlinear_cylindrical_wave