Adaptive Mesh Refinement
One challenge when solving nonlinear problems is that the mesh should potentially resolve many harmonics to get accurate solutions. To remedy this, adaptive mesh refinement technology can be used. The method will automatically refine the mesh to resolve large gradients, that is, sharp signal details that include several harmonics. The approach is useful for modeling the propagation of spatially localized signals like tone bursts or Gaussian pulses.
To use the adaptive mesh refinement in a model follow these steps:
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Mesh to resolve only the fundamental frequency in the model.
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In the Time Dependent study step, under the Adaptation section, select Adaptive mesh refinement. Then generate the default solver sequence.
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Expand the solver tree and go to the Adaptive Mesh Refinement node. Some changes need to be done here. For the Adaptation method select General modifications. Do not enable Allow coarsening as the mesh needs to resolve the fundamental frequency. Finally, update the Error indicator expression to use the pressure gradient norm. In a 2D axisymmetric model the expression is sqrt(comp1.pr^2+comp1.pz^2) and in a 3D model the expression is sqrt(comp1.px^2+comp1.py^2+comp1.pz^2).
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For highly localized signals, where the mesh adaptation generates a localized region with small elements, it can also be advantageous to switch from the default Runge-Kutta (RK4) solver method to the Adams-Bashforth 3 (local) method.
For an example of a nonlinear problem with pulse propagation that uses mesh adaptation see the High-Intensity Focused Ultrasound (HIFU) Propagation Through a Tissue Phantom tutorial model. The Application Library path: Acoustics_Module/Nonlinear_Acoustics/hifu_tissue_sample