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Shallow Water Gravity Waves Equations are presented below: Here are my code cuttings:

Shallow Water Gravity Waves Equations are presented below: Here are my code cuttings:

Furthermore I’ve also googled some other different options for NDSolveValue function from here and here, but none of them helped me to stabilize calculation process near the boundary of the simulation region. At the small simulation times I can clearly see my tsunami propagating correctly. In contrast, at the large times numerical interpolation solution explodes with enormous water surface height values without any reason.

Furthermore, I’ve also googled some other different options for NDSolveValue function from here and here, but none of them helped me to stabilize calculation process near the boundary of the simulation region. At the small simulation times I can clearly see my tsunami propagating correctly. In contrast, at the large times numerical interpolation solution explodes with enormous water surface height values without any reason.

Being frustrated about FEM's accuracy by the discussion, I've tried to play with "SpatialDiscretization" -> {"TensorProductGrid", "DifferenceOrder" -> "Pseudospectral"} as it was recommended in the post. This attempt corresponds to initialconditions2 & method2 & region2 parameters for RunNDSolveValue function. Boundary conditions here are still periodic, but future complexification of spatial domain is unavailable. Unfortunately, this hopeful scheme also crashes with the same error "At t == ~1200, step size is effectively zero; singularity or stiff system suspected." and new warning "An insufficient number of boundary conditions have been specified for the direction of independent variable [Theta]. Artificial boundary effects may be present in the solution."

Being frustrated about FEM's accuracy by the discussion, I've tried to play with "SpatialDiscretization" -> {"TensorProductGrid", "DifferenceOrder" -> "Pseudospectral"} as it was recommended in the post. This attempt corresponds to initialconditions2 & method2 & region2 parameters for RunNDSolveValue function. Boundary conditions are still periodic here, but further complexification of the spatial domain is unavailable. Unfortunately, this hopeful scheme also crashes with the same error "At t == ~1200, step size is effectively zero; singularity or stiff system suspected." and new warning "An insufficient number of boundary conditions have been specified for the direction of independent variable [Theta]. Artificial boundary effects may be present in the solution."