Waves at a fluid-solid interface: Explicit versus implicit formulation of boundary conditions using a discontinuous...

Area of Science:

• Geophysics
• Computational Seismology
• Numerical Methods

Background:

• Accurate wave equation solutions at fluid-solid interfaces depend on correct boundary condition implementation.
• Modeling interface waves like Scholte and leaky Rayleigh waves presents a significant challenge.

Purpose of the Study:

• To implement and evaluate natural boundary conditions within a nodal discontinuous Galerkin (dG) finite-element method for fluid-solid interfaces.
• To assess the accuracy and stability of explicit and implicit numerical flux methods for simulating interface waves.

Main Methods:

• Utilized a nodal discontinuous Galerkin (dG) finite-element method with unstructured uniform triangular meshes.
• Implemented natural boundary conditions using explicit upwind and implicit penalty numerical fluxes.
• Validated numerical solutions against analytical solutions for sources and receivers at and away from the interface.

Main Results:

• Both explicit and implicit boundary condition implementations yielded accurate numerical solutions.
• The study confirmed the correct simulation of Scholte and leaky Rayleigh waves.
• The numerical flux was found to be crucial for both implementing boundary conditions and ensuring the energy stability of the dG scheme.

Conclusions:

• The discontinuous Galerkin (dG) finite-element method, with appropriate numerical flux implementation, accurately solves the wave equation at fluid-solid interfaces.
• Explicit and implicit boundary conditions are effective for modeling challenging interface waves.
• The dG scheme demonstrates stability and accuracy for geophysical wave propagation problems.