Numerical accuracy of staircase fluid-solid and free-surface boundary conditions for staggered-grid finite-differences

Te-Yang Yeh, & Kim B. Olsen

Published August 14, 2019, SCEC Contribution #9667, 2019 SCEC Annual Meeting Poster #090

Accurate boundary conditions along fluid-solid and free-surface interfaces are needed in wave propagation simulations where the effects from non-planar surface topography and bathymetry are non-negligible. Okamoto and Takenaka (2005) and later Takenaka et al. (2009) proposed a unified and simple approach to approximate a realistic topography and bathymetry model in a staircase fashion along both fluid-solid and free-surface interfaces in the 4th-order staggered-grid finite-difference (FD) scheme. The proposed boundary condition is located at the shear stress grid points, and downgrades the velocity and stress updates near the boundaries to 2nd order accuracy to avoid the use of velocities and stresses that are discontinuous across the boundary in the FD update. The lower-order FD update results in a reduction of numerical accuracy, particularly for surface waves traveling along the interfaces. Later simulation studies used this boundary condition to model regional high-frequency ground motion with relatively low resolution (e.g., 8 points per minimum S wavelength, Takemura et al., 2015). In order to determine how many points per minimum wavelength this boundary condition requires for different simulation distances, we compared FD solutions for various propagation distances and resolution to SpecFEM2D (Komatitsch & Vilotte, 1998) results. We show that 20 points per minimum wavelength are needed for propagation distances up to about 100 km using models with planar interfaces, with or without the presence of a thick water layer. When nonplanar topography and bathymetry are included in the model, the staircase generates additional scattered waves, further degrading the accuracy. We estimate the minimum grid resolution required for accurate modeling in the presence of various free surface and bathymetry complexity using this boundary condition.

Key Words
Wave propagation, finite-differences, topography, bathymetry

Citation
Yeh, T., & Olsen, K. B. (2019, 08). Numerical accuracy of staircase fluid-solid and free-surface boundary conditions for staggered-grid finite-differences. Poster Presentation at 2019 SCEC Annual Meeting.

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