Stable discontinuous curvilinear grids: Implementation and validation in a polar-coordinate overset-grid finite-difference method for planetary seismic wave simulation

Efficient seismic wavefield simulation in large-scale spherical planetary models is essential for investigating planetary interiors. Near-surface low-velocity layers can force uniformly fine discretization, while the radius-dependent contraction of lateral spacing in polar grids further oversamples deeper, faster regions and imposes unnecessarily small global time steps. We introduce a discontinuous-grid formulation for a polar-coordinate overset-grid finite-difference method. Fine curvilinear grids are used in shallow low-velocity regions and coarser regular grids at depth; the current implementation supports integer grid ratios. Fine-grid ghost values are reconstructed by Lagrange interpolation. In the tested n = 2 cases, no additional downsampling filtering was required for coarse-grid transfer, whereas n = 3 requires prefiltering of fine-grid donor values to suppress aliasing. Comparisons with analytical solutions and uniform-grid simulations show stable and accurate wave propagation across discontinuous interfaces. In a lunar benchmark, the method achieves an average waveform correlation of 0.997 while reducing the grid count by 48%; the maximum stable time step increases from 0.092 to 0.186 s, and the measured calculation time decreases by 48%. The method provides an efficient numerical framework for large-scale seismic simulations in spherical planetary models.