Boundary-optimized summation-by-parts operators for finite difference approximations of second derivatives with variable coefficients

Boundary-optimized summation-by-parts (SBP) finite difference operators for second derivatives with variable coefficients are presented. The operators achieve increased accuracy by utilizing non-equispaced grid points close to the boundaries of the grid. Using the optimized operators we formulate SBP schemes for the acoustic and elastic operators defined directly on curvilinear multiblock domains. Numerical studies of the acoustic and elastic wave equations demonstrate that, compared to traditional SBP difference operators, the new operators provide increased accuracy for surface waves as well as block interfaces in multiblock grids. For instance, simulations of Rayleigh waves demonstrate that the boundary-optimized operators more than halve the runtime required for a given error tolerance. •SBP difference operators for variable-coefficient second derivatives are presented.•Operator accuracy is increased using non-equispaced grid points close to boundaries.•Provides full compatibility with existing boundary-optimized SBP first derivatives.•Simulations of acoustic and elastic wave equations demonstrate increased accuracy.•Simulations of Rayleigh waves demonstrate increased efficiency.