A New Class of Central Compact Finite-difference Scheme with High Spectral Resolution for Acoustic Wave Equation
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Summary: Based on the existing cell-node and cell-centered compact finite difference schemes, we developed a new central compact scheme with a high spectral resolution for the acoustic wave equation. In the new scheme, both the function values on the cell-nodes and cell-centers are used to compute the second-order spatial derivatives on the cell-nodes. The cell-centered values are stored and updated as independent variables in the modeling. The spatial derivatives on the cell-centers are evaluated by half shifting the indices in the formula designed for the cell-nodes. Compared to the conventional compact interpolation scheme, the proposed approach can avoid introducing transfer errors. Either Taylor-series expansion-based or optimized least-squares-based methods are used to calculate the finite difference coefficients. This new scheme can promise higher accuracy considering the same formal truncation errors and model parameters. Thus, it can maintain superior precision while using a shorter spatial finite difference stencil and yield equally as accurate results with less time consuming.