Abstract
By using non-equispaced grid points near boundaries, we derive boundary optimized first derivative finite difference operators, of orders up to twelve. The boundary closures are based on a diagonal-norm summation-by-parts (SBP) framework, thereby guaranteeing linear stability on piecewise curvilinear multi-block grids. The new operators lead to significantly more efficient numerical approximations, compared with traditional SBP operators on equidistant grids. We also show that the non-uniform grids make it possible to derive operators with fewer one-sided boundary stencils than their traditional counterparts. Numerical experiments with the 2D compressible Euler equations on a curvilinear multi-block grid demonstrate the accuracy and stability properties of the new operators.
Original language | English |
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Pages (from-to) | 1261-1266 |
Number of pages | 6 |
Journal | Journal of computational physics |
Volume | 374 |
DOIs | |
Publication status | Published - 1 Dec 2018 |
Keywords
- Euler equations
- Finite difference methods
- High order accuracy
- Stability
- Boundary treatment