Optimal recovery using thin plate splines in finite volume methods for the numerical solution of hyperbolic conservation laws
Optimal recovery using thin plate splines in finite volume methods for the numerical solution of hyperbolic conservation laws
复制标题
双曲守恒定律数值求解的有限体积方法中使用薄板样条的最佳恢复
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
T. Sonar
中科院分区：
文献类型：
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作者：
T. Sonar
最优恢复理论应用于有限体积方法，用于多空间维度守恒定律的数值求解。根据该理论，经典多项式 ENO（本质上非振荡）算法可以解释为点泛函的平凡恢复算子。薄板样条被认为是 Beppo-Levi 空间中的最佳恢复函数，并且可以被视为三次样条的多维类似物。开发了基于薄板样条的ENO型恢复算法，并将其应用于包括可压缩气体动力学欧拉方程在内的测试问题。
The theory of optimal recovery is applied to finite volume methods for the numerical solution of conservation laws in multiple space dimensions. Classical polynomial ENO (essentially non-oscillatory) algorithms can be interpreted as trivial recovery operators for the point functional in the light of this theory. Thin plate splines are identified as optimal recovery functions in Beppo-Levi spaces and can be seen as multi-dimensional analogues of cubic splines. Recovery algorithms of ENO-type based on thin plate splines are developed and applied to test problems including the Euler equations of compressible gas dynamics.