标题： 本质上非振荡的谱体积方法 显示英文标题

标题： Essentially Non-oscillatory Spectral Volume Methods

摘要： 开发了一种新的本质上非振荡（ENO）重构算法，并在有限体积法中进行了测试。该构建方法基于将重构重新表述为变分问题的解。经典ENO算法的符号特性被表示为对此变分问题的可接受解集的限制。结合一种用于猜测间断点可能位置的智能算法，构造了一个没有分裂差分或光滑性指标的ENO重构算法。除了所需的阶数和模板宽度外，不存在可调参数。所需阶数原则上是任意的，但需要更大的模板。虽然经典的ENO方法考虑了围绕所考虑单元的所有连接模板，但所提出的恢复方法使用固定模板，简化了高效的高阶实现。 显示英文摘要

摘要： A new Essentially Non-oscillatory (ENO) recovery algorithm is developed and tested in a Finite Volume method. The construction is hinged on a reformulation of the reconstruction as the solution to a variational problem. The sign property of the classical ENO algorithm is expressed as restrictions on the admissible set of solutions to this variational problem. In conjunction with an educated guessing algorithm for possible locations of discontinuities an ENO reconstruction algorithm without divided differences or smoothness indicators is constructed. No tunable parameters exist apart from the desired order and stencil width. The desired order is in principle arbitrary, but growing stencils are needed. While classical ENO methods consider all connected stencils that surround a cell under consideration the proposed recovery method uses a fixed stencil, simplifying efficient high order implementations.