We consider accurate and stable interpolation procedures for numerical simulations utilizing time dependent adaptive meshes. The interpolation of numerical solution values between meshes is considered as a transmission problem with respect to the underlying semi-discretized equations, and a theoretical framework using inner product preserving operators is developed, which allows for both explicit and implicit implementations. The theory is supplemented with numerical experiments demonstrating practical benefits of the new stable framework. For this purpose, new interpolation operators have been designed to be used with multi-block finite difference schemes involving non-collocated, moving interfaces.

我们考虑利用时间相关的自适应网格进行数值模拟的准确和稳定的内插程序。网格之间的数值解值的插值被认为是相对于底层半离散方程的传递问题，并且开发了使用内积保留算子的理论框架，该框架允许显式和隐式实现。该理论还辅以数值实验，证明了新稳定框架的实际好处。为此，已经设计了新的插值运算符，以用于涉及非并置移动接口的多块有限差分方案。