Non-uniform, dynamically adaptive meshes are a useful tool for reducing computational complexities for geophysical simulations that exhibit strongly localised features such as is the case for tsunami, hurricane or typhoon prediction. Using the example of a shallow water solver, this study explores a set of metrics as a tool to distinguish the performance of numerical methods using adaptively refined versus uniform meshes independent of computational architecture or implementation. These metrics allow us to quantify how a numerical simulation benefits from the use of adaptive mesh refinement. The type of meshes we are focusing on are adaptive triangular meshes that are non-uniform and structured. Refinement is controlled by physics-based indicators that capture relevant physical processes and determine the areas of mesh refinement and coarsening. The proposed performance metrics take into account a number of characteristics of numerical simulations such as numerical errors, spatial resolution, as well as computing time. Using a number of test cases we demonstrate that correlating different quantities offers insight into computational overhead, the distribution of numerical error across various mesh resolutions as well as the evolution of numerical error and run-time per degree of freedom.

动态非均匀网格是降低地球物理模拟计算复杂性的有用工具，这些地球物理模拟表现出强烈的局部特征，例如海啸，飓风或台风预报。以浅水求解器为例，本研究探索了一组度量，将其作为一种工具来区分使用自适应细化网格与统一网格的数值方法的性能，而这些网格独立于计算体系结构或实现。这些指标使我们能够量化数值模拟如何从自适应网格细化的使用中受益。我们关注的网格类型是非均匀且结构化的自适应三角形网格。细化由基于物理的指标控制，这些指标捕获相关的物理过程并确定网格细化和粗化的区域。提出的性能指标考虑了数值模拟的许多特征，例如数值误差，空间分辨率以及计算时间。通过使用多个测试案例，我们证明了关联不同的数量可以深入了解计算开销，各种网格分辨率下的数值误差分布以及每自由度数值误差和运行时间的演变。